It is advantageous for cells to be small because: a small cell size prevents a cell from weighing too much a small cell size occupies less space in nature where space is limited a small cell has a small volume relative to surface area, thereby increasing efficient transport a small cell has a small surface area relative to volume, thereby facilitating ion balance a small cell is better able to conserve energy than a larger cell.

It is advantageous for cells to be small because: a small cell size prevents a cell from weighing too much a small cell size occupies less space in nature where space is limited a small cell has a small volume relative to surface area, thereby increasing efficient transport a small cell has a small surface area relative to volume, thereby facilitating ion balance a small cell is better able to conserve energy than a larger cell.

It is advantageous for cells to be small because: a … Read More...
What evidence suggests that proteins are synthesized and modified in the rough ER as opposed to the smooth ER? Select one: ribosomes are associated with the surface of the rough ER. ribosomes are associated with the surface of the smooth ER. proteins can be found in the membrane of the rough ER but not the smooth ER. the smooth ER functions in the synthesis of phospholipids. smooth ER is continuous with rough ER.

What evidence suggests that proteins are synthesized and modified in the rough ER as opposed to the smooth ER? Select one: ribosomes are associated with the surface of the rough ER. ribosomes are associated with the surface of the smooth ER. proteins can be found in the membrane of the rough ER but not the smooth ER. the smooth ER functions in the synthesis of phospholipids. smooth ER is continuous with rough ER.

What evidence suggests that proteins are synthesized and modified in … Read More...
Assignment 9 Due: 11:59pm on Friday, April 11, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Problem 11.2 Part A Evaluate the dot product if and . Express your answer using two significant figures. ANSWER: Correct Part B Evaluate the dot product if and . Express your answer using two significant figures. ANSWER: Correct Problem 11.4  A B = 5 − 6 A i ^ j ^ = −9 − 5 B i ^ j ^ A  B  = -15  A B = −5 + 9 A i ^ j ^ = 5 + 6 B i ^ j ^ A  B  = 29 Part A What is the angle between vectors and if and ? Express your answer as an integer and include the appropriate units. ANSWER: Correct Part B What is the angle between vectors and if and ? Express your answer as an integer and include the appropriate units. ANSWER: Correct ± All Work and No Play Learning Goal: To be able to calculate work done by a constant force directed at different angles relative to displacement If an object undergoes displacement while being acted upon by a force (or several forces), it is said that work is being done on the object. If the object is moving in a straight line and the displacement and the force are known, the work done by the force can be calculated as , where is the work done by force on the object that undergoes displacement directed at angle relative to .  A B A = 2 + 5 ı ^  ^ B = −2 − 4 ı ^  ^  = 175  A B A = −6 + 2 ı ^  ^ B = − − 3 ı ^  ^  = 90 W =  = cos  F  s  F   s  W F  s  F  Note that depending on the value of , the work done can be positive, negative, or zero. In this problem, you will practice calculating work done on an object moving in a straight line. The first series of questions is related to the accompanying figure. Part A What can be said about the sign of the work done by the force ? ANSWER: Correct When , the cosine of is zero, and therefore the work done is zero. Part B cos  F  1 It is positive. It is negative. It is zero. There is not enough information to answer the question.  = 90  What can be said about the work done by force ? ANSWER: Correct When , is positive, and so the work done is positive. Part C The work done by force is ANSWER: Correct When , is negative, and so the work done is negative. Part D The work done by force is ANSWER: F  2 It is positive. It is negative. It is zero. 0 <  < 90 cos  F  3 positive negative zero 90 <  < 180 cos  F  4 Correct Part E The work done by force is ANSWER: Correct positive negative zero F  5 positive negative zero Part F The work done by force is ANSWER: Correct Part G The work done by force is ANSWER: Correct In the next series of questions, you will use the formula to calculate the work done by various forces on an object that moves 160 meters to the right. F  6 positive negative zero F  7 positive negative zero W =  = cos  F  s  F   s  Part H Find the work done by the 18-newton force. Use two significant figures in your answer. Express your answer in joules. ANSWER: Correct Part I Find the work done by the 30-newton force. Use two significant figures in your answer. Express your answer in joules. ANSWER: Correct Part J Find the work done by the 12-newton force. Use two significant figures in your answer. Express your answer in joules. W W = 2900 J W W = 4200 J W ANSWER: Correct Part K Find the work done by the 15-newton force. Use two significant figures in your answer. Express your answer in joules. ANSWER: Correct Introduction to Potential Energy Learning Goal: Understand that conservative forces can be removed from the work integral by incorporating them into a new form of energy called potential energy that must be added to the kinetic energy to get the total mechanical energy. The first part of this problem contains short-answer questions that review the work-energy theorem. In the second part we introduce the concept of potential energy. But for now, please answer in terms of the work-energy theorem. Work-Energy Theorem The work-energy theorem states , where is the work done by all forces that act on the object, and and are the initial and final kinetic energies, respectively. Part A The work-energy theorem states that a force acting on a particle as it moves over a ______ changes the ______ energy of the particle if the force has a component parallel to the motion. W = -1900 J W W = -1800 J Kf = Ki + Wall Wall Ki Kf Choose the best answer to fill in the blanks above: ANSWER: Correct It is important that the force have a component acting in the direction of motion. For example, if a ball is attached to a string and whirled in uniform circular motion, the string does apply a force to the ball, but since the string's force is always perpendicular to the motion it does no work and cannot change the kinetic energy of the ball. Part B To calculate the change in energy, you must know the force as a function of _______. The work done by the force causes the energy change. Choose the best answer to fill in the blank above: ANSWER: Correct Part C To illustrate the work-energy concept, consider the case of a stone falling from to under the influence of gravity. Using the work-energy concept, we say that work is done by the gravitational _____, resulting in an increase of the ______ energy of the stone. Choose the best answer to fill in the blanks above: distance / potential distance / kinetic vertical displacement / potential none of the above acceleration work distance potential energy xi xf ANSWER: Correct Potential Energy You should read about potential energy in your text before answering the following questions. Potential energy is a concept that builds on the work-energy theorem, enlarging the concept of energy in the most physically useful way. The key aspect that allows for potential energy is the existence of conservative forces, forces for which the work done on an object does not depend on the path of the object, only the initial and final positions of the object. The gravitational force is conservative; the frictional force is not. The change in potential energy is the negative of the work done by conservative forces. Hence considering the initial and final potential energies is equivalent to calculating the work done by the conservative forces. When potential energy is used, it replaces the work done by the associated conservative force. Then only the work due to nonconservative forces needs to be calculated. In summary, when using the concept of potential energy, only nonconservative forces contribute to the work, which now changes the total energy: , where and are the final and initial potential energies, and is the work due only to nonconservative forces. Now, we will revisit the falling stone example using the concept of potential energy. Part D Rather than ascribing the increased kinetic energy of the stone to the work of gravity, we now (when using potential energy rather than work-energy) say that the increased kinetic energy comes from the ______ of the _______ energy. Choose the best answer to fill in the blanks above: ANSWER: force / kinetic potential energy / potential force / potential potential energy / kinetic Kf + Uf = Ef = Wnc + Ei = Wnc + Ki + Ui Uf Ui Wnc Correct Part E This process happens in such a way that total mechanical energy, equal to the ______ of the kinetic and potential energies, is _______. Choose the best answer to fill in the blanks above: ANSWER: Correct Problem 11.7 Part A How much work is done by the force 2.2 6.6 on a particle that moves through displacement 3.9 Express your answer to two significant figures and include the appropriate units. ANSWER: work / potential force / kinetic change / potential sum / conserved sum / zero sum / not conserved difference / conserved F  = (− + i ^ ) N j ^ ! = r m i ^ Correct Part B How much work is done by the force 2.2 6.6 on a particle that moves through displacement 3.9 Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.10 A 1.8 book is lying on a 0.80- -high table. You pick it up and place it on a bookshelf 2.27 above the floor. Part A How much work does gravity do on the book? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B W = -8.6 J F  = (− + i ^ ) N j ^ ! = r m? j ^ W = 26 J kg m m Wg = -26 J How much work does your hand do on the book? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.12 The three ropes shown in the bird's-eye view of the figure are used to drag a crate 3.3 across the floor. Part A How much work is done by each of the three forces? Express your answers using two significant figures. Enter your answers numerically separated by commas. ANSWER: WH = 26 J m W1 , W2 , W3 = 1.9,1.2,-2.1 kJ Correct Enhanced EOC: Problem 11.16 A 1.2 particle moving along the x-axis experiences the force shown in the figure. The particle's velocity is 4.6 at . You may want to review ( pages 286 - 287) . For help with math skills, you may want to review: The Definite Integral Part A What is its velocity at ? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the work–kinetic energy theorem? What is the kinetic energy at ? How is the work done in going from to related to force shown in the graph? Using the work–kinetic energy theorem, what is the kinetic energy at ? What is the velocity at ? ANSWER: kg m/s x = 0m x = 2m x = 0 m x = 0 m x = 2 m x = 2 m x = 2 m Correct Part B What is its velocity at ? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the work–kinetic energy theorem? What is the kinetic energy at ? How is the work done in going from to related to force shown in the graph? Can the work be negative? Using the work–kinetic energy theorem, what is the kinetic energy at ? What is the velocity at ? ANSWER: Correct Work on a Sliding Block A block of weight sits on a frictionless inclined plane, which makes an angle with respect to the horizontal, as shown. A force of magnitude , applied parallel to the incline, pulls the block up the plane at constant speed. v = 6.2 ms x = 4m x = 0 m x = 0 m x = 4 m x = 4 m x = 4 m v = 4.6 ms w  F Part A The block moves a distance up the incline. The block does not stop after moving this distance but continues to move with constant speed. What is the total work done on the block by all forces? (Include only the work done after the block has started moving, not the work needed to start the block moving from rest.) Express your answer in terms of given quantities. Hint 1. What physical principle to use To find the total work done on the block, use the work-energy theorem: . Hint 2. Find the change in kinetic energy What is the change in the kinetic energy of the block, from the moment it starts moving until it has been pulled a distance ? Remember that the block is pulled at constant speed. Hint 1. Consider kinetic energy If the block's speed does not change, its kinetic energy cannot change. ANSWER: ANSWER: L Wtot Wtot = Kf − Ki L Kf − Ki = 0 Wtot = 0 Correct Part B What is , the work done on the block by the force of gravity as the block moves a distance up the incline? Express the work done by gravity in terms of the weight and any other quantities given in the problem introduction. Hint 1. Force diagram Hint 2. Force of gravity component What is the component of the force of gravity in the direction of the block's displacement (along the inclined plane)? Express your answer in terms of and . Hint 1. Relative direction of the force and the motion Remember that the force of gravity acts down the plane, whereas the block's displacement is directed up the plane. ANSWER: Wg L w w  ANSWER: Correct Part C What is , the work done on the block by the applied force as the block moves a distance up the incline? Express your answer in terms of and other given quantities. Hint 1. How to find the work done by a constant force Remember that the work done on an object by a particular force is the integral of the dot product of the force and the instantaneous displacement of the object, over the path followed by the object. In this case, since the force is constant and the path is a straight segment of length up the inclined plane, the dot product becomes simple multiplication. ANSWER: Correct Part D What is , the work done on the block by the normal force as the block moves a distance up the inclined plane? Express your answer in terms of given quantities. Hint 1. First step in computing the work Fg|| = −wsin() Wg = −wLsin() WF F L F L WF = FL Wnormal L The work done by the normal force is equal to the dot product of the force vector and the block's displacement vector. The normal force and the block's displacement vector are perpendicular. Therefore, what is their dot product? ANSWER: ANSWER: Correct Problem 11.20 A particle moving along the -axis has the potential energy , where is in . Part A What is the -component of the force on the particle at ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the -component of the force on the particle at ? Express your answer to two significant figures and include the appropriate units. N  L = 0 Wnormal = 0 y U = 3.2y3 J y m y y = 0 m Fy = 0 N y y = 1 m ANSWER: Correct Part C What is the -component of the force on the particle at ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.28 A cable with 25.0 of tension pulls straight up on a 1.08 block that is initially at rest. Part A What is the block's speed after being lifted 2.40 ? Solve this problem using work and energy. Express your answer with the appropriate units. ANSWER: Correct Fy = -9.6 N y y = 2 m Fy = -38 N N kg m vf = 8.00 ms Problem 11.29 Part A How much work does an elevator motor do to lift a 1500 elevator a height of 110 ? Express your answer with the appropriate units. ANSWER: Correct Part B How much power must the motor supply to do this in 50 at constant speed? Express your answer with the appropriate units. ANSWER: Correct Problem 11.32 How many energy is consumed by a 1.20 hair dryer used for 10.0 and a 11.0 night light left on for 16.0 ? Part A Hair dryer: Express your answer with the appropriate units. kg m Wext = 1.62×106 J s = 3.23×104 P W kW min W hr ANSWER: Correct Part B Night light: Express your answer with the appropriate units. ANSWER: Correct Problem 11.42 A 2500 elevator accelerates upward at 1.20 for 10.0 , starting from rest. Part A How much work does gravity do on the elevator? Express your answer with the appropriate units. ANSWER: Correct W = 7.20×105 J = 6.34×105 W J kg m/s2 m −2.45×105 J Part B How much work does the tension in the elevator cable do on the elevator? Express your answer with the appropriate units. ANSWER: Correct Part C Use the work-kinetic energy theorem to find the kinetic energy of the elevator as it reaches 10.0 . Express your answer with the appropriate units. ANSWER: Correct Part D What is the speed of the elevator as it reaches 10.0 ? Express your answer with the appropriate units. ANSWER: Correct 2.75×105 J m 3.00×104 J m 4.90 ms Problem 11.47 A horizontal spring with spring constant 130 is compressed 17 and used to launch a 2.4 box across a frictionless, horizontal surface. After the box travels some distance, the surface becomes rough. The coefficient of kinetic friction of the box on the surface is 0.15. Part A Use work and energy to find how far the box slides across the rough surface before stopping. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.49 Truck brakes can fail if they get too hot. In some mountainous areas, ramps of loose gravel are constructed to stop runaway trucks that have lost their brakes. The combination of a slight upward slope and a large coefficient of rolling friction as the truck tires sink into the gravel brings the truck safely to a halt. Suppose a gravel ramp slopes upward at 6.0 and the coefficient of rolling friction is 0.45. Part A Use work and energy to find the length of a ramp that will stop a 15,000 truck that enters the ramp at 30 . Express your answer to two significant figures and include the appropriate units. ANSWER: Correct N/m cm kg l = 53 cm kg m/s l = 83 m Problem 11.51 Use work and energy to find an expression for the speed of the block in the following figure just before it hits the floor. Part A Find an expression for the speed of the block if the coefficient of kinetic friction for the block on the table is . Express your answer in terms of the variables , , , , and free fall acceleration . ANSWER: Part B Find an expression for the speed of the block if the table is frictionless. Express your answer in terms of the variables , , , and free fall acceleration . ANSWER: μk M m h μk g v = M m h g Problem 11.57 The spring shown in the figure is compressed 60 and used to launch a 100 physics student. The track is frictionless until it starts up the incline. The student's coefficient of kinetic friction on the incline is 0.12 . Part A What is the student's speed just after losing contact with the spring? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How far up the incline does the student go? Express your answer to two significant figures and include the appropriate units. ANSWER: v = cm kg 30 v = 17 ms Correct Score Summary: Your score on this assignment is 93.6%. You received 112.37 out of a possible total of 120 points. !s = 41 m

Assignment 9 Due: 11:59pm on Friday, April 11, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Problem 11.2 Part A Evaluate the dot product if and . Express your answer using two significant figures. ANSWER: Correct Part B Evaluate the dot product if and . Express your answer using two significant figures. ANSWER: Correct Problem 11.4  A B = 5 − 6 A i ^ j ^ = −9 − 5 B i ^ j ^ A  B  = -15  A B = −5 + 9 A i ^ j ^ = 5 + 6 B i ^ j ^ A  B  = 29 Part A What is the angle between vectors and if and ? Express your answer as an integer and include the appropriate units. ANSWER: Correct Part B What is the angle between vectors and if and ? Express your answer as an integer and include the appropriate units. ANSWER: Correct ± All Work and No Play Learning Goal: To be able to calculate work done by a constant force directed at different angles relative to displacement If an object undergoes displacement while being acted upon by a force (or several forces), it is said that work is being done on the object. If the object is moving in a straight line and the displacement and the force are known, the work done by the force can be calculated as , where is the work done by force on the object that undergoes displacement directed at angle relative to .  A B A = 2 + 5 ı ^  ^ B = −2 − 4 ı ^  ^  = 175  A B A = −6 + 2 ı ^  ^ B = − − 3 ı ^  ^  = 90 W =  = cos  F  s  F   s  W F  s  F  Note that depending on the value of , the work done can be positive, negative, or zero. In this problem, you will practice calculating work done on an object moving in a straight line. The first series of questions is related to the accompanying figure. Part A What can be said about the sign of the work done by the force ? ANSWER: Correct When , the cosine of is zero, and therefore the work done is zero. Part B cos  F  1 It is positive. It is negative. It is zero. There is not enough information to answer the question.  = 90  What can be said about the work done by force ? ANSWER: Correct When , is positive, and so the work done is positive. Part C The work done by force is ANSWER: Correct When , is negative, and so the work done is negative. Part D The work done by force is ANSWER: F  2 It is positive. It is negative. It is zero. 0 <  < 90 cos  F  3 positive negative zero 90 <  < 180 cos  F  4 Correct Part E The work done by force is ANSWER: Correct positive negative zero F  5 positive negative zero Part F The work done by force is ANSWER: Correct Part G The work done by force is ANSWER: Correct In the next series of questions, you will use the formula to calculate the work done by various forces on an object that moves 160 meters to the right. F  6 positive negative zero F  7 positive negative zero W =  = cos  F  s  F   s  Part H Find the work done by the 18-newton force. Use two significant figures in your answer. Express your answer in joules. ANSWER: Correct Part I Find the work done by the 30-newton force. Use two significant figures in your answer. Express your answer in joules. ANSWER: Correct Part J Find the work done by the 12-newton force. Use two significant figures in your answer. Express your answer in joules. W W = 2900 J W W = 4200 J W ANSWER: Correct Part K Find the work done by the 15-newton force. Use two significant figures in your answer. Express your answer in joules. ANSWER: Correct Introduction to Potential Energy Learning Goal: Understand that conservative forces can be removed from the work integral by incorporating them into a new form of energy called potential energy that must be added to the kinetic energy to get the total mechanical energy. The first part of this problem contains short-answer questions that review the work-energy theorem. In the second part we introduce the concept of potential energy. But for now, please answer in terms of the work-energy theorem. Work-Energy Theorem The work-energy theorem states , where is the work done by all forces that act on the object, and and are the initial and final kinetic energies, respectively. Part A The work-energy theorem states that a force acting on a particle as it moves over a ______ changes the ______ energy of the particle if the force has a component parallel to the motion. W = -1900 J W W = -1800 J Kf = Ki + Wall Wall Ki Kf Choose the best answer to fill in the blanks above: ANSWER: Correct It is important that the force have a component acting in the direction of motion. For example, if a ball is attached to a string and whirled in uniform circular motion, the string does apply a force to the ball, but since the string's force is always perpendicular to the motion it does no work and cannot change the kinetic energy of the ball. Part B To calculate the change in energy, you must know the force as a function of _______. The work done by the force causes the energy change. Choose the best answer to fill in the blank above: ANSWER: Correct Part C To illustrate the work-energy concept, consider the case of a stone falling from to under the influence of gravity. Using the work-energy concept, we say that work is done by the gravitational _____, resulting in an increase of the ______ energy of the stone. Choose the best answer to fill in the blanks above: distance / potential distance / kinetic vertical displacement / potential none of the above acceleration work distance potential energy xi xf ANSWER: Correct Potential Energy You should read about potential energy in your text before answering the following questions. Potential energy is a concept that builds on the work-energy theorem, enlarging the concept of energy in the most physically useful way. The key aspect that allows for potential energy is the existence of conservative forces, forces for which the work done on an object does not depend on the path of the object, only the initial and final positions of the object. The gravitational force is conservative; the frictional force is not. The change in potential energy is the negative of the work done by conservative forces. Hence considering the initial and final potential energies is equivalent to calculating the work done by the conservative forces. When potential energy is used, it replaces the work done by the associated conservative force. Then only the work due to nonconservative forces needs to be calculated. In summary, when using the concept of potential energy, only nonconservative forces contribute to the work, which now changes the total energy: , where and are the final and initial potential energies, and is the work due only to nonconservative forces. Now, we will revisit the falling stone example using the concept of potential energy. Part D Rather than ascribing the increased kinetic energy of the stone to the work of gravity, we now (when using potential energy rather than work-energy) say that the increased kinetic energy comes from the ______ of the _______ energy. Choose the best answer to fill in the blanks above: ANSWER: force / kinetic potential energy / potential force / potential potential energy / kinetic Kf + Uf = Ef = Wnc + Ei = Wnc + Ki + Ui Uf Ui Wnc Correct Part E This process happens in such a way that total mechanical energy, equal to the ______ of the kinetic and potential energies, is _______. Choose the best answer to fill in the blanks above: ANSWER: Correct Problem 11.7 Part A How much work is done by the force 2.2 6.6 on a particle that moves through displacement 3.9 Express your answer to two significant figures and include the appropriate units. ANSWER: work / potential force / kinetic change / potential sum / conserved sum / zero sum / not conserved difference / conserved F  = (− + i ^ ) N j ^ ! = r m i ^ Correct Part B How much work is done by the force 2.2 6.6 on a particle that moves through displacement 3.9 Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.10 A 1.8 book is lying on a 0.80- -high table. You pick it up and place it on a bookshelf 2.27 above the floor. Part A How much work does gravity do on the book? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B W = -8.6 J F  = (− + i ^ ) N j ^ ! = r m? j ^ W = 26 J kg m m Wg = -26 J How much work does your hand do on the book? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.12 The three ropes shown in the bird's-eye view of the figure are used to drag a crate 3.3 across the floor. Part A How much work is done by each of the three forces? Express your answers using two significant figures. Enter your answers numerically separated by commas. ANSWER: WH = 26 J m W1 , W2 , W3 = 1.9,1.2,-2.1 kJ Correct Enhanced EOC: Problem 11.16 A 1.2 particle moving along the x-axis experiences the force shown in the figure. The particle's velocity is 4.6 at . You may want to review ( pages 286 - 287) . For help with math skills, you may want to review: The Definite Integral Part A What is its velocity at ? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the work–kinetic energy theorem? What is the kinetic energy at ? How is the work done in going from to related to force shown in the graph? Using the work–kinetic energy theorem, what is the kinetic energy at ? What is the velocity at ? ANSWER: kg m/s x = 0m x = 2m x = 0 m x = 0 m x = 2 m x = 2 m x = 2 m Correct Part B What is its velocity at ? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the work–kinetic energy theorem? What is the kinetic energy at ? How is the work done in going from to related to force shown in the graph? Can the work be negative? Using the work–kinetic energy theorem, what is the kinetic energy at ? What is the velocity at ? ANSWER: Correct Work on a Sliding Block A block of weight sits on a frictionless inclined plane, which makes an angle with respect to the horizontal, as shown. A force of magnitude , applied parallel to the incline, pulls the block up the plane at constant speed. v = 6.2 ms x = 4m x = 0 m x = 0 m x = 4 m x = 4 m x = 4 m v = 4.6 ms w  F Part A The block moves a distance up the incline. The block does not stop after moving this distance but continues to move with constant speed. What is the total work done on the block by all forces? (Include only the work done after the block has started moving, not the work needed to start the block moving from rest.) Express your answer in terms of given quantities. Hint 1. What physical principle to use To find the total work done on the block, use the work-energy theorem: . Hint 2. Find the change in kinetic energy What is the change in the kinetic energy of the block, from the moment it starts moving until it has been pulled a distance ? Remember that the block is pulled at constant speed. Hint 1. Consider kinetic energy If the block's speed does not change, its kinetic energy cannot change. ANSWER: ANSWER: L Wtot Wtot = Kf − Ki L Kf − Ki = 0 Wtot = 0 Correct Part B What is , the work done on the block by the force of gravity as the block moves a distance up the incline? Express the work done by gravity in terms of the weight and any other quantities given in the problem introduction. Hint 1. Force diagram Hint 2. Force of gravity component What is the component of the force of gravity in the direction of the block's displacement (along the inclined plane)? Express your answer in terms of and . Hint 1. Relative direction of the force and the motion Remember that the force of gravity acts down the plane, whereas the block's displacement is directed up the plane. ANSWER: Wg L w w  ANSWER: Correct Part C What is , the work done on the block by the applied force as the block moves a distance up the incline? Express your answer in terms of and other given quantities. Hint 1. How to find the work done by a constant force Remember that the work done on an object by a particular force is the integral of the dot product of the force and the instantaneous displacement of the object, over the path followed by the object. In this case, since the force is constant and the path is a straight segment of length up the inclined plane, the dot product becomes simple multiplication. ANSWER: Correct Part D What is , the work done on the block by the normal force as the block moves a distance up the inclined plane? Express your answer in terms of given quantities. Hint 1. First step in computing the work Fg|| = −wsin() Wg = −wLsin() WF F L F L WF = FL Wnormal L The work done by the normal force is equal to the dot product of the force vector and the block's displacement vector. The normal force and the block's displacement vector are perpendicular. Therefore, what is their dot product? ANSWER: ANSWER: Correct Problem 11.20 A particle moving along the -axis has the potential energy , where is in . Part A What is the -component of the force on the particle at ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the -component of the force on the particle at ? Express your answer to two significant figures and include the appropriate units. N  L = 0 Wnormal = 0 y U = 3.2y3 J y m y y = 0 m Fy = 0 N y y = 1 m ANSWER: Correct Part C What is the -component of the force on the particle at ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.28 A cable with 25.0 of tension pulls straight up on a 1.08 block that is initially at rest. Part A What is the block's speed after being lifted 2.40 ? Solve this problem using work and energy. Express your answer with the appropriate units. ANSWER: Correct Fy = -9.6 N y y = 2 m Fy = -38 N N kg m vf = 8.00 ms Problem 11.29 Part A How much work does an elevator motor do to lift a 1500 elevator a height of 110 ? Express your answer with the appropriate units. ANSWER: Correct Part B How much power must the motor supply to do this in 50 at constant speed? Express your answer with the appropriate units. ANSWER: Correct Problem 11.32 How many energy is consumed by a 1.20 hair dryer used for 10.0 and a 11.0 night light left on for 16.0 ? Part A Hair dryer: Express your answer with the appropriate units. kg m Wext = 1.62×106 J s = 3.23×104 P W kW min W hr ANSWER: Correct Part B Night light: Express your answer with the appropriate units. ANSWER: Correct Problem 11.42 A 2500 elevator accelerates upward at 1.20 for 10.0 , starting from rest. Part A How much work does gravity do on the elevator? Express your answer with the appropriate units. ANSWER: Correct W = 7.20×105 J = 6.34×105 W J kg m/s2 m −2.45×105 J Part B How much work does the tension in the elevator cable do on the elevator? Express your answer with the appropriate units. ANSWER: Correct Part C Use the work-kinetic energy theorem to find the kinetic energy of the elevator as it reaches 10.0 . Express your answer with the appropriate units. ANSWER: Correct Part D What is the speed of the elevator as it reaches 10.0 ? Express your answer with the appropriate units. ANSWER: Correct 2.75×105 J m 3.00×104 J m 4.90 ms Problem 11.47 A horizontal spring with spring constant 130 is compressed 17 and used to launch a 2.4 box across a frictionless, horizontal surface. After the box travels some distance, the surface becomes rough. The coefficient of kinetic friction of the box on the surface is 0.15. Part A Use work and energy to find how far the box slides across the rough surface before stopping. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.49 Truck brakes can fail if they get too hot. In some mountainous areas, ramps of loose gravel are constructed to stop runaway trucks that have lost their brakes. The combination of a slight upward slope and a large coefficient of rolling friction as the truck tires sink into the gravel brings the truck safely to a halt. Suppose a gravel ramp slopes upward at 6.0 and the coefficient of rolling friction is 0.45. Part A Use work and energy to find the length of a ramp that will stop a 15,000 truck that enters the ramp at 30 . Express your answer to two significant figures and include the appropriate units. ANSWER: Correct N/m cm kg l = 53 cm kg m/s l = 83 m Problem 11.51 Use work and energy to find an expression for the speed of the block in the following figure just before it hits the floor. Part A Find an expression for the speed of the block if the coefficient of kinetic friction for the block on the table is . Express your answer in terms of the variables , , , , and free fall acceleration . ANSWER: Part B Find an expression for the speed of the block if the table is frictionless. Express your answer in terms of the variables , , , and free fall acceleration . ANSWER: μk M m h μk g v = M m h g Problem 11.57 The spring shown in the figure is compressed 60 and used to launch a 100 physics student. The track is frictionless until it starts up the incline. The student's coefficient of kinetic friction on the incline is 0.12 . Part A What is the student's speed just after losing contact with the spring? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How far up the incline does the student go? Express your answer to two significant figures and include the appropriate units. ANSWER: v = cm kg 30 v = 17 ms Correct Score Summary: Your score on this assignment is 93.6%. You received 112.37 out of a possible total of 120 points. !s = 41 m

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Chapter 06 Homework Due: 11:59pm on Friday, May 23, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Concept Review: Species Interactions Can you identify the type of species interaction that each label describes? Part A Drag each description to the appropriate bin. ANSWER: Activity: Food Webs Click here to complete this activity. Then answer the questions. Part A In an ecosystem, phytoplankton are _____. ANSWER: Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 1 of 9 5/21/2014 8:01 PM Correct Autotrophs, such as phytoplankton, are producers. Part B An earthworm that feeds on the remains of plants and animals is acting as a _____. ANSWER: Correct The earthworm is feeding on the remains of dead organisms. Part C When a human eats a steak, the human is acting as a _____. ANSWER: Correct By feeding on a primary consumer, the human is acting as a secondary consumer. Part D A cow eating grass is an example of a _____. ANSWER: Correct By feeding on a producer, the cow is acting as a primary consumer. Part E primary consumers tertiary consumers detritivores producers secondary consumers tertiary consumer secondary consumer producer detritivore primary consumer primary consumer detritivore secondary consumer producer tertiary consumer detritivore producer tertiary consumer secondary consumer primary consumer Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 2 of 9 5/21/2014 8:01 PM A seal that just ate a clam is eaten by a shark. The shark is acting as a _____. ANSWER: Correct The shark that ate the seal that ate the clam that ate the algae is the tertiary consumer. Activity: Pyramids of Production Click here to complete this activity. Then answer the questions. Part A _____ are secondary consumers. ANSWER: Correct Secondary consumers are animals that eat other animals; thus, they are carnivores. Part B Approximately _____% of the energy at one trophic level is passed on to the next highest trophic level. ANSWER: Correct Approximately 5–10% of the energy at one trophic level is passed on to the next highest trophic level. producer primary consumer tertiary consumer secondary consumer detritivore Producers Herbivores Plants Cows Carnivores 0–5 5–10 10–15 15–20 90–100 Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 3 of 9 5/21/2014 8:01 PM Part C 10,000 kcal of producer could support approximately _____ kcal of tertiary consumer. ANSWER: Correct This is the number of kcal of tertiary consumer that could be supported. Activity: Primary Succession Click here to complete this activity. Then answer the question. Part A Which of these is a starting point for primary succession? ANSWER: Correct Such a surface lacks any life and is thus a starting point for primary succession. Part B The first colonizing organisms during primary succession tend to be: ANSWER: 1,000 100 10 1 0 a surface exposed by a retreating glacier abandoned farmland an abandoned city a neglected yard none of these is a starting point for primary succession small shrubs trees lichens and mosses herbs Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 4 of 9 5/21/2014 8:01 PM Correct After the glacier retreats, bare ground is eventually colonized by lichens and mosses. Part C Which one of the following is a general characteristic of plants that are early colonizers during primary succession? ANSWER: Correct After the glacier retreats, bare ground is eventually colonized by lichens and mosses, then by deciduous trees with wind-borne seeds. Concept Review: Secondary Succession Can you order the steps of secondary succession? Part A Order the labels in the flowchart to complete the model of secondary succession as observed in a deciduous forest of eastern North America. ANSWER: Current Events: In Yellowstone, Killing One Kind of Trout to Save Another (New York Times, 8/23/2011) Read this New York Times article and then answer the questions. In Yellowstone, Killing One Kind of Trout to Save Another (8/23/2011) Registration with The New York Times provides instant access to breaking news on NYTimes.com. To register, go to http://www.nytimes.com/register. Visit http://www.nytimes.com/content/help/rights/terms/terms-of-service.html to review the current NYT Terms of Service. Part A Which of the following would be the best discovery regarding the Judas fish? ANSWER: plants are able to fix their own nitrogen plants can outcompete other plants that invade the area plants have wind-dispersed seeds plants are shade-tolerant Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 5 of 9 5/21/2014 8:01 PM Part B Which of the following is true? ANSWER: Part C Why is protecting cutthroat trout in Yellowstone so important? ANSWER: Part D Which of the following is true? ANSWER: Part E Why don’t bears in Yellowstone eat lake trout? ANSWER: Part F How did rainbow trout become established worldwide? ANSWER: Learning where lake trout feed. Learning where lake trout hibernate. Learning where lake trout spawn. Learning where lake trout migrate to during fall. Officials are working only in certain areas to eliminate lake trout. Officials are working to eliminate lake trout throughout Wyoming. Officials are working to eliminate lake trout throughout the Great Lakes. All states in the U.S. are working to eliminate lake trout. Because many other species depend on cutthroat trout. Because local people depend on cutthroat trout for food. Because Yellowstone is the only place cutthroat trout are found. Because cutthroat trout are listed as a threatened species. Cutthroat trout are to Yellowstone Lake as rainbow trout are to Yellowstone Lake. Cutthroat trout are to Yellowstone Lake as Asian carp are to the Great Lakes. Lake trout are to Yellowstone Lake as see lamprey are to the Great Lakes. Lake trout are to the Great Lakes as Asian carp are to the Yellowstone Lake. They don’t like the taste. They cannot find them. Lake trout skin is too tough. Lake trout are too small for bears to be interested. Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 6 of 9 5/21/2014 8:01 PM Current Events: In Thailand, Love of Food Carries Deadly Risks (New York Times, 4/25/2011) Read this New York Times article and then answer the questions. In Thailand, Love of Food Carries Deadly Risks (4/25/2011) Registration with The New York Times provides instant access to breaking news on NYTimes.com. To register, go to http://www.nytimes.com/register. Visit http://www.nytimes.com/content/help/rights/terms/terms-of-service.html to review the current NYT Terms of Service. Part A Rather than stop eating fish, what should Thai people do to eliminate the risk of liver fluke infection? ANSWER: Part B Liver flukes are transmitted through which of the following? ANSWER: Part C Getting rid of which of the following would help decrease the population of liver flukes? ANSWER: Part D Pla som is a unique dish because it is what? ANSWER: Part E Due to warming oceans caused by climate change. Natural process of migration. Accidental introduction via ships. Purposeful stocking. Consume ethyl alcohol while eating fish. Add more garlic. Cook it thoroughly. Pick the flukes out by hand. urine saliva feces blood rats mosquitoes frogs snails pickled frozen fermented blanched Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 7 of 9 5/21/2014 8:01 PM You have liver flukes. What are your chances of getting liver cancer? ANSWER: Part F You are a scientist studying liver flukes in Thailand. Where should you look for them? ANSWER: ABC News Video: The Cuttlefish Watch the ABC News video (2:20 minutes). Then answer the questions below. Part A The changes to the cuttlefish’s skin are related to _______. ANSWER: Correct Part B Camouflage contributes to the cuttlefish’s survival by enabling it to _______. 1-5% 5-10% 10-15% 15-20% The northwestern part of the country. The southeastern part of the country. The southwestern part of the country. The northeastern part of the country. camouflage elimination of waste reproductive strategies feeding behavior Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 8 of 9 5/21/2014 8:01 PM ANSWER: Correct Part C Cuttlefish placed in a sandy environment with white rocks will camouflage their skin in a pattern called _______. ANSWER: Correct Part D In the presence of a black-and-white striped background, a cuttlefish was observed to _______. ANSWER: Correct Part E Which question was raised but not answered in the video? ANSWER: Correct Score Summary: Your score on this assignment is 48.5%. You received 16 out of a possible total of 33 points. sneak up on prey mimic poisonous species hide from predators warn potential predators that it is poisonous universal camouflage disruptive camouflage warning coloration camouflage tide-pool camouflage move its arm to match the orientation of the stripes turn completely white and hide in the white stripe turn completely black and hide in the black stripe exhibit the exact striping pattern of its surroundings Why does the cuttlefish change its skin pattern? What happens when a cuttlefish is placed in an unnatural environment? Is the cuttlefish able to grow a protective shell? How do cuttlefish camouflage themselves even though they are colorblind? Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 9 of 9 5/21/2014 8:01 PM

Chapter 06 Homework Due: 11:59pm on Friday, May 23, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Concept Review: Species Interactions Can you identify the type of species interaction that each label describes? Part A Drag each description to the appropriate bin. ANSWER: Activity: Food Webs Click here to complete this activity. Then answer the questions. Part A In an ecosystem, phytoplankton are _____. ANSWER: Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 1 of 9 5/21/2014 8:01 PM Correct Autotrophs, such as phytoplankton, are producers. Part B An earthworm that feeds on the remains of plants and animals is acting as a _____. ANSWER: Correct The earthworm is feeding on the remains of dead organisms. Part C When a human eats a steak, the human is acting as a _____. ANSWER: Correct By feeding on a primary consumer, the human is acting as a secondary consumer. Part D A cow eating grass is an example of a _____. ANSWER: Correct By feeding on a producer, the cow is acting as a primary consumer. Part E primary consumers tertiary consumers detritivores producers secondary consumers tertiary consumer secondary consumer producer detritivore primary consumer primary consumer detritivore secondary consumer producer tertiary consumer detritivore producer tertiary consumer secondary consumer primary consumer Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 2 of 9 5/21/2014 8:01 PM A seal that just ate a clam is eaten by a shark. The shark is acting as a _____. ANSWER: Correct The shark that ate the seal that ate the clam that ate the algae is the tertiary consumer. Activity: Pyramids of Production Click here to complete this activity. Then answer the questions. Part A _____ are secondary consumers. ANSWER: Correct Secondary consumers are animals that eat other animals; thus, they are carnivores. Part B Approximately _____% of the energy at one trophic level is passed on to the next highest trophic level. ANSWER: Correct Approximately 5–10% of the energy at one trophic level is passed on to the next highest trophic level. producer primary consumer tertiary consumer secondary consumer detritivore Producers Herbivores Plants Cows Carnivores 0–5 5–10 10–15 15–20 90–100 Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 3 of 9 5/21/2014 8:01 PM Part C 10,000 kcal of producer could support approximately _____ kcal of tertiary consumer. ANSWER: Correct This is the number of kcal of tertiary consumer that could be supported. Activity: Primary Succession Click here to complete this activity. Then answer the question. Part A Which of these is a starting point for primary succession? ANSWER: Correct Such a surface lacks any life and is thus a starting point for primary succession. Part B The first colonizing organisms during primary succession tend to be: ANSWER: 1,000 100 10 1 0 a surface exposed by a retreating glacier abandoned farmland an abandoned city a neglected yard none of these is a starting point for primary succession small shrubs trees lichens and mosses herbs Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 4 of 9 5/21/2014 8:01 PM Correct After the glacier retreats, bare ground is eventually colonized by lichens and mosses. Part C Which one of the following is a general characteristic of plants that are early colonizers during primary succession? ANSWER: Correct After the glacier retreats, bare ground is eventually colonized by lichens and mosses, then by deciduous trees with wind-borne seeds. Concept Review: Secondary Succession Can you order the steps of secondary succession? Part A Order the labels in the flowchart to complete the model of secondary succession as observed in a deciduous forest of eastern North America. ANSWER: Current Events: In Yellowstone, Killing One Kind of Trout to Save Another (New York Times, 8/23/2011) Read this New York Times article and then answer the questions. In Yellowstone, Killing One Kind of Trout to Save Another (8/23/2011) Registration with The New York Times provides instant access to breaking news on NYTimes.com. To register, go to http://www.nytimes.com/register. Visit http://www.nytimes.com/content/help/rights/terms/terms-of-service.html to review the current NYT Terms of Service. Part A Which of the following would be the best discovery regarding the Judas fish? ANSWER: plants are able to fix their own nitrogen plants can outcompete other plants that invade the area plants have wind-dispersed seeds plants are shade-tolerant Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 5 of 9 5/21/2014 8:01 PM Part B Which of the following is true? ANSWER: Part C Why is protecting cutthroat trout in Yellowstone so important? ANSWER: Part D Which of the following is true? ANSWER: Part E Why don’t bears in Yellowstone eat lake trout? ANSWER: Part F How did rainbow trout become established worldwide? ANSWER: Learning where lake trout feed. Learning where lake trout hibernate. Learning where lake trout spawn. Learning where lake trout migrate to during fall. Officials are working only in certain areas to eliminate lake trout. Officials are working to eliminate lake trout throughout Wyoming. Officials are working to eliminate lake trout throughout the Great Lakes. All states in the U.S. are working to eliminate lake trout. Because many other species depend on cutthroat trout. Because local people depend on cutthroat trout for food. Because Yellowstone is the only place cutthroat trout are found. Because cutthroat trout are listed as a threatened species. Cutthroat trout are to Yellowstone Lake as rainbow trout are to Yellowstone Lake. Cutthroat trout are to Yellowstone Lake as Asian carp are to the Great Lakes. Lake trout are to Yellowstone Lake as see lamprey are to the Great Lakes. Lake trout are to the Great Lakes as Asian carp are to the Yellowstone Lake. They don’t like the taste. They cannot find them. Lake trout skin is too tough. Lake trout are too small for bears to be interested. Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 6 of 9 5/21/2014 8:01 PM Current Events: In Thailand, Love of Food Carries Deadly Risks (New York Times, 4/25/2011) Read this New York Times article and then answer the questions. In Thailand, Love of Food Carries Deadly Risks (4/25/2011) Registration with The New York Times provides instant access to breaking news on NYTimes.com. To register, go to http://www.nytimes.com/register. Visit http://www.nytimes.com/content/help/rights/terms/terms-of-service.html to review the current NYT Terms of Service. Part A Rather than stop eating fish, what should Thai people do to eliminate the risk of liver fluke infection? ANSWER: Part B Liver flukes are transmitted through which of the following? ANSWER: Part C Getting rid of which of the following would help decrease the population of liver flukes? ANSWER: Part D Pla som is a unique dish because it is what? ANSWER: Part E Due to warming oceans caused by climate change. Natural process of migration. Accidental introduction via ships. Purposeful stocking. Consume ethyl alcohol while eating fish. Add more garlic. Cook it thoroughly. Pick the flukes out by hand. urine saliva feces blood rats mosquitoes frogs snails pickled frozen fermented blanched Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 7 of 9 5/21/2014 8:01 PM You have liver flukes. What are your chances of getting liver cancer? ANSWER: Part F You are a scientist studying liver flukes in Thailand. Where should you look for them? ANSWER: ABC News Video: The Cuttlefish Watch the ABC News video (2:20 minutes). Then answer the questions below. Part A The changes to the cuttlefish’s skin are related to _______. ANSWER: Correct Part B Camouflage contributes to the cuttlefish’s survival by enabling it to _______. 1-5% 5-10% 10-15% 15-20% The northwestern part of the country. The southeastern part of the country. The southwestern part of the country. The northeastern part of the country. camouflage elimination of waste reproductive strategies feeding behavior Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 8 of 9 5/21/2014 8:01 PM ANSWER: Correct Part C Cuttlefish placed in a sandy environment with white rocks will camouflage their skin in a pattern called _______. ANSWER: Correct Part D In the presence of a black-and-white striped background, a cuttlefish was observed to _______. ANSWER: Correct Part E Which question was raised but not answered in the video? ANSWER: Correct Score Summary: Your score on this assignment is 48.5%. You received 16 out of a possible total of 33 points. sneak up on prey mimic poisonous species hide from predators warn potential predators that it is poisonous universal camouflage disruptive camouflage warning coloration camouflage tide-pool camouflage move its arm to match the orientation of the stripes turn completely white and hide in the white stripe turn completely black and hide in the black stripe exhibit the exact striping pattern of its surroundings Why does the cuttlefish change its skin pattern? What happens when a cuttlefish is placed in an unnatural environment? Is the cuttlefish able to grow a protective shell? How do cuttlefish camouflage themselves even though they are colorblind? Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 9 of 9 5/21/2014 8:01 PM

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Derive an expression for the capillary-height change h for a fluid of surface tension Y and contact angle between two paraller plates W apart Evaluate h for water at 20c if W=0.5mm

Derive an expression for the capillary-height change h for a fluid of surface tension Y and contact angle between two paraller plates W apart Evaluate h for water at 20c if W=0.5mm

EGR 3323 HW2 1) For points P(1, -2, 1) , Q(0, -2, 5) and R(4, -6, 7) , a) Find the vector v from point P to point Q? b) Find the vector k from R to P? c) Calculate the dot product of v and k. d) Calculate the cross product of v and k. e) The projection of v on k. f) The angle between v and k. For question 1, Write a MATLAB program to verify your answers. Submit the output displayed.(Use matlab functions such as dot, cross, norm, acos) 2) Solar panels have to be installed carefully so that the tilt of the roof and direction to the sun rays should maximize the power absorbed from the sun. P2 P1 P3 P4 Here are the coordinates of the corners of the roof at the picture P1(8,6,4) , P2(8,10,4), P3(6,8,8) and P4(6,4,8). Determine the following for this roof. a) What are the edge vectors that define the roof surface? Write them in component form. b) What is the unit vector (p) perpendicular to these edge vectors of the roof surface? c) If the flow of solar energy is in s=[4 -3 2] direction with magnitude of 1000 watts/meter2, calculate the dot product of E=1000us and p. (where us is the unit vector of s). d) Calculate the angle between s and p. What do you say about this angle for maximum solar energy? 3) Find the unit vector perpendicular to the plane -3x + 7y – 2z = 8. 4) A wheel is rotating about x-axis with angular speed w=20sec-1 (you can take this quantity as it is, no need to transform to rads/sec, the units for this angular speed is revolutions/secs) The rotation is clockwise if one sits at the origin and looks at this wheel in the positive x direction. Find the velocity and speed at point [4 3 0]. Make a sketch. 5) Two forces of equal magnitude are applied to the wrench. If a moment of 50N-m is required to loosen the nut and determine the Force vectors.

EGR 3323 HW2 1) For points P(1, -2, 1) , Q(0, -2, 5) and R(4, -6, 7) , a) Find the vector v from point P to point Q? b) Find the vector k from R to P? c) Calculate the dot product of v and k. d) Calculate the cross product of v and k. e) The projection of v on k. f) The angle between v and k. For question 1, Write a MATLAB program to verify your answers. Submit the output displayed.(Use matlab functions such as dot, cross, norm, acos) 2) Solar panels have to be installed carefully so that the tilt of the roof and direction to the sun rays should maximize the power absorbed from the sun. P2 P1 P3 P4 Here are the coordinates of the corners of the roof at the picture P1(8,6,4) , P2(8,10,4), P3(6,8,8) and P4(6,4,8). Determine the following for this roof. a) What are the edge vectors that define the roof surface? Write them in component form. b) What is the unit vector (p) perpendicular to these edge vectors of the roof surface? c) If the flow of solar energy is in s=[4 -3 2] direction with magnitude of 1000 watts/meter2, calculate the dot product of E=1000us and p. (where us is the unit vector of s). d) Calculate the angle between s and p. What do you say about this angle for maximum solar energy? 3) Find the unit vector perpendicular to the plane -3x + 7y – 2z = 8. 4) A wheel is rotating about x-axis with angular speed w=20sec-1 (you can take this quantity as it is, no need to transform to rads/sec, the units for this angular speed is revolutions/secs) The rotation is clockwise if one sits at the origin and looks at this wheel in the positive x direction. Find the velocity and speed at point [4 3 0]. Make a sketch. 5) Two forces of equal magnitude are applied to the wrench. If a moment of 50N-m is required to loosen the nut and determine the Force vectors.

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