Chapter 10 Energy and Work 10.1 Quantitative 1) A child does 350 J of work while pulling a box from the ground up to his tree house with a rope. The tree house is 4.8 m above the ground. What is the mass of the box? Karl William Parrott A) 7.4 kg B) 4.4 kg C) 5.6 kg D) 6.7 kg 2) You carry a 7.0 kg bag of groceries 1.2 m above the ground at constant velocity across a 2.2 m room. How much work do you do on the bag in the process? A) 0.0 J B) 82 J C) 151 J D) 128 J 3) A crane lifts a 425 kg steel beam vertically upward a distance of 31 m. How much work does the crane do on the beam if the beam accelerates upward at 1.8 m/s 2? Neglect frictional forces. A) B) C) D) 5 1.5 10 J 5 0.9 10 J 5 1.0 10 J 5 1.3 10 J 1
4) A traveler pulls on a suitcase strap at an angle 36 above the horizontal. If 408 J of work are done by the strap while moving the suitcase a horizontal distance of 15 m, what is the tension in the strap? A) 34 N B) 28 N C) 38 N D) 41 N 5) A car drives 5.0 km north, then 7.3 km east, then 7.9 km northeast, all at a constant velocity. If 6 the car had to perform 2.6 10 J of work during this trip, what was the magnitude of the average frictional force on the car? A) B) C) 2 1.3 2 1.8 2 2.4 2 D) 2.8 6) You do 138 J of work while pulling your sister back on a swing, whose chain is 5.10 m long, until the swing makes an angle of 32.0 with the vertical. What is your sister s mass? A) 18.2 kg B) 15.5 kg C) 20.9 kg D) 22.6 kg 7) Find the net work done by friction between the ground and the body of a snake slithering in a complete circle of 2.23 m radius. The coefficient of friction between the ground and the snake is 0.23, and the snake s weight is 70.0 N. Karl William Parrott A) 250 J B) 0 J C) 2400 J D) 490 J 2
8) Calculate the kinetic energy of a 0.300 kg baseball thrown at a velocity of 28 m/s. A) 120 J B) 240 J C) 180 J D) 210 J 9 5 9) 4.00 10 J of work are done on a 1228 kg car while it accelerates from 10.0 m/s to some final velocity. Find this final velocity. A) 27.4 m/s B) 21.9 m/s C) 24.7 m/s D) 30.1 m/s 10) A 1000.0 kg car experiences a net force of 9500 N while decelerating from 30.0 m/s to 18.4 m/s. How far does it travel while slowing down? A) 30 m B) 27 m C) 32 m D) 35 m 11) A helicopter descends vertically to land with a speed of 8.0 m/s. If the shock absorbers have an initial length of 0.50 m, they compress to 87% of their original length and the air in the tires absorbs 13% of the initial energy as heat, what is the ratio of the spring constant to the helicopter s mass? Assume one landing gear in the craft. Karl William Parrott A) 13 Kn/kg-m B) 13 N/kg-m C) 13 N/kg-m D) 1.3 kn/kg-m 3
12) The frame of a cart has a mass of 30 kg, and the cart rolls on four railroad car wheels, each with a mass of 25 kg. The cart is being ridden at a speed of 5.0 m/s by a 75 kg man. What is its total kinetic energy? (Model the railroad car wheels as solid uniform disks of radius 20 cm.) A) 1900 J B) 1500 J C) 620 J D) 1300 J 13) A spring stretches by 21.0 cm when a 135 N object is attached. What is the weight of a fish that would stretch the spring by 66.8 cm? A) 429 N B) 42 N C) 236 N D) 601 N 14) A prankster drops a water balloon from the top of a building on an unsuspecting person on the sidewalk below. If the balloon is traveling at 32.1 m/s when it strikes a person s head (1.5 m above the ground), how tall is the building? Neglect air resistance. A) 54 m B) 53 m C) 56 m D) 57 m 15) An airplane is observed to be 5.33 km from its takeoff point, at a horizontal distance of 4.90 km. What is the gravitational potential energy of the plane with respect to the ground? The plane s mass is 22.0 metric tons. Karl William Parrott A) 454 MJ B) 1060 MJ C) 1060 J D) 452 J 4
16) A massless spring hangs from the ceiling. How much does its potential energy increase, if a 40.5-kg mass is attached to it? The spring constant is 2700 N/m. A) 29 J B) 29 kj C) 58 kj D) 58 J 17) A horizontal spring-mass system oscillates on a frictionless table. If the ratio of the mass to the spring constant is 0.077 kg m/n, and the maximum speed of the mass was measured to be 11.49 m/s, find the maximum extension of the spring. A) 3.2 m B) 3.2 cm C) 0.88 cm D) 88 cm 18) A block slides down a frictionless inclined ramp. If the ramp angle is 21.0 and the length of it is 27.0 m, find the speed of the block as it reaches the end of the ramp, assuming it stated sliding from rest at the top. A) 13.8 m/s B) 190 m/s C) 9.76 m/s D) 22.4 m/s 19) A block starts from rest at the top of a 13.0 inclined plane and encounters a spring, of constant 4.5 kn/m, rigidly attached to the plane. If the block s mass is 64.0 kg and it compresses the spring by 60.0 cm, find the distance the block traveled before it encountered the spring. Karl William Parrott A) 5.1 m B) 561 cm C) 320 m D) 129.9 cm 5
20) A tennis ball bounces on the floor three times. If each time it loses 21.0% of its energy due to heating, how high does it bounce after the third time, provided we released it 4.6 m from the floor? A) 230 cm B) 23 cm C) 230 mm D) 290 cm 21) A 6.7 kg object moving at 7.3 m/s collides inelastically with a 4.0 kg object which is initially at rest. What percentage of the initial kinetic energy of the system is lost during the collision? A) 37% B) 43% C) 33% D) 30% 22) Two pendulums of equal length l = 0.45 m are suspended from the same point. The pendulum bobs are steel spheres. The first bob is drawn back to make a 35 angle with the vertical. If the first bob has mass 0.25 kg and the second has mass 0.75 kg, how high will the second bob rise above its initial position when struck elastically by the first bob after it is released? A) 2.0 cm B) 1.7 cm C) 2.3 cm D) 2.7 cm 23) A child pulls on a wagon with a force of 75 N. If the wagon moves a total of 42 m in 1.7 min, what is the average power generated by the child, in watts? A) 31 W B) 38 W C) 41 W D) 47 W Var: 29 6
24) A car needs to generate 75.0 hp in order to maintain a constant velocity of 29.0 m/s on a flat road. What is the magnitude of the total resistive force acting on the car (due to friction, air resistance, etc.)? Karl William Parrott check A) 3 1.93 B) 2.59 N C) 3 0.97 3 D) 2.70 25) Calculate the average power output necessary for a 85.0 kg person to run up a 12.0 m long hillside, which is inclined at 25.0 above the horizontal, in 3.00 s. Express your answer in horsepower. A) 1.89 hp B) 4.46 hp C) 2.84 hp D) 1.13 hp 10.2 True/False 1) As a stone slides down a frictionless ice-covered hill, its mechanical energy is conserved but its momentum is not conserved. Answer: TRUE 2) Two cars collide, lock bumpers and eventually slide to a stop due to friction with the roadway. During this entire process, mechanical energy and momentum are both conserved. Answer: FALSE 3) Kinetic energy is conserved only in perfectly elastic collisions, but momentum is conserved in all collisions. Answer: TRUE 4) When a moving object hits a stationary object and causes it to move, some of the moving object s kinetic energy is transformed into momentum in the object that was at rest. Answer: FALSE 7
5) If a force acts perpendicular to an object s direction of motion, that force cannot change the object s kinetic energy or momentum. Karl William Parrott check Answer: FALSE 6) A 2.0 kg stone slides from rest down a hill 5.0 m high and is observed to be moving at 6.0 m/s at the bottom. During this process, 62 J of thermal energy have been produced. Answer: TRUE 7) A 3.5 kg mass is pressed against a spring of spring constant 90.0 N/m, compressing it 25.0 cm. The greatest amount of kinetic energy this mass could gain after it is released is 2.81 J. Answer: TRUE 10.3 Conceptual 1) Describe the energy transfers that take place as you use a slingshot to shoot a rock into the air, it rises to a peak, then falls, and finally hits the ground and stops without bouncing. Answer: Chemical energy in your muscles is transformed into elastic potential energy as you stretch the slingshot; the elastic potential energy changes to kinetic energy of the rock as the sling is released; the rock s kinetic energy gradually changes to gravitational potential energy as it rises and stops at its peak; the gravitational potential energy is transformed back into kinetic energy as the rock falls; the rock s kinetic energy changes to heat in the ground and the rock itself, once the rock hits the ground and stops. 2) A child does work to climb to the top of a slide, thus giving herself potential energy. Explain what has happened to all this potential energy as the child, still moving, nears the bottom of the (not frictionless) slide. Answer: Some of the potential energy she had at the top of the slide has been transformed into kinetic energy of her motion; the rest of the PE has been transformed into heat in the slide, the air, and the body of the child. 8
3) Particle 1 has 1 the mass of Particle 2, yet they both have the same kinetic energy. Compare the 2 momenta of two particles. Answer: Since the kinetic energies of the two particles are equal, 1 1 mv = m v 2 1 12 2 2 22 or p p 12 22 =, where p= mv. 2m 2m 1 2 1 Since m = m, we see that 1 2 2 1 p = p = 0.707 p. 1 2 2 2 4) Is energy conserved during a two-car collision? Answer: It depends how one defines the system to be observed. If the system only accounts for the kinetic energies of the cars, then it is not conserved. If the system accounts for the friction and deformation of the vehicles, then it is conserved. 5) A cannon recoils after it fires a shell. If you measure the range of the shell, can you find the energy released by the gunpowder? Answer: No. During the same time it takes the shell to clear the barrel of the cannon, there are frictional forces acting on it. These are external to the components of the explosion. 6) A rubber ball is dropped from a height h above the ground. Describe the motion of the ball for many bounces if the collision is completely elastic. Answer: If the collision is completely elastic, the ball will continue to bounce to the same height h after every bounce, forever. It should be noted that this is not completely realistic, which implies that the collisions are not 100% elastic in real life. Karl William Parrott check 9
7) A person stands on the edge of a cliff. She throws three identical rocks with the same speed. Rock X is thrown vertically upward, rock Y is thrown horizontally, and rock Z is thrown vertically downward. Assuming the elevation loss of the three rocks is the same (the base of the cliff is flat), which rock hits the ground with the highest speed? A) They all hit the ground with the same speed. B) Rock X C) Rock Y D) Rock Z 8) Joe and Bill throw identical balls vertically upward. Joe throws his ball with an initial speed of twice as high as Bill. The maximum height of Joe s ball will be A) four times that of Bill s ball. B) two times that of Bill s ball. C) equal to that of Bill s ball. D) eight times that of Bill s ball. E) roughly 1.3 times that of Bill s ball. 9) A ball can be rolled down one of four different ramps, as shown below. The final elevation loss of each of the ramps is the same. Neglecting friction, for which ramp will the speed of the ball be the highest at the bottom? A) The speed of the ball will be the same for all ramps. B) Ramp X C) Ramp Y D) Ramp Z 10
10) A child swings on a ball of mass m on a rope in a uniform, vertical circle of radius r at a constant speed v. How much work is done by the centripetal force on the ball during one complete revolution? Answer: The centripetal force is always directed radially inward. Since theis force is always perpendicular to the displacement of the ball, we can conclude that the centripetal force does no work on the ball. Mathematically, W = Fxcos90 = 0 11) You push a heavy box of mass m up a frictionless inclined plane of length l and height h in some time t 0. Later, you push the same box up a similar inclined plane of length l/2 and height h in the same time t 0. What can you say about the relationship between your power output(s) during these two processes? Assume the box is moved at a constant velocity in both cases. Answer: Your power output was the same in both cases. Since the inclined planes are work mgh frictionless, the total work done is W = mgh. Since Power = =, the power time t 0 is the same in both cases. 12) A pendulum in a grandfather clock swings back and forth. Does the force of gravity do positive work on the pendulum at any point in its trajectory? If so, where? Answer: The force of gravity does positive work on the pendulum while the pendulum is swinging from a high-point to a low-point in its trajectory. The work is positive in this situation because there is a displacement component directed vertically downward (in the same direction as the gravitational force). 13) Viscous friction allows oil to reduce the heating and wear of moving machine parts. But viscous friction depends on velocity. Is that a nonconservative force? Answer: Yes, whatever the functional dependence of a force to other physical quantities, the fact that the frictional effect removes energy (heat) from the moving parts classifies it as a nonconservative force. 14) Two lumps of clay are thrown at each other such that they come completely to rest after the collision. Obviously, kinetic energy is not conserved. Where did the energy go? Answer: The kinetic energy of the two lumps of clay is used up as the pieces of clay deform. Some small amounts are also converted into heat and sound. 11
15) If one lifts a box and walks up a couple of floors, how would the change in potential energy be accounted for? Answer: The act of lifting the box gives some gravitational potential energy to the box with respect to the floor. Walking up the stairs increases the gravitational potential of both the worker and the box, with respect to the ground floor. However, the box still has the same potential as when it was lifted, with respect to the worker s feet. 16) Three cars (car F, car G, and car H) are moving with the same velocity, and slam on the brakes. The most massive car is car F, and the least massive is car H. Assuming all three cars have identical tires, which car travels the longest distance to skid to a stop? Karl William Parrott check A) They all travel the same distance in stopping. B) Car F C) Car G D) Car H 17) Two cyclists, who weigh the same and have identical bicycles, ride up the same mountain, both starting at the same time. Joe rides straight up the mountain, and Bob rides up the longer road that has a lower grade. Joe gets to the top before Bob. Which statement is true? A) Ignoring friction and wind resistance, the amount of work done by Joe is equal to the amount of work done by Bob, but the average power exerted by Joe is greater than that of Bob. B) Ignoring friction and wind resistance, the amount of work done by Joe is greater than the amount of work done by Bob, and the average power exerted by Joe is greater than that of Bob. C) Ignoring friction and wind resistance, Bob and Joe exerted the same amount of work, and the average power of each cyclist was also the same. D) Ignoring friction and wind resistance, the average power exerted by Bob and Joe was the same, but Joe exerted more work in getting there. 12
18) A person drops one rock from rest and it falls 100 meters down a cliff before hitting the ground. The person then throws an identical rock downward. The amount of kinetic energy gained by the rock dropped from rest is that of the second rock, and the magnitude of the change in speed (between hitting the ground and its initial speed) of the rock dropped from rest is that of the second rock. A) equal to, greater than B) equal to, equal to C) less than, less than D) equal to, less than 13