Name Lesson 7. Homework Work and Energy Problem Solving Outcomes

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1 Physics 1 Name Lesson 7. Homework Work and Energy Problem Solving Outcomes Date 1. Define work. 2. Define energy. 3. Determine the work done by a constant force. Period 4. Determine the work done by a force exerted on or by a spring. 5. Determine he kinetic energy of a moving object. 6. Apply the work energy theorem to solve problems. 7. Determine gravitational potential energy and elastic potential energy. 8. Apply the Law of Conservation of energy to solve problems. Multiple Choice Practice Answer Question Question 1. Which of the following is true for a system consisting of a mass oscillating on the end of an ideal spring? a) The kinetic and potential energies are equal at all times. b) The kinetic and potential energies are both constant. c) The maximum potential energy is achieved when the mass passes through its equilibrium position. d) The maximum kinetic energy and maximum potential energy are equal, but occur at different times From the top of a high cliff, a ball is thrown horizontally with initial speed v 0. Which of the following graphs best represents the ball's kinetic energy K as a function of time t? 2. a) b) c) d) e) Use this diagram for questions 3-4. A block oscillates without friction on the end of a spring as shown above. The minimum and maximum lengths of the spring as it oscillates are, respectively, x min and x max The graphs below can represent quantities associated with the oscillation as functions of the length x of the spring. Which graph can represent the total mechanical energy of the block-spring system as a function of x? 3. a) c) e) 4. b) d) Which graph can represent the kinetic energy of the block as a function of x? a) A b) B c) C d) D e) E 1

2 5. The figure above shows a rough semicircular track whose ends are at a vertical height h. A block placed at point P at one end of the track is released from rest and slides past the bottom of the track. Which of the following is true of the height to which the block rises on the other side of the track? (A) It is equal to h/2π. (B) It is equal to h/4. (C) It is equal to h/2. (D) It is equal to h. (E) It is between zero and h; the exact height depends on how much energy is lost to friction. 6. A plane 5 meters in length is inclined at an angle of 37, as shown above. A block of weight 20 newtons is placed at the top of the plane and allowed to slide down. The work done on the block by the gravitational force during the 5-meter slide down the plane is most nearly (A) 20 J (C) 80 (E) 130 J (B) 60 J (D) A block of mass 3.0 kg is hung from a spring, causing it to stretch 12 cm at equilibrium, as shown above. The 3.0 kg block is then replaced by a 4.0 kg block, and the new block is released from the position shown above, at which the spring is unstretched. How far will the 4.0 kg block fall before its direction is reversed? (A) 9 cm (B) 18 cm (C) 24 cm (D) 32 cm (E) 48 cm What is the kinetic energy of the rock just before it hits the ground? 1 2 a) mυ 0 b) mgh 1 2 c) mυ 0 mgh d) mυ 0 + mgh e) mgh 1 mυ A rock of mass m is thrown horizontally off a building from a height h, as shown above. The speed of the rock as it leaves the thrower's hand at the edge of the building is υ 0. 2

3 9. A sphere of mass m 1, which is attached to a spring, is displaced downward from its equilibrium position as shown above left and released from rest. A sphere of mass m 2, which is suspended from a string of length l, is displaced to the right as shown above right and released from rest so that it swings as a simple pendulum with small amplitude. Assume that both spheres undergo simple harmonic motion. Which of the following is true for both spheres? a) The maximum kinetic energy is attained as the sphere passes through its equilibrium position. b) The maximum kinetic energy is attained as the sphere reaches its point of release. c) The minimum gravitational potential energy is attained as the sphere passes through its equilibrium position. d) The maximum gravitational potential energy is attained when the sphere reaches its point of release. e) The maximum total energy is attained only as the sphere passes through its equilibrium position. 10. An object of mass m is initially at rest and free to move without friction in any direction in the xy-plane. A constant net force of magnitude F directed in the +x direction acts on the object for 1 s. Immediately thereafter a constant net force of the same magnitude F directed in the +y direction acts on the object for 1 s. After this, no forces act on the object. Which of the following graphs best represents the kinetic energy K of the object as a function of time? a) b) c) d) e) Work is being done when a force A) of gravitational attraction acts on a person standing on the surface of the Earth B) is exerted by one team in a tug-of-war when there is no movement C) acts vertically on a cart that can only move horizontally D) is exerted while pulling a wagon up a hill A 2.2-kilogram mass is pulled by a 30.-newton force through a distance of 5.0 meters as shown in the diagram below. What amount of work is done? A) 330 J B) 150 J C) 11 J D) 66 J In the diagram below, 55 joules of work is needed to raise a 10.-newton weight 5.0 meters at a constant speed. How much work is done to overcome friction as the weight is raised? A) 50. J B) 5 J C) 5.5 J D) 11 J The diagram below represents a 20-newton force pulling an object up a hill at a constant rate of 2 meters per second. The work done by the force in pulling the object from A to B is A) 500 J B) 50 J C) 100 J D) 600 J 3

4 15. A 1.0-kilogram mass falls a distance of 0.50 meter causing a 2.0-kilogram mass to slide the same distance along a table top, as represented in the diagram below. How much work is done by the falling mass? A) 4.9 J B) 9.8 J C) 14.7 J D) 1.5 J Which graph best represents the relationship between potential energy (PE) and height above ground (h) for a freely falling object released from rest? a) b) c) d) If the velocity of an automobile is doubled, its kinetic energy A) decreases to one-half B) quadruples C) decreases to one-fourth D) doubles 18. A train of mass M on a frictionless track starts from rest at the top of a hill having height h 1, as shown in the diagram below. What is the kinetic energy of the train when it reaches the top of the next hill, having height h 2? A) Mg(h 2 -h 3 ) B) Mg(h 1 -h 2 ) C) 0 D) Mgh The diagram below represents a 20-newton force pulling an object up a hill at a constant rate of 2 meters per second. The kinetic energy of the moving object is A) 10 J B) 15 J C) 5 J D) 50 J 20. Questions 20 and 21 refer to the following: The graph below represents the velocity-time relationship for a 2.0-kilogram mass moving along a horizontal frictionless surface. The kinetic energy of the mass is greatest during interval A) BC B) DE C) CD D) AB Net work is not being done on the mass during interval A) EF B) CD C) DE D) AB A 10.-kilogram object and a 5.0-kilogram object are released simultaneously from a height of 50. meters above the ground. After falling freely for 2.0 seconds, the objects will have different A) displacements B) accelerations C) kinetic energies D) speeds 4

5 Which graph best represents the relationship between the kinetic energy (KE) of a moving object as a function of its velocity (v)? 23. A) B) C) D) 24. Questions 24 through 26 refer to the following: The diagram below represents a 2.0-kilogram mass placed on a frictionless track at point A and released from rest. Assume the gravitational potential energy of the system to be zero at point E. The gravitational potential energy of the system at point A is approximately A) 20. joules B) 80. joules C) 8.0 x 10 2 joules D) 7.0 x 10 2 joules Compared to the kinetic energy of the mass at point B, the kinetic energy of the mass at point E is A) 1\2 as great B) the same C) twice as great D) 4 times greater If the mass were released from rest at point B, its speed at point C would be A) 0 m/sec B) 10. m/sec C) 14 m/sec D) 0.50 m/sec 27. Questions 27 through 29 refer to the following: The diagram below represents a frictionless track. A 10- kilogram block starts from rest at point A and slides along the track. As the block moves from point A to point B, the total amount of gravitational potential energy changed to kinetic energy is approximately A) 5 J B) 500 J C) 20 J D) 50 J What is the approximate speed of the block at point B? A) 50 m/s B) 100 m/s C) 1 m/s D) 10 m/s What is the approximate kinetic energy of the block at point C? A) 200 J B) 300 J C) 20 J D) 500 J Spring A has a spring constant of 140 newtons per meter and spring B has a spring constant of 280 newtons per meter. Both springs are stretched the same distance. Compared to the potential energy stored in spring A, the potential energy stored in spring B is A) half as great B) twice as great C) four times as great D) the same Which graph best represents the relationship between the elongation of an ideal spring and the applied force? 31. A) B) C) D) Graphs A and B below represent the results of applying an increasing force to stretch a spring which did not exceed its elastic limit. The spring constant can be represented by the 32. A) reciprocal of the slope of graph B B) slope of graph A C) reciprocal of the slope of graph A D) slope of graph B 5

6 33. The graph below represents the relationship between the force applied to a spring and the elongation of the spring. What is the spring constant? A) 20. N/m B) 9.8 N/kg C) m/n D) 0.80 N m 34. A 20.-newton weight is attached to a spring, causing it to stretch, as shown in the diagram below. What is the spring constant of this spring? A) N/m B) 20. N/m C) 0.25 N/m D) 40. N/m 35. The speed of the pendulum bob when it is in position II is most nearly 36. 6

7 37. 7

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11 Free Response I. A 10-kilogram block is pushed along a rough horizontal surface by a constant horizontal force F as shown above. At time t = 0, the velocity v of the block is 6.0 meters per second in the same direction as the force. The coefficient of sliding friction is 0.2. Assume g = 10 m 2. a. Calculate the force F necessary to keep the velocity constant. The force is now changed to a larger constant value F'. The block accelerates so that its kinetic energy increases by 60 joules while it slides a distance of 4.0 meters. b. Calculate the force F'. c. Calculate the acceleration of the block. II. One end of a spring is attached to a solid wall while the other end just reaches to the edge of a horizontal, frictionless tabletop, which is a distance h above the floor. A block of mass M is placed against the end of the spring and pushed toward the wall until the spring has been compressed a distance X, as shown above. The block is released, follows the trajectory shown, and strikes the floor a horizontal distance D from the edge of the table. Air resistance is negligible. Determine expressions for the following quantities in terms of M, X, D, h, and g. Note that these symbols do not include the spring constant. a. The time elapsed from the instant the block leaves the table to the instant it strikes the floor b. The horizontal component of the velocity of the block just before it hits the floor c. The work done on the block by the spring d. The spring constant 11

12 III. A 0.20 kg object moves along a straight line. The net force acting on the object varies with the object's displacement as shown in the graph above. The object starts from rest at displacement x = 0 and time t = 0 and is displaced a distance of 20 m. Determine each of the following. a. The acceleration of the particle when its displacement x is 6 m. b. The time taken for the object to be displaced the first 12 m. c. The amount of work done by the net force in displacing the object the first 12 m. d. The speed of the object at displacement x = 12 m. e. The final speed of the object at displacement x = 20 m. IV. The diagram below shows a spring compressed by a force of 6.0 newtons from its rest position to its compressed position. (a) Calculate the spring constant for this spring. [Show all work.] (b) Calculate the calculated the work done compressing the spring. [Show all work.] (c) Calculate the Ue invested in the spring at a displacement of m [Show all work.] (d) A 0.5kg block is placed at the end of the compressed spring. The spring is released and pushes the block to the right. What is the velocity of the block when the spring reaches its rest position again? Assume no friction.[show all your work.] 12