## 09/20 -09/26 Week 3 Chapter 3 : Chemistry of Global Climate Change Reading: CIC: Chapter 3 Review PowerPoint Discussion Posting (One Initial Post of 300 with cited references by Wednesday, two follow-ups by Saturday, posted on separate days ) Complete Connect Module 09/27-10/03 Week 4 Chapter 4 Energy from Combustion Reading: CIC :Chapter 4 Energy From Combustion Review PowerPoint Discussion (One Initial Post of 300 words with cited references by Wednesday, two follow-ups by Saturday ) Complete Connect Module 10/04-10/10 Week 5 Water for Life Chapter 5 Reading: CIC : Chapter 5 Review PowerPoint Discussion (One Initial Post of 300 words with cited references by Wednesday, two follow-ups by Saturday, posted on separate days). Complete Connect Module 10/11-10/17 Week 6 Acid Rain Reading Chapter 6 Review PowerPoint (One Initial Post of 300 words with cited references by Wednesday, two follow-ups by Saturday, POSTED ON SEPERATE DAYS ) Complete Connect Module 10/18-10/24 Week 7 Nuclear Fission Read Chapter 7 Review PPT (One Initial Post of 300 words with cited references by Wednesday two follow- ups by Saturday, POSTED ON SEPERATE DAYS) Complete Connect Module

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## “How to Date a Black girl, Brown girl, Halfie or White girl” written by Junot Diaz

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## Assignment 8 Due: 11:59pm on Friday, April 4, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 10.3 Part A If a particle’s speed increases by a factor of 5, by what factor does its kinetic energy change? ANSWER: Correct Conceptual Question 10.11 A spring is compressed 1.5 . Part A How far must you compress a spring with twice the spring constant to store the same amount of energy? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct = 25 K2 K1 cm x = 1.1 cm Problem 10.2 The lowest point in Death Valley is below sea level. The summit of nearby Mt. Whitney has an elevation of 4420 . Part A What is the change in potential energy of an energetic 80 hiker who makes it from the floor of Death Valley to the top of Mt.Whitney? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 10.3 Part A At what speed does a 1800 compact car have the same kinetic energy as a 1.80×104 truck going 21.0 ? Express your answer with the appropriate units. ANSWER: Correct Problem 10.5 A boy reaches out of a window and tosses a ball straight up with a speed of 13 . The ball is 21 above the ground as he releases it. 85m m kg U = 3.5×106 J kg kg km/hr vc = 66.4 km hr m/s m Part A Use energy to find the ball’s maximum height above the ground. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B Use energy to find the ball’s speed as it passes the window on its way down. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C Use energy to find the speed of impact on the ground. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Hmax = 30 m v = 13 ms v = 24 ms Problem 10.8 A 59.0 skateboarder wants to just make it to the upper edge of a “quarter pipe,” a track that is one-quarter of a circle with a radius of 2.30 . Part A What speed does he need at the bottom? Express your answer with the appropriate units. ANSWER: Correct Problem 10.12 A 1500 car traveling at 12 suddenly runs out of gas while approaching the valley shown in the figure. The alert driver immediately puts the car in neutral so that it will roll. Part A kg m 6.71 ms kg m/s What will be the car’s speed as it coasts into the gas station on the other side of the valley? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Ups and Downs Learning Goal: To apply the law of conservation of energy to an object launched upward in the gravitational field of the earth. In the absence of nonconservative forces such as friction and air resistance, the total mechanical energy in a closed system is conserved. This is one particular case of the law of conservation of energy. In this problem, you will apply the law of conservation of energy to different objects launched from the earth. The energy transformations that take place involve the object’s kinetic energy and its gravitational potential energy . The law of conservation of energy for such cases implies that the sum of the object’s kinetic energy and potential energy does not change with time. This idea can be expressed by the equation , where “i” denotes the “initial” moment and “f” denotes the “final” moment. Since any two moments will work, the choice of the moments to consider is, technically, up to you. That choice, though, is usually suggested by the question posed in the problem. First, let us consider an object launched vertically upward with an initial speed . Neglect air resistance. Part A As the projectile goes upward, what energy changes take place? ANSWER: v = 6.8 ms K = (1/2)mv2 U = mgh Ki + Ui = Kf + Uf v Correct Part B At the top point of the flight, what can be said about the projectile’s kinetic and potential energy? ANSWER: Correct Strictly speaking, it is not the ball that possesses potential energy; rather, it is the system “Earth-ball.” Although we will often talk about “the gravitational potential energy of an elevated object,” it is useful to keep in mind that the energy, in fact, is associated with the interactions between the earth and the elevated object. Part C The potential energy of the object at the moment of launch __________. ANSWER: Both kinetic and potential energy decrease. Both kinetic and potential energy increase. Kinetic energy decreases; potential energy increases. Kinetic energy increases; potential energy decreases. Both kinetic and potential energy are at their maximum values. Both kinetic and potential energy are at their minimum values. Kinetic energy is at a maximum; potential energy is at a minimum. Kinetic energy is at a minimum; potential energy is at a maximum. Correct Usually, the zero level is chosen so as to make the relevant calculations simpler. In this case, it makes good sense to assume that at the ground level–but this is not, by any means, the only choice! Part D Using conservation of energy, find the maximum height to which the object will rise. Express your answer in terms of and the magnitude of the acceleration of gravity . ANSWER: Correct You may remember this result from kinematics. It is comforting to know that our new approach yields the same answer. Part E At what height above the ground does the projectile have a speed of ? Express your answer in terms of and the magnitude of the acceleration of gravity . ANSWER: is negative is positive is zero depends on the choice of the “zero level” of potential energy U = 0 hmax v g hmax = v2 2g h 0.5v v g h = 3 v2 8g Correct Part F What is the speed of the object at the height of ? Express your answer in terms of and . Use three significant figures in the numeric coefficient. Hint 1. How to approach the problem You are being asked for the speed at half of the maximum height. You know that at the initial height ( ), the speed is . All of the energy is kinetic energy, and so, the total energy is . At the maximum height, all of the energy is potential energy. Since the gravitational potential energy is proportional to , half of the initial kinetic energy must have been converted to potential energy when the projectile is at . Thus, the kinetic energy must be half of its original value (i.e., when ). You need to determine the speed, as a multiple of , that corresponds to such a kinetic energy. ANSWER: Correct Let us now consider objects launched at an angle. For such situations, using conservation of energy leads to a quicker solution than can be produced by kinematics. Part G A ball is launched as a projectile with initial speed at an angle above the horizontal. Using conservation of energy, find the maximum height of the ball’s flight. Express your answer in terms of , , and . Hint 1. Find the final kinetic energy Find the final kinetic energy of the ball. Here, the best choice of “final” moment is the point at which the ball reaches its maximum height, since this is the point we are interested in. u (1/2)hmax v g h = 0 v (1/2)mv2 h (1/2)hmax (1/4)mv2 h = (1/2)hmax v u = 0.707v v hmax v g Kf Express your answer in terms of , , and . Hint 1. Find the speed at the maximum height The speed of the ball at the maximum height is __________. ANSWER: ANSWER: ANSWER: Correct Part H A ball is launched with initial speed from ground level up a frictionless slope. The slope makes an angle with the horizontal. Using conservation of energy, find the maximum vertical height to which the ball will climb. Express your answer in terms of , , and . You may or may not use all of these quantities. v m 0 v v cos v sin v tan Kf = 0.5m(vcos())2 hmax = (vsin())2 2g v hmax v g ANSWER: Correct Interestingly, the answer does not depend on . The difference between this situation and the projectile case is that the ball moving up a slope has no kinetic energy at the top of its trajectory whereas the projectile launched at an angle does. Part I A ball is launched with initial speed from the ground level up a frictionless hill. The hill becomes steeper as the ball slides up; however, the ball remains in contact with the hill at all times. Using conservation of energy, find the maximum vertical height to which the ball will climb. Express your answer in terms of and . ANSWER: Correct The profile of the hill does not matter; the equation would have the same terms regardless of the steepness of the hill. Problem 10.14 A 12- -long spring is attached to the ceiling. When a 2.2 mass is hung from it, the spring stretches to a length of 17 . Part A What is the spring constant ? Express your answer to two significant figures and include the appropriate units. hmax = v2 2g v hmax v g hmax = v2 2g Ki + Ui = Kf + Uf cm kg cm k ANSWER: Correct Part B How long is the spring when a 3.0 mass is suspended from it? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Enhanced EOC: Problem 10.17 A 6.2 mass hanging from a spring scale is slowly lowered onto a vertical spring, as shown in . You may want to review ( pages 255 – 257) . For help with math skills, you may want to review: Solving Algebraic Equations = 430 k Nm kg y = 19 cm kg Part A What does the spring scale read just before the mass touches the lower spring? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem Draw a picture showing the forces acting on the mass before it touches the scale. What is the net force on the mass? What is the force on the mass due to gravity? What is the force on the mass due to the scale? ANSWER: Correct Part B The scale reads 22 when the lower spring has been compressed by 2.7 . What is the value of the spring constant for the lower spring? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem Draw a picture showing the forces acting on the mass. What is the net force on the mass? What is the force on the mass due to gravity? What is the force on the mass due to the scale? Use these to determine the force on the mass by the spring, taking note of the directions from your picture. How is the spring constant related to the force by the spring and the compression of the spring? Check your units. ANSWER: F = 61 N N cm k = 1400 k Nm Correct Part C At what compression length will the scale read zero? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem Draw a picture showing the forces on the mass. When the scale reads zero, what is the force on the mass due to the scale? What is the gravitational force on the mass? What is the force on the mass by the spring? How is the compression length related to the force by the spring and the spring constant? Check your units. ANSWER: Correct Problem 10.18 Part A How far must you stretch a spring with = 800 to store 180 of energy? Express your answer to two significant figures and include the appropriate units. ANSWER: y = 4.2 cm k N/m J Correct Problem 10.22 A 15 runaway grocery cart runs into a spring with spring constant 230 and compresses it by 57 . Part A What was the speed of the cart just before it hit the spring? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Spring Gun A spring-loaded toy gun is used to shoot a ball straight up in the air. The ball reaches a maximum height , measured from the equilibrium position of the spring. s = 0.67 m kg N/m cm v = 2.2 ms H Part A The same ball is shot straight up a second time from the same gun, but this time the spring is compressed only half as far before firing. How far up does the ball go this time? Neglect friction. Assume that the spring is ideal and that the distance by which the spring is compressed is negligible compared to . Hint 1. Potential energy of the spring The potential energy of a spring is proportional to the square of the distance the spring is compressed. The spring was compressed half the distance, so the mass, when launched, has one quarter of the energy as in the first trial. Hint 2. Potential energy of the ball At the highest point in the ball’s trajectory, all of the spring’s potential energy has been converted into gravitational potential energy of the ball. ANSWER: Correct A Bullet Is Fired into a Wooden Block A bullet of mass is fired horizontally with speed at a wooden block of mass resting on a frictionless table. The bullet hits the block and becomes completely embedded within it. After the bullet has come to rest within the block, the block, with the bullet in it, is traveling at speed . H height = H 4 mb vi mw vf Part A Which of the following best describes this collision? Hint 1. Types of collisions An inelastic collision is a collision in which kinetic energy is not conserved. In a partially inelastic collision, kinetic energy is lost, but the objects colliding do not stick together. From this information, you can infer what completely inelastic and elastic collisions are. ANSWER: Correct Part B Which of the following quantities, if any, are conserved during this collision? Hint 1. When is kinetic energy conserved? Kinetic energy is conserved only in perfectly elastic collisions. ANSWER: perfectly elastic partially inelastic perfectly inelastic Correct Part C What is the speed of the block/bullet system after the collision? Express your answer in terms of , , and . Hint 1. Find the momentum after the collision What is the total momentum of the block/bullet system after the collision? Express your answer in terms of and other given quantities. ANSWER: Hint 2. Use conservation of momentum The momentum of the block/bullet system is conserved. Therefore, the momentum before the collision is the same as the momentum after the collision. Find a second expression for , this time expressed as the total momentum of the system before the collision. Express your answer in terms of and other given quantities. ANSWER: kinetic energy only momentum only kinetic energy and momentum neither momentum nor kinetic energy vi mw mb ptotal vf ptotal = (mw + mb)vf ptotal vi ptotal = mbvi ANSWER: Correct Problem 10.31 Ball 1, with a mass of 150 and traveling at 15.0 , collides head on with ball 2, which has a mass of 340 and is initially at rest. Part A What are the final velocities of each ball if the collision is perfectly elastic? Express your answer with the appropriate units. ANSWER: Correct Part B Express your answer with the appropriate units. ANSWER: Correct Part C vf = mb vi mb+mw g m/s g (vfx) = -5.82 1 ms (vfx) = 9.18 2 ms What are the final velocities of each ball if the collision is perfectly inelastic? Express your answer with the appropriate units. ANSWER: Correct Part D Express your answer with the appropriate units. ANSWER: Correct Enhanced EOC: Problem 10.43 A package of mass is released from rest at a warehouse loading dock and slides down the = 2.2 – high, frictionless chute to a waiting truck. Unfortunately, the truck driver went on a break without having removed the previous package, of mass , from the bottom of the chute. You may want to review ( pages 265 – 269) . For help with math skills, you may want to review: Solving Algebraic Equations (vfx) = 4.59 1 ms (vfx) = 4.59 2 ms m h m 2m Part A Suppose the packages stick together. What is their common speed after the collision? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem There are two parts to this problem: the block sliding down the frictionless incline and the collision. What conservation laws are valid in each part? In terms of , what are the kinetic and potential energies of the block at the top of the incline? What is the potential energy of the same block at the bottom just before the collision? What are the kinetic energy and velocity of block just before the collision? What is conserved during the collision? What is the total momentum of the two blocks before the collision? What is the momentum of the two blocks stuck together after the collision? What is the velocity of the two blocks after the collision? ANSWER: Correct Part B Suppose the collision between the packages is perfectly elastic. To what height does the package of mass rebound? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem There are three parts to this problem: the block sliding down the incline, the collision, and mass going back up the incline. What conservation laws are valid in each part? m m v = 2.2 ms m m What is an elastic collision? For an elastic collision, how are the initial and final velocities related when one of the masses is initially at rest? Using the velocity of just before the collision from Part A, what is the velocity of just after the collision in this case? What are the kinetic and potential energies of mass just after the collision? What is the kinetic energy of mass at its maximum rebound height? Using conservation of energy, what is the potential energy of mass at its maximum height? What is the maximum height? ANSWER: Correct Problem 10.35 A cannon tilted up at a 35.0 angle fires a cannon ball at 79.0 from atop a 21.0 -high fortress wall. Part A What is the ball’s impact speed on the ground below? Express your answer with the appropriate units. ANSWER: Correct Problem 10.45 A 1000 safe is 2.5 above a heavy-duty spring when the rope holding the safe breaks. The safe hits the spring and compresses it 48 . m m m m m h = 24 cm $ m/s m vf = 81.6 ms kg m cm Part A What is the spring constant of the spring? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 10.49 A 100 block on a frictionless table is firmly attached to one end of a spring with = 21 . The other end of the spring is anchored to the wall. A 30 ball is thrown horizontally toward the block with a speed of 6.0 . Part A If the collision is perfectly elastic, what is the ball’s speed immediately after the collision? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the maximum compression of the spring? Express your answer to two significant figures and include the appropriate units. ANSWER: = 2.5×105 k Nm g k N/m g m/s v = 3.2 ms Correct Part C Repeat part A for the case of a perfectly inelastic collision. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part D Repeat part B for the case of a perfectly inelastic collision. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Score Summary: Your score on this assignment is 99.4%. You received 120.28 out of a possible total of 121 points. x = 0.19 m v = 1.4 ms x = 0.11 m

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## Assignment 6 Due: 11:59pm on Friday, March 7, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 7.7 A small car is pushing a large truck. They are speeding up. Part A Is the force of the truck on the car larger than, smaller than, or equal to the force of the car on the truck? ANSWER: Correct Conceptual Question 7.12 The figure shows two masses at rest. The string is massless and the pulley is frictionless. The spring scale reads in . Assume that = 4 . The force of the truck on the car is larger than the force of the car on the truck. The force of the truck on the car is equal to the force of the car on the truck. The force of the truck on the car is smaller than the force of the car on the truck. kg m kg Part A What is the reading of the scale? Express your answer to one significant figure and include the appropriate units. ANSWER: Correct Problem 7.1 A weightlifter stands up at constant speed from a squatting position while holding a heavy barbell across his shoulders. Part A Draw a free-body diagram for the barbells. Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded. ANSWER: m = 4 kg Correct Part B Draw a free-body diagram for the weight lifter. Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded. ANSWER: Correct Problem 7.6 Block A in the figure is sliding down the incline. The rope is massless, and the massless pulley turns on frictionless bearings, but the surface is not frictionless. The rope and the pulley are among the interacting objects, but you’ll have to decide if they’re part of the system. Part A Draw a free-body diagram for the block A. The orientation of your vectors will be graded. The exact length of your vectors will not be graded. ANSWER: Correct Part B Draw a free-body diagram for the block B. The orientation of your vectors will be graded. The exact length of your vectors will not be graded. ANSWER: Correct A Space Walk Part A An astronaut is taking a space walk near the shuttle when her safety tether breaks. What should the astronaut do to get back to the shuttle? Hint 1. How to approach the problem Newton’s 3rd law tells us that forces occur in pairs. Within each pair, the forces, often called action and reaction, have equal magnitude and opposite direction. Which of the actions suggested in the problem will result in the force pushing the astronaut back to the shuttle? ANSWER: Correct As the astronaut throws the tool away from the shuttle, she exerts a force in the direction away from the shuttle. Then, by Newton’s 3rd law, the tool will exert an opposite force on her. Thus, as she throws the tool, a force directed toward the shuttle will act on the astronaut. Newton’s 2nd law stipulates that the astronaut would acquire an acceleration toward the shuttle. Part B Assuming that the astronaut can throw any tool with the same force, what tool should be thrown to get back to the shuttle as quickly as possible? You should consider how much mass is left behind as the object is thrown as well as the mass of the object itself. Hint 1. How to approach the problem Recall that the force acting on the astronaut is equal in magnitude and opposite in direction to the force that she exerts on the tool. Hint 2. Newton’s 2nd law Newton’s 2nd law states that . If force is held constant, then acceleration is inversely proportional to mass. For example, when the same force is applied to objects of different mass, the object with the largest mass will experience the smallest acceleration. ANSWER: Attempt to “swim” toward the shuttle. Take slow steps toward the shuttle. Take a tool from her tool belt and throw it away from the shuttle. Take the portion of the safety tether still attached to her belt and throw it toward the shuttle. F = ma Correct The force that acts on the astronaut must equal in magnitude the force that she exerts on the tool. Therefore, if she exerts the same force on any tool, the force acting on her will be independent of the mass of the tool. However, the acceleration that the astronaut would acquire is inversely proportional to her mass since she is acted upon by a constant force. If she throws the tool with the largest mass, the remaining mass (the astronaut plus her remaining tools) would be smallest—and the acceleration the greatest! Part C If the astronaut throws the tool with a force of 16.0 , what is the magnitude of the acceleration of the astronaut during the throw? Assume that the total mass of the astronaut after she throws the tool is 80.0 . Express your answer in meters per second squared. Hint 1. Find the force acting on the astronaut What is the magnitude of the force acting on the astronaut as she throws the tool? Express your answer in newtons. ANSWER: Hint 2. Newton’s 2nd law An object of mass acted upon by a net force has an acceleration given by . ANSWER: The tool with the smallest mass. The tool with the largest mass. Any tool, since the mass of the tool would make no difference. N a kg F F = 16.0 N m F a F = ma a = 0.200 m/s2 Correct Problem 7.10 Blocks with masses of 2 , 4 , and 6 are lined up in a row on a frictionless table. All three are pushed forward by a 60 force applied to the 2 block. Part A How much force does the 4 block exert on the 6 block? Express your answer to one significant figure and include the appropriate units. ANSWER: Correct Part B How much force does the 4 block exert on the 2 block? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 7.9 A 1000 car pushes a 2100 truck that has a dead battery. When the driver steps on the accelerator, the drive wheels of the car push against the ground with a force of 4500 . Rolling friction can kg kg kg N kg kg kg F = 30 N kg kg F = 50 N kg kg N be neglected. Part A What is the magnitude of the force of the car on the truck? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the magnitude of the force of the truck on the car? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Atwood Machine Special Cases An Atwood machine consists of two blocks (of masses and ) tied together with a massless rope that passes over a fixed, perfect (massless and frictionless) pulley. In this problem you’ll investigate some special cases where physical variables describing the Atwood machine take on limiting values. Often, examining special cases will simplify a problem, so that the solution may be found from inspection or from the results of a problem you’ve already seen. For all parts of this problem, take upward to be the positive direction and take the gravitational constant, , to be positive. F = 3000 N F = 3000 N m1 m2 g Part A Consider the case where and are both nonzero, and . Let be the magnitude of the tension in the rope connected to the block of mass , and let be the magnitude of the tension in the rope connected to the block of mass . Which of the following statements is true? ANSWER: Correct Part B Now, consider the special case where the block of mass is not present. Find the magnitude, , of the tension in the rope. Try to do this without equations; instead, think about the physical consequences. Hint 1. How to approach the problem If the block of mass is not present, and the rope connecting the two blocks is massless, will the motion of the block of mass be any different from free fall? Hint 2. Which physical law to use Use Newton’s 2nd law on the block of mass . m1 m2 m2 > m1 T1 m1 T2 m2 is always equal to . is greater than by an amount independent of velocity. is greater than but the difference decreases as the blocks increase in velocity. There is not enough information to determine the relationship between and . T1 T2 T2 T1 T2 T1 T1 T2 m1 T m1 m2 m2 ANSWER: Correct Part C For the same special case (the block of mass not present), what is the acceleration of the block of mass ? Express your answer in terms of , and remember that an upward acceleration should be positive. ANSWER: Correct Part D Next, consider the special case where only the block of mass is present. Find the magnitude, , of the tension in the rope. ANSWER: Correct Part E For the same special case (the block of mass not present) what is the acceleration of the end of the rope where the block of mass would have been attached? Express your answer in terms of , and remember that an upward acceleration should be positive. T = 0 m1 m2 g a2 = -9.80 m1 T T = 0 m2 m2 g ANSWER: Correct Part F Next, consider the special case . What is the magnitude of the tension in the rope connecting the two blocks? Use the variable in your answer instead of or . ANSWER: Correct Part G For the same special case ( ), what is the acceleration of the block of mass ? ANSWER: Correct Part H Finally, suppose , while remains finite. What value does the the magnitude of the tension approach? Hint 1. Acceleration of block of mass a2 = 9.80 m1 = m2 = m m m1 m2 T = mg m1 = m2 = m m2 a2 = 0 m1 m2 m1 As becomes large, the finite tension will have a neglible effect on the acceleration, . If you ignore , you can pretend the rope is gone without changing your results for . As , what value does approach? ANSWER: Hint 2. Acceleration of block of mass As , what value will the acceleration of the block of mass approach? ANSWER: Hint 3. Net force on block of mass What is the magnitude of the net force on the block of mass . Express your answer in terms of , , , and any other given quantities. Take the upward direction to be positive. ANSWER: ANSWER: Correct Imagining what would happen if one or more of the variables approached infinity is often a good way to investigate the behavior of a system. m1 T a1 T a1 m1 a1 a1 = -9.80 m2 m1 m2 a2 = 9.80 m2 Fnet m2 T m2 g Fnet = T − m2g T = 2m2g Problem 7.17 A 5.9 rope hangs from the ceiling. Part A What is the tension at the midpoint of the rope? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 7.23 The sled dog in figure drags sleds A and B across the snow. The coefficient of friction between the sleds and the snow is 0.10. Part A If the tension in rope 1 is 100 , what is the tension in rope 2? Express your answer to two significant figures and include the appropriate units. ANSWER: kg T = 29 N N T2 = 180 N Correct Enhanced EOC: Problem 7.31 Two packages at UPS start sliding down the ramp shown in the figure. Package A has a mass of 4.50 and a coefficient of kinetic friction of 0.200. Package B has a mass of 11.0 and a coefficient of kinetic friction of 0.150. You may want to review ( pages 177 – 181) . For help with math skills, you may want to review: Vector Components Part A How long does it take package A to reach the bottom? Express your answer with the appropriate units. Hint 1. How to approach the problem Start by drawing force identification diagrams for package A and package B separately. What are the four forces acting on each block? Which of the forces are related by Newton’s third law? Draw separate free-body diagrams for block A and for block B. What is a good coordinate system to use to describe the motion of the blocks down the ramp? Label your coordinate system on the free-body diagram. In your coordinate system, compute the x and y components of each force on block A. What are the x and y components of the net force on block A? What are the x and y components of the net force on block B? Given that the coefficient of friction of block A is greater than the coefficient of friction of block B, do you think the blocks will stay together as they slide down the ramp? Assuming that they do stay together, how is the acceleration of the two blocks related? (We can check this assumption later.) Using the components of the forces and Newton’s second law, what is the acceleration of the blocks? What is the initial velocity of the blocks? Given the initial velocity and the acceleration, 20 kg kg how long does it take block A to go the given distance? To check that the blocks do indeed stay together, solve for the force of block B on block A. If the force is directed toward the bottom of the ramp, then the blocks stay together. ANSWER: Correct Problem 7.33 The 1.0 kg block in the figure is tied to the wall with a rope. It sits on top of the 2.0 kg block. The lower block is pulled to the right with a tension force of 20 N. The coefficient of kinetic friction at both the lower and upper surfaces of the 2.0 kg block is = 0.420. 1.48 s μk Part A What is the tension in the rope holding the 1.0 kg block to the wall? Express your answer with the appropriate units. ANSWER: Correct Part B What is the acceleration of the 2.0 kg block? Express your answer with the appropriate units. ANSWER: Correct Problem 7.38 The 100 kg block in figure takes 5.60 to reach the floor after being released from rest. 4.12 N 1.77 m s2 s Part A What is the mass of the block on the left? Express your answer with the appropriate units. ANSWER: Correct Problem 7.41 Figure shows a block of mass m resting on a 20 slope. The block has coefficients of friction 0.82 and 0.51 with the surface. It is connected via a massless string over a massless, frictionless pulley to a hanging block of mass 2.0 . Part A What is the minimum mass that will stick and not slip? 98.7 kg kg m Express your answer to three significant figures and include the appropriate units. ANSWER: Correct If you need to use the rounded answer you submitted here in a subsequent part, instead use the full precision answer and only round as a final step before submitting an answer. Part B If this minimum mass is nudged ever so slightly, it will start being pulled up the incline. What acceleration will it have? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Problem 7.46 A house painter uses the chair and pulley arrangement of the figure to lift himself up the side of a house. The painter’s mass is 75 and the chair’s mass is 12 . m = 1.80 kg a = 1.35 m s2 kg kg Part A With what force must he pull down on the rope in order to accelerate upward at 0.22 ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Score Summary: Your score on this assignment is 98.6%. You received 104.5 out of a possible total of 106 points. m/s2 F = 440 N

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