the disk is rotating at a constant rate w=4 rad/s , and as it falls freely , its center has an acceleration of 32.2 rad s. Determine the acceleration of point B on the rim of the disk at the instant shown .

the disk is rotating at a constant rate w=4 rad/s , and as it falls freely , its center has an acceleration of 32.2 rad s. Determine the acceleration of point B on the rim of the disk at the instant shown .

PHSX 220 Homework 12 D2L – Due Thursday April 13 – 5:00 pm Exam 3 MC Review Problem 1: A 1.0-kg with a velocity of 2.0m/s perpendicular towards a wall rebounds from the wall at 1.5m/s perpendicularlly away from the wall. The change in the momentum of the ball is: A. zero B. 0.5 N s away from wall C. 0.5 N s toward wall D. 3.5 N s away from wall E. 3.5 N s toward wall Problem 2: A 64 kg man stands on a frictionless surface with a 0.10 kg stone at his feet. Both the man and the person are initially at rest. He kicks the stone with his foot so that his end velocity is 0.0017m/s in the forward direction. The velocity of the stone is now: A. 1.1m/s forward B. 1.1m/s backward C. 0.0017m/s forward D. 0.0017m/s backward E. none of these Problem 3: A 2-kg cart, traveling on a rctionless surface with a speed of 3m/s, collides with a stationary 4-kg cart. The carts then stick together. Calculate the magnitude of the impulse exerted by one cart on the other: A. 0 B. 4N s C. 6N s D. 9N s E. 12N s Problem 4: A disc has an initial angular velocity of 18 radians per second. It has a constant angular acceleration of 2.0 radians per second every second and is slowing at rst. How much time elapses before its angular velocity is 18 rad/s in the direction opposite to its initial angular velocity? A. 3.0 s B. 6.0 s C. 9.0 s D. 18 s E. 36 s Problem 5: Three point masses of M, 2M, and 3M, are fastened to a massless rod of length L as shown. The rotational inertia about the rotational axis shown is: A. (ML2=2) B. (ML2) C. (3ML2)=2 D. (6ML2) E. (3ML2)=4 Problem 6: A board is allowed to pivot about its center. A 5-N force is applied 2m from the pivot and another 5-N force is applied 4m from the pivot. These forces are applied at the angles shown in the gure. The magnitude of the net torque about the pivot is: A. 0 Nm B. 5 Nm C. 8.7 Nm D. 15 Nm E. 26 Nm Problem 7: A solid disk (r=0.03 m) and a rotational inertia of 4:5×10􀀀3kgm2 hangs from the ceiling. A string passes over it with a 2.0-kg block and a 4.0-kg block hanging on either end of the string and does not slip as the system starts to move. When the speed of the 4 kg block is 2.0m/s the kinetic energy of the pulley is: A. 0.15 J B. 0.30 J C. 1.0J D. 10 J E. 20 J Problem 8: A merry go round (r= 3.0m, I =600 kgm2) is initially spinning with an angular velocity of 0.80 radians per second when a 20 kg point mass moves from the center to the rim. Calculate the nal angular velocity of the system: A. 0.62 rad/s B. 0.73 rad/s C. 0.80 rad/s D. 0.89 rad/s E. 1.1 rad/s

PHSX 220 Homework 12 D2L – Due Thursday April 13 – 5:00 pm Exam 3 MC Review Problem 1: A 1.0-kg with a velocity of 2.0m/s perpendicular towards a wall rebounds from the wall at 1.5m/s perpendicularlly away from the wall. The change in the momentum of the ball is: A. zero B. 0.5 N s away from wall C. 0.5 N s toward wall D. 3.5 N s away from wall E. 3.5 N s toward wall Problem 2: A 64 kg man stands on a frictionless surface with a 0.10 kg stone at his feet. Both the man and the person are initially at rest. He kicks the stone with his foot so that his end velocity is 0.0017m/s in the forward direction. The velocity of the stone is now: A. 1.1m/s forward B. 1.1m/s backward C. 0.0017m/s forward D. 0.0017m/s backward E. none of these Problem 3: A 2-kg cart, traveling on a rctionless surface with a speed of 3m/s, collides with a stationary 4-kg cart. The carts then stick together. Calculate the magnitude of the impulse exerted by one cart on the other: A. 0 B. 4N s C. 6N s D. 9N s E. 12N s Problem 4: A disc has an initial angular velocity of 18 radians per second. It has a constant angular acceleration of 2.0 radians per second every second and is slowing at rst. How much time elapses before its angular velocity is 18 rad/s in the direction opposite to its initial angular velocity? A. 3.0 s B. 6.0 s C. 9.0 s D. 18 s E. 36 s Problem 5: Three point masses of M, 2M, and 3M, are fastened to a massless rod of length L as shown. The rotational inertia about the rotational axis shown is: A. (ML2=2) B. (ML2) C. (3ML2)=2 D. (6ML2) E. (3ML2)=4 Problem 6: A board is allowed to pivot about its center. A 5-N force is applied 2m from the pivot and another 5-N force is applied 4m from the pivot. These forces are applied at the angles shown in the gure. The magnitude of the net torque about the pivot is: A. 0 Nm B. 5 Nm C. 8.7 Nm D. 15 Nm E. 26 Nm Problem 7: A solid disk (r=0.03 m) and a rotational inertia of 4:5×10􀀀3kgm2 hangs from the ceiling. A string passes over it with a 2.0-kg block and a 4.0-kg block hanging on either end of the string and does not slip as the system starts to move. When the speed of the 4 kg block is 2.0m/s the kinetic energy of the pulley is: A. 0.15 J B. 0.30 J C. 1.0J D. 10 J E. 20 J Problem 8: A merry go round (r= 3.0m, I =600 kgm2) is initially spinning with an angular velocity of 0.80 radians per second when a 20 kg point mass moves from the center to the rim. Calculate the nal angular velocity of the system: A. 0.62 rad/s B. 0.73 rad/s C. 0.80 rad/s D. 0.89 rad/s E. 1.1 rad/s

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1-Two notions serve as the basis for all torts: wrongs and compensation. True False 2-The goal of tort law is to put a defendant in the position that he or she would have been in had the tort occurred to the defendant. True False 3-Hayley is injured in an accident precipitated by Isolde. Hayley files a tort action against Isolde, seeking to recover for the damage suffered. Damages that are intended to compensate or reimburse a plaintiff for actual losses are: compensatory damages. reimbursement damages. actual damages. punitive damages. 4-Ladd throws a rock intending to hit Minh but misses and hits Nasir instead. On the basis of the tort of battery, Nasir can sue: Ladd. Minh. the rightful owner of the rock. no one. 4-Luella trespasses on Merchandise Mart’s property. Through the use of reasonable force, Merchandise Mart’s security guard detains Luella until the police arrive. Merchandise Mart is liable for: assault. battery. false imprisonment. none of the choice 6-The extreme risk of an activity is a defense against imposing strict liability. True False 7-Misrepresentation in an ad is enough to show an intent to induce the reliance of anyone who may use the product. True False 8-Luke is playing a video game on a defective disk that melts in his game player, starting a fire that injures his hands. Luke files a suit against Mystic Maze, Inc., the game’s maker under the doctrine of strict liability. A significant application of this doctrine is in the area of: cyber torts. intentional torts. product liability. unintentional torts 9-More than two hundred years ago, the Declaration of Independence recognized the importance of protecting creative works. True False 10-n 2014, Cloud Computing Corporation registers its trademark as provided by federal law. After the first renewal, this registration: is renewable every ten years. is renewable every twenty years. runs for life of the corporation plus seventy years. runs forever. 11-Wendy works as a weather announcer for a TV station under the character name Weather Wendy. Wendy can register her character’s name as: a certification mark. a trade name. a service mark. none of the choices 12-Much of the material on the Internet, including software and database information, is not copyrighted. True False 13-In a criminal case, the state must prove its case by a preponderance of the evidence. True False 14-Under the Fourth Amendmentt, general searches through a person’s belongings are permissible. True False 15-Maura enters a gas station and points a gun at the clerk Nate. She then forces Nate to open the cash register and give her all the money. Maura can be charged with: burglary. robbery. larceny. receiving stolen property. 16-Reno, driving while intoxicated, causes a car accident that results in the death of Santo. Reno is arrested and charged with a felony. A felony is a crime punishable by death or imprisonment for: any period of time. more than one year. more than six months. more than ten days. 17-Corporate officers and directors may be held criminally liable for the actions of employees under their supervision. True False 18-Sal assures Tom that she will deliver a truckload of hay to his cattle ranch. A person’s declaration to do a certain act is part of the definition of: an expectation. a moral obligation. a prediction. a promise. 19-Lark promises to buy Mac’s used textbook for $60. Lark is: an offeror. an offeree a promisee. a promisor. 20-Casey offers to sell a certain used forklift to DIY Lumber Outlet, but Casey dies before DIY accepts. Most likely, Casey’s death: did not affect the offer. shortened the time of the offer but did not terminated it. extended the time of the offer. terminated the offer.

1-Two notions serve as the basis for all torts: wrongs and compensation. True False 2-The goal of tort law is to put a defendant in the position that he or she would have been in had the tort occurred to the defendant. True False 3-Hayley is injured in an accident precipitated by Isolde. Hayley files a tort action against Isolde, seeking to recover for the damage suffered. Damages that are intended to compensate or reimburse a plaintiff for actual losses are: compensatory damages. reimbursement damages. actual damages. punitive damages. 4-Ladd throws a rock intending to hit Minh but misses and hits Nasir instead. On the basis of the tort of battery, Nasir can sue: Ladd. Minh. the rightful owner of the rock. no one. 4-Luella trespasses on Merchandise Mart’s property. Through the use of reasonable force, Merchandise Mart’s security guard detains Luella until the police arrive. Merchandise Mart is liable for: assault. battery. false imprisonment. none of the choice 6-The extreme risk of an activity is a defense against imposing strict liability. True False 7-Misrepresentation in an ad is enough to show an intent to induce the reliance of anyone who may use the product. True False 8-Luke is playing a video game on a defective disk that melts in his game player, starting a fire that injures his hands. Luke files a suit against Mystic Maze, Inc., the game’s maker under the doctrine of strict liability. A significant application of this doctrine is in the area of: cyber torts. intentional torts. product liability. unintentional torts 9-More than two hundred years ago, the Declaration of Independence recognized the importance of protecting creative works. True False 10-n 2014, Cloud Computing Corporation registers its trademark as provided by federal law. After the first renewal, this registration: is renewable every ten years. is renewable every twenty years. runs for life of the corporation plus seventy years. runs forever. 11-Wendy works as a weather announcer for a TV station under the character name Weather Wendy. Wendy can register her character’s name as: a certification mark. a trade name. a service mark. none of the choices 12-Much of the material on the Internet, including software and database information, is not copyrighted. True False 13-In a criminal case, the state must prove its case by a preponderance of the evidence. True False 14-Under the Fourth Amendmentt, general searches through a person’s belongings are permissible. True False 15-Maura enters a gas station and points a gun at the clerk Nate. She then forces Nate to open the cash register and give her all the money. Maura can be charged with: burglary. robbery. larceny. receiving stolen property. 16-Reno, driving while intoxicated, causes a car accident that results in the death of Santo. Reno is arrested and charged with a felony. A felony is a crime punishable by death or imprisonment for: any period of time. more than one year. more than six months. more than ten days. 17-Corporate officers and directors may be held criminally liable for the actions of employees under their supervision. True False 18-Sal assures Tom that she will deliver a truckload of hay to his cattle ranch. A person’s declaration to do a certain act is part of the definition of: an expectation. a moral obligation. a prediction. a promise. 19-Lark promises to buy Mac’s used textbook for $60. Lark is: an offeror. an offeree a promisee. a promisor. 20-Casey offers to sell a certain used forklift to DIY Lumber Outlet, but Casey dies before DIY accepts. Most likely, Casey’s death: did not affect the offer. shortened the time of the offer but did not terminated it. extended the time of the offer. terminated the offer.

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5 { GRAVITATION Last Updated: July 16, 2012 Problem List 5.1 Total mass of a shell 5.2 Tunnel through the moon 5.3 Gravitational eld above the center of a thin hoop 5.4 Gravitational force near a metal-cored planet surrounded by a gaseous cloud 5.5 Sphere with linearly increasing mass density 5.6 Jumping o Vesta 5.7 Gravitational force between two massive rods 5.8 Potential energy { Check your answer! 5.9 Ways of solving gravitational problems 5.10 Rod with linearly increasing mass density 5.11 Sphere with constant internal gravitational eld 5.12 Throwing a rock o the moon These problems are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Un- ported License. Please share and/or modify. Back to Problem List 1 5 { GRAVITATION Last Updated: July 16, 2012 5.1 Total mass of a shell Given: Marino { Fall 2011 Consider a spherical shell that extends from r = R to r = 2R with a non-uniform density (r) = 0r. What is the total mass of the shell? Back to Problem List 2 5 { GRAVITATION Last Updated: July 16, 2012 5.2 Tunnel through the moon Given: Marino { Fall 2011 Imagine that NASA digs a straight tunnel through the center of the moon (see gure) to access the Moon’s 3He deposits. An astronaut places a rock in the tunnel at the surface of the moon, and releases it (from rest). Show that the rock obeys the force law for a mass connected to a spring. What is the spring constant? Find the oscillation period for this motion if you assume that Moon has a mass of 7.351022 kg and a radius of 1.74106 m. Assume the moon’s density is uniform throughout its volume, and ignore the moon’s rotation. Given: Pollock { Spring 2011 Imagine (in a parallel universe of unlimited budgets) that NASA digs a straight tunnel through the center of the moon (see gure). A robot place a rock in the tunnel at position r = r0 from the center of the moon, and releases it (from rest). Use Newton’s second law to write the equation of motion of the rock and solve for r(t). Explain in words the rock’s motion. Does the rock return to its initial position at any later time? If so, how long does it takes to return to it? (Give a formula, and a number.) Assume the moon’s density is uniform throughout its volume, and ignore the moon’s rotation. Given: Pollock { Spring 2012 Now lets consider our (real) planet Earth, with total mass M and radius R which we will approximate as a uniform mass density, (r) = 0. (a) Neglecting rotational and frictional e ects, show that a particle dropped into a hole drilled straight through the center of the earth all the way to the far side will oscillate between the two endpoints. (Hint: you will need to set up, and solve, an ODE for the motion) (b) Find the period of the oscillation of this motion. Get a number (in minutes) as a nal result, using data for the earth’s size and mass. (How does that compare to ying to Perth and back?!) Extra Credit: OK, even with unlimited budgets, digging a tunnel through the center of the earth is preposterous. But, suppose instead that the tunnel is a straight-line \chord” through the earth, say directly from New York to Los Angeles. Show that your nal answer for the time taken does not depend on the location of that chord! This is rather remarkable – look again at the time for a free-fall trip (no energy required, except perhaps to compensate for friction) How long would that trip take? Could this work?! Back to Problem List 3 5 { GRAVITATION Last Updated: July 16, 2012 5.3 Gravitational eld above the center of a thin hoop Given: Pollock { Spring 2011, Spring 2012 Consider a very (in nitesimally!) thin but massive loop, radius R (total mass M), centered around the origin, sitting in the x-y plane. Assume it has a uniform linear mass density  (which has units of kg/m) all around it. (So, it’s like a skinny donut that is mostly hole, centered around the z-axis) (a) What is  in terms of M and R? What is the direction of the gravitational eld generated by this mass distribution at a point in space a distance z above the center of the donut, i.e. at (0; 0; z) Explain your reasoning for the direction carefully, try not to simply \wave your hands.” (The answer is extremely intuitive, but can you justify that it is correct?) (b) Compute the gravitational eld, ~g, at the point (0; 0; z) by directly integrating Newton’s law of gravity, summing over all in nitesimal \chunks” of mass along the loop. (c) Compute the gravitational potential at the point (0; 0; z) by directly integrating ?Gdm=r, sum- ming over all in nitesimal \chunks” dm along the loop. Then, take the z-component of the gradient of this potential to check that you agree with your result from the previous part. (d) In the two separate limits z << R and z >> R, Taylor expand your g- eld (in the z-direction)out only to the rst non-zero term, and convince us that both limits make good physical sense. (e) Can you use Gauss’ law to gure out the gravitational potential at the point (0; 0; z)? (If so, do it and check your previous answers. If not, why not?) Extra credit: If you place a small mass a small distance z away from the center, use your Taylor limit for z << R above to write a simple ODE for the equation of motion. Solve it, and discuss the motion Back to Problem List 4 5 { GRAVITATION Last Updated: July 16, 2012 5.4 Gravitational force near a metal-cored planet surrounded by a gaseous cloud Given: Pollock { Spring 2011 Jupiter is composed of a dense spherical core (of liquid metallic hydrogen!) of radius Rc. It is sur- rounded by a spherical cloud of gaseous hydrogen of radius Rg, where Rg > Rc. Let’s assume that the core is of uniform density c and the gaseous cloud is also of uniform density g. What is the gravitational force on an object of mass m that is located at a radius r from the center of Jupiter? Note that you must consider the cases where the object is inside the core, within the gas layer, and outside of the planet. Back to Problem List 5 5 { GRAVITATION Last Updated: July 16, 2012 5.5 Sphere with linearly increasing mass density Given: Pollock { Spring 2011 A planet of mass M and radius R has a nonuniform density that varies with r, the distance from the center according to  = Ar for 0  r  R. (a) What is the constant A in terms of M and R? Does this density pro le strike you as physically plausible, or is just designed as a mathematical exercise? (Brie y, explain) (b) Determine the gravitational force on a satellite of mass m orbiting this planet. In words, please outline the method you plan to use for your solution. (Use the easiest method you can come up with!) In your calculation, you will need to argue that the magnitude of ~g(r; ; ) depends only on r. Be very explicit about this – how do you know that it doesn’t, in fact, depend on  or ? (c) Determine the gravitational force felt by a rock of mass m inside the planet, located at radius r < R. (If the method you use is di erent than in part b, explain why you switched. If not, just proceed!) Explicitly check your result for this part by considering the limits r ! 0 and r ! R. Back to Problem List 6 5 { GRAVITATION Last Updated: July 16, 2012 5.6 Jumping o Vesta Given: Pollock { Spring 2011 You are stranded on the surface of the asteroid Vesta. If the mass of the asteroid is M and its radius is R, how fast would you have to jump o its surface to be able to escape from its gravitational eld? (Your estimate should be based on parameters that characterize the asteroid, not parameters that describe your jumping ability.) Given your formula, look up the approximate mass and radius of the asteroid Vesta 3 and determine a numerical value of the escape velocity. Could you escape in this way? (Brie y, explain) If so, roughly how big in radius is the maximum the asteroid could be, for you to still escape this way? If not, estimate how much smaller an asteroid you would need, to escape from it in this way? Figure 1: Back to Problem List 7 5 { GRAVITATION Last Updated: July 16, 2012 5.7 Gravitational force between two massive rods Given: Pollock { Spring 2011 Consider two identical uniform rods of length L and mass m lying along the same line and having their closest points separated by a distance d as shown in the gure (a) Calculate the mutual force between these rods, both its direction and magnitude. (b) Now do several checks. First, make sure the units worked out (!) The, nd the magnitude of the force in the limit L ! 0. What do you expect? Brie y, discuss. Lastly, nd the magnitude of the force in the limit d ! 1 ? Again, is it what you expect? Brie y, discuss. Figure 2: Given: Pollock { Spring 2012 Determining the gravitational force between two rods: (a) Consider a thin, uniform rod of mass m and length L (and negligible other dimensions) lying on the x axis (from x=-L to 0), as shown in g 1a. Derive a formula for the gravitational eld \g" at any arbitrary point x to the right of the origin (but still on the x-axis!) due to this rod. (b) Now suppose a second rod of length L and mass m sits on the x axis as shown in g 1b, with the left edge a distance \d" away. Calculate the mutual gravitational force between these rods. (c) Let's do some checks! Show that the units work out in parts a and b. Find the magnitude of the force in part a, in the limit x >> L: What do you expect? Brie y, discuss! Finally, verify that your answer to part b gives what you expect in the limit d >> L. ( Hint: This is a bit harder! You need to consistently expand everything to second order, not just rst, because of some interesting cancellations) Fig 1a Fig 1b L m +x x=0 L x=0 x=d m Fig 1a Fig 1b L m +x x=0 L +x x=0 x=d L m m Back to Problem List 8 5 { GRAVITATION Last Updated: July 16, 2012 5.8 Potential energy { Check your answer! Given: Pollock { Spring 2011 On the last exam, we had a problem with a at ring, uniform mass per unit area of , inner radius of R, outer radius of 2R. A satellite (mass m) sat a distance z above the center of the ring. We asked for the gravitational potential energy, and the answer was U(z) = ?2Gm( p 4R2 + z2 ? p R2 + z2) (1) (a) If you are far from the disk (on the z axis), what do you expect for the formula for U(z)? (Don’t say \0″ – as usual, we want the functional form of U(z) as you move far away. Also, explicitly state what we mean by \far away”. (Please don’t compare something with units to something without units!) (b) Show explicitly that the formula above does indeed give precisely the functional dependence you expect. Back to Problem List 9 5 { GRAVITATION Last Updated: July 16, 2012 5.9 Ways of solving gravitational problems Given: Pollock { Spring 2011, Spring 2012 Infinite cylinder ρ=cr x z (a) Half-infinite line mass, uniform linear mass density, λ x (b) R z  P Figure 3: (a) An in nite cylinder of radius R centered on the z-axis, with non-uniform volume mass density  = cr, where r is the radius in cylindrical coordinates. (b) A half-in nite line of mass on the x-axis extending from x = 0 to x = +1, with uniform linear mass density . There are two general methods we use to solve gravitational problems (i.e. nd ~g given some distribution of mass). (a) Describe these two methods. We claim one of these methods is easiest to solve for ~g of mass distribution (a) above, and the other method is easiest to solve for ~g of the mass distribution (b) above. Which method goes with which mass distribution? Please justify your answer. (b) Find ~g of the mass distribution (a) above for any arbitrary point outside the cylinder. (c) Find the x component of the gravitational acceleration, gx, generated by the mass distribution labeled (b) above, at a point P a given distance z up the positive z-axis (as shown). Back to Problem List 10 5 { GRAVITATION Last Updated: July 16, 2012 5.10 Rod with linearly increasing mass density Given: Pollock { Spring 2012 Consider a very (in nitesimally!) thin but massive rod, length L (total mass M), centered around the origin, sitting along the x-axis. (So the left end is at (-L/2, 0,0) and the right end is at (+L/2,0,0) Assume the mass density  (which has units of kg/m)is not uniform, but instead varies linearly with distance from the origin, (x) = cjxj. (a) What is that constant \c” in terms of M and L? What is the direction of the gravitational eld generated by this mass distribution at a point in space a distance z above the center of the rod, i.e. at (0; 0; z) Explain your reasoning for the direction carefully, try not to simply \wave your hands.” (The answer is extremely intuitive, but can you justify that it is correct?) (b) Compute the gravitational eld, ~g, at the point (0; 0; z) by directly integrating Newton’s law of gravity, summing over all in nitesimal \chunks” of mass along the rod. (c) Compute the gravitational potential at the point (0; 0; z) by directly integrating ?Gdm=r, sum- ming over all in nitesimal \chunks” dm along the rod. Then, take the z-component of the gradient of this potential to check that you agree with your result from the previous part. (d) In the limit of large z what do you expect for the functional form for gravitational potential? (Hint: Don’t just say it goes to zero! It’s a rod of mass M, when you’re far away what does it look like? How does it go to zero?) What does \large z” mean here? Use the binomial (or Taylor) expansion to verify that your formula does indeed give exactly what you expect. (Hint: you cannot Taylor expand in something BIG, you have to Taylor expand in something small.) (e) Can you use Gauss’ law to gure out the gravitational potential at the point (0; 0; z)? (If so, do it and check your previous answers. If not, why not?) Back to Problem List 11 5 { GRAVITATION Last Updated: July 16, 2012 5.11 Sphere with constant internal gravitational eld Given: Pollock { Spring 2012 (a) Imagine a planet of total mass M and radius R which has a nonuniform mass density that varies just with r, the distance from the center. For this (admittedly very unusual!) planet, suppose the gravitational eld strength inside the planet turns out to be independent of the radial distance within the sphere. Find the function describing the mass density  = (r) of this planet. (Your nal answer should be written in terms of the given constants.) (b) Now, determine the gravitational force on a satellite of mass m orbiting this planet at distance r > R. (Use the easiest method you can come up with!) Explain your work in words as well as formulas. For instance, in your calculation, you will need to argue that the magnitude of ~g(r; ; ) depends only on r. Be explicit about this – how do you know that it doesn’t, in fact, depend on  or ? (c) As a nal check, explicitly show that your solutions inside and outside the planet (parts a and b) are consistent when r = R. Please also comment on whether this density pro le strikes you as physically plausible, or is it just designed as a mathematical exercise? Defend your reasoning. Back to Problem List 12 5 { GRAVITATION Last Updated: July 16, 2012 5.12 Throwing a rock o the moon Given: Pollock { Spring 2012 Assuming that asteroids have roughly the same mass density as the moon, make an estimate of the largest asteroid that an astronaut could be standing on, and still have a chance of throwing a small object (with their arms, no machinery!) so that it completely escapes the asteroid’s gravitational eld. (This minimum speed is called \escape velocity”) Is the size you computed typical for asteroids in our solar system? Back to Problem List 13

5 { GRAVITATION Last Updated: July 16, 2012 Problem List 5.1 Total mass of a shell 5.2 Tunnel through the moon 5.3 Gravitational eld above the center of a thin hoop 5.4 Gravitational force near a metal-cored planet surrounded by a gaseous cloud 5.5 Sphere with linearly increasing mass density 5.6 Jumping o Vesta 5.7 Gravitational force between two massive rods 5.8 Potential energy { Check your answer! 5.9 Ways of solving gravitational problems 5.10 Rod with linearly increasing mass density 5.11 Sphere with constant internal gravitational eld 5.12 Throwing a rock o the moon These problems are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Un- ported License. Please share and/or modify. Back to Problem List 1 5 { GRAVITATION Last Updated: July 16, 2012 5.1 Total mass of a shell Given: Marino { Fall 2011 Consider a spherical shell that extends from r = R to r = 2R with a non-uniform density (r) = 0r. What is the total mass of the shell? Back to Problem List 2 5 { GRAVITATION Last Updated: July 16, 2012 5.2 Tunnel through the moon Given: Marino { Fall 2011 Imagine that NASA digs a straight tunnel through the center of the moon (see gure) to access the Moon’s 3He deposits. An astronaut places a rock in the tunnel at the surface of the moon, and releases it (from rest). Show that the rock obeys the force law for a mass connected to a spring. What is the spring constant? Find the oscillation period for this motion if you assume that Moon has a mass of 7.351022 kg and a radius of 1.74106 m. Assume the moon’s density is uniform throughout its volume, and ignore the moon’s rotation. Given: Pollock { Spring 2011 Imagine (in a parallel universe of unlimited budgets) that NASA digs a straight tunnel through the center of the moon (see gure). A robot place a rock in the tunnel at position r = r0 from the center of the moon, and releases it (from rest). Use Newton’s second law to write the equation of motion of the rock and solve for r(t). Explain in words the rock’s motion. Does the rock return to its initial position at any later time? If so, how long does it takes to return to it? (Give a formula, and a number.) Assume the moon’s density is uniform throughout its volume, and ignore the moon’s rotation. Given: Pollock { Spring 2012 Now lets consider our (real) planet Earth, with total mass M and radius R which we will approximate as a uniform mass density, (r) = 0. (a) Neglecting rotational and frictional e ects, show that a particle dropped into a hole drilled straight through the center of the earth all the way to the far side will oscillate between the two endpoints. (Hint: you will need to set up, and solve, an ODE for the motion) (b) Find the period of the oscillation of this motion. Get a number (in minutes) as a nal result, using data for the earth’s size and mass. (How does that compare to ying to Perth and back?!) Extra Credit: OK, even with unlimited budgets, digging a tunnel through the center of the earth is preposterous. But, suppose instead that the tunnel is a straight-line \chord” through the earth, say directly from New York to Los Angeles. Show that your nal answer for the time taken does not depend on the location of that chord! This is rather remarkable – look again at the time for a free-fall trip (no energy required, except perhaps to compensate for friction) How long would that trip take? Could this work?! Back to Problem List 3 5 { GRAVITATION Last Updated: July 16, 2012 5.3 Gravitational eld above the center of a thin hoop Given: Pollock { Spring 2011, Spring 2012 Consider a very (in nitesimally!) thin but massive loop, radius R (total mass M), centered around the origin, sitting in the x-y plane. Assume it has a uniform linear mass density  (which has units of kg/m) all around it. (So, it’s like a skinny donut that is mostly hole, centered around the z-axis) (a) What is  in terms of M and R? What is the direction of the gravitational eld generated by this mass distribution at a point in space a distance z above the center of the donut, i.e. at (0; 0; z) Explain your reasoning for the direction carefully, try not to simply \wave your hands.” (The answer is extremely intuitive, but can you justify that it is correct?) (b) Compute the gravitational eld, ~g, at the point (0; 0; z) by directly integrating Newton’s law of gravity, summing over all in nitesimal \chunks” of mass along the loop. (c) Compute the gravitational potential at the point (0; 0; z) by directly integrating ?Gdm=r, sum- ming over all in nitesimal \chunks” dm along the loop. Then, take the z-component of the gradient of this potential to check that you agree with your result from the previous part. (d) In the two separate limits z << R and z >> R, Taylor expand your g- eld (in the z-direction)out only to the rst non-zero term, and convince us that both limits make good physical sense. (e) Can you use Gauss’ law to gure out the gravitational potential at the point (0; 0; z)? (If so, do it and check your previous answers. If not, why not?) Extra credit: If you place a small mass a small distance z away from the center, use your Taylor limit for z << R above to write a simple ODE for the equation of motion. Solve it, and discuss the motion Back to Problem List 4 5 { GRAVITATION Last Updated: July 16, 2012 5.4 Gravitational force near a metal-cored planet surrounded by a gaseous cloud Given: Pollock { Spring 2011 Jupiter is composed of a dense spherical core (of liquid metallic hydrogen!) of radius Rc. It is sur- rounded by a spherical cloud of gaseous hydrogen of radius Rg, where Rg > Rc. Let’s assume that the core is of uniform density c and the gaseous cloud is also of uniform density g. What is the gravitational force on an object of mass m that is located at a radius r from the center of Jupiter? Note that you must consider the cases where the object is inside the core, within the gas layer, and outside of the planet. Back to Problem List 5 5 { GRAVITATION Last Updated: July 16, 2012 5.5 Sphere with linearly increasing mass density Given: Pollock { Spring 2011 A planet of mass M and radius R has a nonuniform density that varies with r, the distance from the center according to  = Ar for 0  r  R. (a) What is the constant A in terms of M and R? Does this density pro le strike you as physically plausible, or is just designed as a mathematical exercise? (Brie y, explain) (b) Determine the gravitational force on a satellite of mass m orbiting this planet. In words, please outline the method you plan to use for your solution. (Use the easiest method you can come up with!) In your calculation, you will need to argue that the magnitude of ~g(r; ; ) depends only on r. Be very explicit about this – how do you know that it doesn’t, in fact, depend on  or ? (c) Determine the gravitational force felt by a rock of mass m inside the planet, located at radius r < R. (If the method you use is di erent than in part b, explain why you switched. If not, just proceed!) Explicitly check your result for this part by considering the limits r ! 0 and r ! R. Back to Problem List 6 5 { GRAVITATION Last Updated: July 16, 2012 5.6 Jumping o Vesta Given: Pollock { Spring 2011 You are stranded on the surface of the asteroid Vesta. If the mass of the asteroid is M and its radius is R, how fast would you have to jump o its surface to be able to escape from its gravitational eld? (Your estimate should be based on parameters that characterize the asteroid, not parameters that describe your jumping ability.) Given your formula, look up the approximate mass and radius of the asteroid Vesta 3 and determine a numerical value of the escape velocity. Could you escape in this way? (Brie y, explain) If so, roughly how big in radius is the maximum the asteroid could be, for you to still escape this way? If not, estimate how much smaller an asteroid you would need, to escape from it in this way? Figure 1: Back to Problem List 7 5 { GRAVITATION Last Updated: July 16, 2012 5.7 Gravitational force between two massive rods Given: Pollock { Spring 2011 Consider two identical uniform rods of length L and mass m lying along the same line and having their closest points separated by a distance d as shown in the gure (a) Calculate the mutual force between these rods, both its direction and magnitude. (b) Now do several checks. First, make sure the units worked out (!) The, nd the magnitude of the force in the limit L ! 0. What do you expect? Brie y, discuss. Lastly, nd the magnitude of the force in the limit d ! 1 ? Again, is it what you expect? Brie y, discuss. Figure 2: Given: Pollock { Spring 2012 Determining the gravitational force between two rods: (a) Consider a thin, uniform rod of mass m and length L (and negligible other dimensions) lying on the x axis (from x=-L to 0), as shown in g 1a. Derive a formula for the gravitational eld \g" at any arbitrary point x to the right of the origin (but still on the x-axis!) due to this rod. (b) Now suppose a second rod of length L and mass m sits on the x axis as shown in g 1b, with the left edge a distance \d" away. Calculate the mutual gravitational force between these rods. (c) Let's do some checks! Show that the units work out in parts a and b. Find the magnitude of the force in part a, in the limit x >> L: What do you expect? Brie y, discuss! Finally, verify that your answer to part b gives what you expect in the limit d >> L. ( Hint: This is a bit harder! You need to consistently expand everything to second order, not just rst, because of some interesting cancellations) Fig 1a Fig 1b L m +x x=0 L x=0 x=d m Fig 1a Fig 1b L m +x x=0 L +x x=0 x=d L m m Back to Problem List 8 5 { GRAVITATION Last Updated: July 16, 2012 5.8 Potential energy { Check your answer! Given: Pollock { Spring 2011 On the last exam, we had a problem with a at ring, uniform mass per unit area of , inner radius of R, outer radius of 2R. A satellite (mass m) sat a distance z above the center of the ring. We asked for the gravitational potential energy, and the answer was U(z) = ?2Gm( p 4R2 + z2 ? p R2 + z2) (1) (a) If you are far from the disk (on the z axis), what do you expect for the formula for U(z)? (Don’t say \0″ – as usual, we want the functional form of U(z) as you move far away. Also, explicitly state what we mean by \far away”. (Please don’t compare something with units to something without units!) (b) Show explicitly that the formula above does indeed give precisely the functional dependence you expect. Back to Problem List 9 5 { GRAVITATION Last Updated: July 16, 2012 5.9 Ways of solving gravitational problems Given: Pollock { Spring 2011, Spring 2012 Infinite cylinder ρ=cr x z (a) Half-infinite line mass, uniform linear mass density, λ x (b) R z  P Figure 3: (a) An in nite cylinder of radius R centered on the z-axis, with non-uniform volume mass density  = cr, where r is the radius in cylindrical coordinates. (b) A half-in nite line of mass on the x-axis extending from x = 0 to x = +1, with uniform linear mass density . There are two general methods we use to solve gravitational problems (i.e. nd ~g given some distribution of mass). (a) Describe these two methods. We claim one of these methods is easiest to solve for ~g of mass distribution (a) above, and the other method is easiest to solve for ~g of the mass distribution (b) above. Which method goes with which mass distribution? Please justify your answer. (b) Find ~g of the mass distribution (a) above for any arbitrary point outside the cylinder. (c) Find the x component of the gravitational acceleration, gx, generated by the mass distribution labeled (b) above, at a point P a given distance z up the positive z-axis (as shown). Back to Problem List 10 5 { GRAVITATION Last Updated: July 16, 2012 5.10 Rod with linearly increasing mass density Given: Pollock { Spring 2012 Consider a very (in nitesimally!) thin but massive rod, length L (total mass M), centered around the origin, sitting along the x-axis. (So the left end is at (-L/2, 0,0) and the right end is at (+L/2,0,0) Assume the mass density  (which has units of kg/m)is not uniform, but instead varies linearly with distance from the origin, (x) = cjxj. (a) What is that constant \c” in terms of M and L? What is the direction of the gravitational eld generated by this mass distribution at a point in space a distance z above the center of the rod, i.e. at (0; 0; z) Explain your reasoning for the direction carefully, try not to simply \wave your hands.” (The answer is extremely intuitive, but can you justify that it is correct?) (b) Compute the gravitational eld, ~g, at the point (0; 0; z) by directly integrating Newton’s law of gravity, summing over all in nitesimal \chunks” of mass along the rod. (c) Compute the gravitational potential at the point (0; 0; z) by directly integrating ?Gdm=r, sum- ming over all in nitesimal \chunks” dm along the rod. Then, take the z-component of the gradient of this potential to check that you agree with your result from the previous part. (d) In the limit of large z what do you expect for the functional form for gravitational potential? (Hint: Don’t just say it goes to zero! It’s a rod of mass M, when you’re far away what does it look like? How does it go to zero?) What does \large z” mean here? Use the binomial (or Taylor) expansion to verify that your formula does indeed give exactly what you expect. (Hint: you cannot Taylor expand in something BIG, you have to Taylor expand in something small.) (e) Can you use Gauss’ law to gure out the gravitational potential at the point (0; 0; z)? (If so, do it and check your previous answers. If not, why not?) Back to Problem List 11 5 { GRAVITATION Last Updated: July 16, 2012 5.11 Sphere with constant internal gravitational eld Given: Pollock { Spring 2012 (a) Imagine a planet of total mass M and radius R which has a nonuniform mass density that varies just with r, the distance from the center. For this (admittedly very unusual!) planet, suppose the gravitational eld strength inside the planet turns out to be independent of the radial distance within the sphere. Find the function describing the mass density  = (r) of this planet. (Your nal answer should be written in terms of the given constants.) (b) Now, determine the gravitational force on a satellite of mass m orbiting this planet at distance r > R. (Use the easiest method you can come up with!) Explain your work in words as well as formulas. For instance, in your calculation, you will need to argue that the magnitude of ~g(r; ; ) depends only on r. Be explicit about this – how do you know that it doesn’t, in fact, depend on  or ? (c) As a nal check, explicitly show that your solutions inside and outside the planet (parts a and b) are consistent when r = R. Please also comment on whether this density pro le strikes you as physically plausible, or is it just designed as a mathematical exercise? Defend your reasoning. Back to Problem List 12 5 { GRAVITATION Last Updated: July 16, 2012 5.12 Throwing a rock o the moon Given: Pollock { Spring 2012 Assuming that asteroids have roughly the same mass density as the moon, make an estimate of the largest asteroid that an astronaut could be standing on, and still have a chance of throwing a small object (with their arms, no machinery!) so that it completely escapes the asteroid’s gravitational eld. (This minimum speed is called \escape velocity”) Is the size you computed typical for asteroids in our solar system? Back to Problem List 13

A proposed space station consists of a large circular disk with the living quarters on the rim of circular ring, 63.0m in diameter. What speed should the rim of the ring have, so that the occupants feel that they have the same weight as they do on Earth?

A proposed space station consists of a large circular disk with the living quarters on the rim of circular ring, 63.0m in diameter. What speed should the rim of the ring have, so that the occupants feel that they have the same weight as they do on Earth?

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Electric Field due to Point Charges 1a. Problem 21.39 b. Problem 21.40 2. Problem 21.38 3. Problem 21.41 Electric Field due to Continuous Distributions 4a. Problem 22.13 Hint: Solve for E(x>5.0m) to complete parts b, c, & d. b. Solve for E(x>5.0m) if the charge density isn’t uniform: λ(x) = C x2 5. Problem 22.20 Extra Credit: We have used point charges to calculate the electric field due to a ring of charge at locations above its center, and then integrated rings to calculate the on-axis electric field due to a disk of uniform charge. Integrate a stack of disks in order to calculate the electric field due to a uniform sphere of radius R and total charge Q, as measured at a distance r>R. Electric Field Lines 6a. Problem 21.13 b. Sketch electric field lines for the charge distribution in Problem 21.12. 7. Sketch the electric field lines emanating from: a. A uniform ring of charge, with radius R and total charge Q (granting a linear density λ=Q/2πR). b. A uniform disk of charge, with radius R and total charge Q (granting a surface density σ=Q/πR2). c. An infinite plane of charge, of uniform charge density σ.

Electric Field due to Point Charges 1a. Problem 21.39 b. Problem 21.40 2. Problem 21.38 3. Problem 21.41 Electric Field due to Continuous Distributions 4a. Problem 22.13 Hint: Solve for E(x>5.0m) to complete parts b, c, & d. b. Solve for E(x>5.0m) if the charge density isn’t uniform: λ(x) = C x2 5. Problem 22.20 Extra Credit: We have used point charges to calculate the electric field due to a ring of charge at locations above its center, and then integrated rings to calculate the on-axis electric field due to a disk of uniform charge. Integrate a stack of disks in order to calculate the electric field due to a uniform sphere of radius R and total charge Q, as measured at a distance r>R. Electric Field Lines 6a. Problem 21.13 b. Sketch electric field lines for the charge distribution in Problem 21.12. 7. Sketch the electric field lines emanating from: a. A uniform ring of charge, with radius R and total charge Q (granting a linear density λ=Q/2πR). b. A uniform disk of charge, with radius R and total charge Q (granting a surface density σ=Q/πR2). c. An infinite plane of charge, of uniform charge density σ.

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A block with mass m =7.1 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.23 m. While at this equilibrium position, the mass is then given an initial push downward at v = 4.4 m/s. The block oscillates on the spring without friction. 1) What is the spring constant of the spring? N/m You currently have 1 submissions for this question. Only 10 submission are allowed. You can make 9 more submissions for this question. 2) What is the oscillation frequency? Hz You currently have 2 submissions for this question. Only 10 submission are allowed. You can make 8 more submissions for this question. 3) After t = 0.37 s what is the speed of the block? m/s You currently have 1 submissions for this question. Only 10 submission are allowed. You can make 9 more submissions for this question. 4) What is the magnitude of the maximum acceleration of the block? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 5) At t = 0.37 s what is the magnitude of the net force on the block? N You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 6) Where is the potential energy of the system the greatest? At the highest point of the oscillation. At the new equilibrium position of the oscillation. At the lowest point of the oscillation. You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. (Survey Question) 7) Below is some space to write notes on this problem A 5.2-kg object on a frictionless horizontal surface is attached to one end of a horizontal spring that has a force constantk = 717 N/m. The spring is stretched 7.9 cm from equilibrium and released. 1) (a) What is the frequency of the motion? Hz You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 2) (b) What is the period of the motion? s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 3) (c) What is the amplitude of the motion? cm You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 4) (d) What is the maximum speed of the motion? m/s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 5) (e) What is the maximum acceleration of the motion? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 6) (f) When does the object first reach its equilibrium position? s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 7) (h) What is its acceleration at this time? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 1) An 86 kg person steps into a car of mass 2437 kg, causing it to sink 2.35 cm on its springs. Assuming no damping, with what frequency will the car and passenger vibrate on the springs? Hz You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 1) A 0.117-kg block is suspended from a spring. When a small pebble of mass 30 g is placed on the block, the spring stretches an additional 5.1 cm. With the pebble on the block, the block oscillates with an amplitude of 12 cm. Find the maximum amplitude of oscillation at which the pebble will remain in contact with the block. Block and Spring SHM ________________________________________ At t = 0 a block with mass M = 5 kg moves with a velocity v = 2 m/s at position xo = -.33 m from the equilibrium position of the spring. The block is attached to a massless spring of spring constant k = 61.2 N/m and slides on a frictionless surface. At what time will the block next pass x = 0, the place where the spring is unstretched? t1 = seconds You currently have 1 submissions for this question. Only 10 submission are allowed. You can make 9 more submissions for this question. A simple pendulum with mass m = 1.9 kg and length L = 2.39 m hangs from the ceiling. It is pulled back to an small angle of θ = 9.9° from the vertical and released at t = 0. 1) What is the period of oscillation? s You currently have 2 submissions for this question. Only 10 submission are allowed. You can make 8 more submissions for this question. 2) What is the magnitude of the force on the pendulum bob perpendicular to the string at t=0? N You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 3) What is the maximum speed of the pendulum? m/s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 4) What is the angular displacement at t = 3.5 s? (give the answer as a negative angle if the angle is to the left of the vertical) ° You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 5) What is the magnitude of the tangential acceleration as the pendulum passes through the equilibrium position? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 6) What is the magnitude of the radial acceleration as the pendulum passes through the equilibrium position? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 7) Which of the following would change the frequency of oscillation of this simple pendulum? increasing the mass decreasing the initial angular displacement increasing the length hanging the pendulum in an elevator accelerating downward You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. (Survey Question) 8) Below is some space to write notes on this problem 1) If the period of a 74-cm-long simple pendulum is 1.72 s, what is the value of g at the location of the pendulum? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. Torsion Pendulum • 1 • 2 • 3 • 4 • 5 A torsion pendulum is made from a disk of mass m = 6.6 kg and radius R = 0.66 m. A force of F = 44.8 N exerted on the edge of the disk rotates the disk 1/4 of a revolution from equilibrium. 1) What is the torsion constant of this pendulum? N-m/rad You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 2) What is the minimum torque needed to rotate the pendulum a full revolution from equilibrium? N-m You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 3) What is the angular frequency of oscillation of this torsion pendulum? rad/s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 4) Which of the following would change the period of oscillation of this torsion pendulum? increasing the mass decreasing the initial angular displacement replacing the disk with a sphere of equal mass and radius hanging the pendulum in an elevator accelerating downward You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. (Survey Question) 5) Below is some space to write notes on this problem You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. Physical Pendulum ________________________________________ A rigid rod of length L= 1 m and mass M = 2.5 kg is attached to a pivot mounted d = 0.17 m from one end. The rod can rotate in the vertical plane, and is influenced by gravity. What is the period for small oscillations of the pendulum shown? T = seconds A circular hoop of radius 57 cm is hung on a narrow horizontal rod and allowed to swing in the plane of the hoop. What is the period of its oscillation, assuming that the amplitude is small? s 1) You are given a wooden rod 68 cm long and asked to drill a small diameter hole in it so that when pivoted about the the hole the period of the pendulum will be a minimum. How far from the center should you drill the hole? cm

A block with mass m =7.1 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.23 m. While at this equilibrium position, the mass is then given an initial push downward at v = 4.4 m/s. The block oscillates on the spring without friction. 1) What is the spring constant of the spring? N/m You currently have 1 submissions for this question. Only 10 submission are allowed. You can make 9 more submissions for this question. 2) What is the oscillation frequency? Hz You currently have 2 submissions for this question. Only 10 submission are allowed. You can make 8 more submissions for this question. 3) After t = 0.37 s what is the speed of the block? m/s You currently have 1 submissions for this question. Only 10 submission are allowed. You can make 9 more submissions for this question. 4) What is the magnitude of the maximum acceleration of the block? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 5) At t = 0.37 s what is the magnitude of the net force on the block? N You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 6) Where is the potential energy of the system the greatest? At the highest point of the oscillation. At the new equilibrium position of the oscillation. At the lowest point of the oscillation. You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. (Survey Question) 7) Below is some space to write notes on this problem A 5.2-kg object on a frictionless horizontal surface is attached to one end of a horizontal spring that has a force constantk = 717 N/m. The spring is stretched 7.9 cm from equilibrium and released. 1) (a) What is the frequency of the motion? Hz You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 2) (b) What is the period of the motion? s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 3) (c) What is the amplitude of the motion? cm You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 4) (d) What is the maximum speed of the motion? m/s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 5) (e) What is the maximum acceleration of the motion? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 6) (f) When does the object first reach its equilibrium position? s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 7) (h) What is its acceleration at this time? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 1) An 86 kg person steps into a car of mass 2437 kg, causing it to sink 2.35 cm on its springs. Assuming no damping, with what frequency will the car and passenger vibrate on the springs? Hz You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 1) A 0.117-kg block is suspended from a spring. When a small pebble of mass 30 g is placed on the block, the spring stretches an additional 5.1 cm. With the pebble on the block, the block oscillates with an amplitude of 12 cm. Find the maximum amplitude of oscillation at which the pebble will remain in contact with the block. Block and Spring SHM ________________________________________ At t = 0 a block with mass M = 5 kg moves with a velocity v = 2 m/s at position xo = -.33 m from the equilibrium position of the spring. The block is attached to a massless spring of spring constant k = 61.2 N/m and slides on a frictionless surface. At what time will the block next pass x = 0, the place where the spring is unstretched? t1 = seconds You currently have 1 submissions for this question. Only 10 submission are allowed. You can make 9 more submissions for this question. A simple pendulum with mass m = 1.9 kg and length L = 2.39 m hangs from the ceiling. It is pulled back to an small angle of θ = 9.9° from the vertical and released at t = 0. 1) What is the period of oscillation? s You currently have 2 submissions for this question. Only 10 submission are allowed. You can make 8 more submissions for this question. 2) What is the magnitude of the force on the pendulum bob perpendicular to the string at t=0? N You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 3) What is the maximum speed of the pendulum? m/s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 4) What is the angular displacement at t = 3.5 s? (give the answer as a negative angle if the angle is to the left of the vertical) ° You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 5) What is the magnitude of the tangential acceleration as the pendulum passes through the equilibrium position? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 6) What is the magnitude of the radial acceleration as the pendulum passes through the equilibrium position? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 7) Which of the following would change the frequency of oscillation of this simple pendulum? increasing the mass decreasing the initial angular displacement increasing the length hanging the pendulum in an elevator accelerating downward You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. (Survey Question) 8) Below is some space to write notes on this problem 1) If the period of a 74-cm-long simple pendulum is 1.72 s, what is the value of g at the location of the pendulum? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. Torsion Pendulum • 1 • 2 • 3 • 4 • 5 A torsion pendulum is made from a disk of mass m = 6.6 kg and radius R = 0.66 m. A force of F = 44.8 N exerted on the edge of the disk rotates the disk 1/4 of a revolution from equilibrium. 1) What is the torsion constant of this pendulum? N-m/rad You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 2) What is the minimum torque needed to rotate the pendulum a full revolution from equilibrium? N-m You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 3) What is the angular frequency of oscillation of this torsion pendulum? rad/s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 4) Which of the following would change the period of oscillation of this torsion pendulum? increasing the mass decreasing the initial angular displacement replacing the disk with a sphere of equal mass and radius hanging the pendulum in an elevator accelerating downward You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. (Survey Question) 5) Below is some space to write notes on this problem You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. Physical Pendulum ________________________________________ A rigid rod of length L= 1 m and mass M = 2.5 kg is attached to a pivot mounted d = 0.17 m from one end. The rod can rotate in the vertical plane, and is influenced by gravity. What is the period for small oscillations of the pendulum shown? T = seconds A circular hoop of radius 57 cm is hung on a narrow horizontal rod and allowed to swing in the plane of the hoop. What is the period of its oscillation, assuming that the amplitude is small? s 1) You are given a wooden rod 68 cm long and asked to drill a small diameter hole in it so that when pivoted about the the hole the period of the pendulum will be a minimum. How far from the center should you drill the hole? cm

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Question 1 When using NTFS as a file system, what can be used to control the amount of hard disk space each user on the machine can have as a maximum? Answer Logical drives Extended partitions Disk quotas Security Center Question 2 Pin 1 of the floppy cable connects to pin 34 of the controller. Answer True False Question 3 What is the primary cause of hard drive failures? Answer Heat Dust Dirty laser lens Moving parts Question 4 The DBR contains the system files. Answer True False Question 5 A spanned volume requires a minimum of three hard drives. Answer True False Question 6 Which situation would not be appropriate for the use of SSDs? Answer A military operation where fast access to data is critical A medical imaging office that needs high-capacity storage A manufacturing plant with heat-sensitive equipment A research facility where noise must be kept to a minimum Question 7 Why are SSDs more susceptible than mechanical hard drives to electrostatic discharge? Answer The internal battery of the SSD provides additional current. SSDs are memory. The voltage level of the SSD is lower than a mechanical hard drive. The SSD is a more fragile component. Question 8 A motherboard has two PATA IDE connectors, A and B. A is nearer the edge than B. The IDE cable from A connects to a 500GB hard drive and then to a 200GB hard drive. The IDE cable from B connects to an R/W optical drive and then to a Blu-ray optical drive. Assuming the setup is optimal, which of the following describes the 500GB hard drive? Answer Primary slave Secondary slave Primary master Secondary master Question 9 The primary IDE motherboard connection normally uses I/O address 1F0 -1F7h and IRQ 15. Answer True False Question 10 A cable with a twist is used when installing two floppy drives. Answer True False Question 11 What does partitioning the hard drive mean? Answer Dividing the hard drive up into three different sections: one for each type of file system Preparing the drive to be mounted Giving the hard drive a drive letter and/or allowing the hard drive to be seen as more than one drive Preparing the drive for an operating system Question 12 The Network Engineering Technology departmental secretary is getting a new computer funded by a grant. The old computer is being moved by the PC technicians to give to the new program facilitator in another department. Which one of the following is most likely to be used before the program facilitator uses the computer? Answer Check Now Tool Backup Tool Disk Management Tool BitLocker Question 13 What is CHKDSK? Answer A command used to scan the disk for viruses during off hours A program used to defragment the hard drive A program used to locate and identify lost clusters A command used to verify the validity of the drive surface before installing a file system or an operating system Question 14 When a disk has been prepared to store data, it has been Answer Cleaned Tracked Enabled Formatted Question 15 Where would you go to enable a SATA port? Answer CMOS BIOS Disk Management Tool Task Manager Question 16 The Windows boot partition is the partition that must contain the majority of the operating system. Answer True False Question 17 Two considerations when adding or installing a floppy drive are an available drive bay and an available power connector. Answer True False Question 18 What is the difference between a SATA 2 and a SATA 3 hard drive? Answer The SATA 3 has a different power connector. The SATA 3 device transmits more simultaneous bits than SATA 2. The SATA 3 device transmits data faster. SATA 3 will always be a larger capacity drive. The SATA 3 device will be physically smaller. Question 19 What command would be used in Windows 7 to repair a partition table? Answer FDISK FORMAT FIXBOOT bootrec /FixMbr FIXMBR Question 20 What file system is optimized for optical media? Answer exFAT FAT32 CDFS NTFS Question 21 One of the most effective ways of increasing computer performance is to increase the size of virtual memory. Answer True False Question 22 Older PATA IDE cables and the Ultra ATA/66 cable differ by Answer Where the twist occurs The number of conductors The number of pins The number of devices they can connect to Question 23 Which of the following is NOT important in assigning SCSI IDs? Answer The hard drive that the system boots to may have a preset ID. ID priority must match the order of appearance on the SCSI chain. All devices must have unique IDs. Slower devices should have higher priority IDs. Question 24 The ATA standard is associated with the SCSI interface. Answer True False Question 25 A striped volume requires a minimum of two hard drives. Answer True False

Question 1 When using NTFS as a file system, what can be used to control the amount of hard disk space each user on the machine can have as a maximum? Answer Logical drives Extended partitions Disk quotas Security Center Question 2 Pin 1 of the floppy cable connects to pin 34 of the controller. Answer True False Question 3 What is the primary cause of hard drive failures? Answer Heat Dust Dirty laser lens Moving parts Question 4 The DBR contains the system files. Answer True False Question 5 A spanned volume requires a minimum of three hard drives. Answer True False Question 6 Which situation would not be appropriate for the use of SSDs? Answer A military operation where fast access to data is critical A medical imaging office that needs high-capacity storage A manufacturing plant with heat-sensitive equipment A research facility where noise must be kept to a minimum Question 7 Why are SSDs more susceptible than mechanical hard drives to electrostatic discharge? Answer The internal battery of the SSD provides additional current. SSDs are memory. The voltage level of the SSD is lower than a mechanical hard drive. The SSD is a more fragile component. Question 8 A motherboard has two PATA IDE connectors, A and B. A is nearer the edge than B. The IDE cable from A connects to a 500GB hard drive and then to a 200GB hard drive. The IDE cable from B connects to an R/W optical drive and then to a Blu-ray optical drive. Assuming the setup is optimal, which of the following describes the 500GB hard drive? Answer Primary slave Secondary slave Primary master Secondary master Question 9 The primary IDE motherboard connection normally uses I/O address 1F0 -1F7h and IRQ 15. Answer True False Question 10 A cable with a twist is used when installing two floppy drives. Answer True False Question 11 What does partitioning the hard drive mean? Answer Dividing the hard drive up into three different sections: one for each type of file system Preparing the drive to be mounted Giving the hard drive a drive letter and/or allowing the hard drive to be seen as more than one drive Preparing the drive for an operating system Question 12 The Network Engineering Technology departmental secretary is getting a new computer funded by a grant. The old computer is being moved by the PC technicians to give to the new program facilitator in another department. Which one of the following is most likely to be used before the program facilitator uses the computer? Answer Check Now Tool Backup Tool Disk Management Tool BitLocker Question 13 What is CHKDSK? Answer A command used to scan the disk for viruses during off hours A program used to defragment the hard drive A program used to locate and identify lost clusters A command used to verify the validity of the drive surface before installing a file system or an operating system Question 14 When a disk has been prepared to store data, it has been Answer Cleaned Tracked Enabled Formatted Question 15 Where would you go to enable a SATA port? Answer CMOS BIOS Disk Management Tool Task Manager Question 16 The Windows boot partition is the partition that must contain the majority of the operating system. Answer True False Question 17 Two considerations when adding or installing a floppy drive are an available drive bay and an available power connector. Answer True False Question 18 What is the difference between a SATA 2 and a SATA 3 hard drive? Answer The SATA 3 has a different power connector. The SATA 3 device transmits more simultaneous bits than SATA 2. The SATA 3 device transmits data faster. SATA 3 will always be a larger capacity drive. The SATA 3 device will be physically smaller. Question 19 What command would be used in Windows 7 to repair a partition table? Answer FDISK FORMAT FIXBOOT bootrec /FixMbr FIXMBR Question 20 What file system is optimized for optical media? Answer exFAT FAT32 CDFS NTFS Question 21 One of the most effective ways of increasing computer performance is to increase the size of virtual memory. Answer True False Question 22 Older PATA IDE cables and the Ultra ATA/66 cable differ by Answer Where the twist occurs The number of conductors The number of pins The number of devices they can connect to Question 23 Which of the following is NOT important in assigning SCSI IDs? Answer The hard drive that the system boots to may have a preset ID. ID priority must match the order of appearance on the SCSI chain. All devices must have unique IDs. Slower devices should have higher priority IDs. Question 24 The ATA standard is associated with the SCSI interface. Answer True False Question 25 A striped volume requires a minimum of two hard drives. Answer True False

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