Chapter 7 PROBLEMS
22 Pages

Chapter 7 PROBLEMS

Course Number: PHYSICS phy 280, Fall 2007

College/University: Bergen Community College

Word Count: 6812

Rating:

Document Preview

Chapter 7 Review and summary\ Print this page R E V I E W & S U M MA RY Kinetic Energy The kinetic energy K associated with the motion of a particle of mass m and speed v, where v is well below the speed of light, is (7-1) Work Work W is energy transferred to or from an object via a force acting on the object. Energy transferred to the object is positive work, and from the object, negative work. Work Done...

Unformatted Document Excerpt
Coursehero >> New Jersey >> Bergen Community College >> PHYSICS phy 280

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

7 Review Chapter and summary\ Print this page R E V I E W & S U M MA RY Kinetic Energy The kinetic energy K associated with the motion of a particle of mass m and speed v, where v is well below the speed of light, is (7-1) Work Work W is energy transferred to or from an object via a force acting on the object. Energy transferred to the object is positive work, and from the object, negative work. Work Done by a Constant Force The work done on a particle by a constant force during displacement is (7-7,7-8) in which is the constant angle between the directions of and . Only the component of that is along the displacement can do work on the object. When two or more forces act on an object, their net work is the sum of the individual works done by the forces, which is also equal to the work that would be done on the object by the net force of those forces. Work and Kinetic Energy For a particle, a change K in the kinetic energy equals the net work W done on the particle: (7-10) in which Ki is the initial kinetic energy of the particle and Kf is the kinetic energy after the work is done. Equation 7-10 rearranged gives us (7-11) Work Done by the Gravitational Force The work Wg done by the gravitational force a displacement on a particle-like object of mass m as the object moves through is given by (7-12) in which is the angle between and . Work Done in Lifting and Lowering an Object The work Wa done by an applied force as a particle-like object is either lifted or lowered is related to the work Wg done by the gravitational force and the change K in the object's kinetic energy by (7-15) If Kf = Ki, then Eq. 7-15 reduces to (7-16) which tells us that the applied force transfers as much energy to the object as the gravitational force transfers from it. Spring Force The force from a spring is (7-20) where is the displacement of the spring's free end from its position when the spring is in its relaxed state (neither compressed nor extended), and k is the spring constant (a measure of the spring's stiffness). If an x axis lies along the spring, with the origin at the location of the spring's free end when the spring is in its relaxed state, Eq. 7-20 can be written as (7-21) A spring force is thus a variable force: It varies with the displacement of the spring's free end. Work Done by a Spring Force If an object is attached to the spring's free end, the work Ws done on the object by the spring force when the object is moved from an initial position xi to a final position xf is (7-25) If xi = 0 and xf = x, then Eq. 7-25 becomes (7-26) Work Done by a Variable Force When the force on a particle-like object depends on the position of the object, the work done by on the object while the object moves from an initial position ri with coordinates (xi, yi, zi) to a final position rf with coordinates (xf, yf, zf) must be found by integrating the force. If we assume that component Fx may depend on x but not on y or z, component Fy may depend on y but not on x or z, and component Fz may depend on z but not on x or y, then the work is (7-36) If has only an x component, then Eq. 7-36 reduces to (7-32) Power The power due to a force is the rate at which that force does work on an object. If the force does work W during a time interval t, the average power due to the force over that time interval is (7-42) Instantaneous power is the instantaneous rate of doing work: (7-43) For a force at an angle to the direction of travel of the instantaneous velocity , the instantaneous power is (7-47,7-48) CHAPETER 7 PROBLEMS PROBLEMS sec. 7-3 Kinetic Energy 1 A proton (mass m = 1.67 10-27 kg) is being accelerated along a straight line at 3.6 1015 m/s2 in a machine. If the proton has an initial speed of 2.4 107 m/s and travels 3.5 cm, what then is (a) its speed and (b) the increase in its kinetic energy? Answer: (a) 2.9 107 m/s; (b) 2.1 10-13 J 2 If a Saturn V rocket with an Apollo spacecraft attached had a combined mass of 2.9 105 kg and reached a speed of 11.2 km/s, how much kinetic energy would it then have? 3 On August 10, 1972, a large meteorite skipped across the atmosphere above the western United States and western Canada, much like a stone skipped across water. The accompanying fireball was so bright that it could be seen in the daytime sky and was brighter than the usual meteorite trail. The meteorite's mass was about 4 106 kg; its speed was about 15 km/s. Had it entered the atmosphere vertically, it would have hit Earth's surface with about the same speed. (a) Calculate the meteorite's loss of kinetic energy (in joules) that would have been associated with the vertical impact. (b) Express the energy as a multiple of the explosive energy of 1 megaton of TNT, which is 4.2 10 15 J. (c) The energy associated with the atomic bomb explosion over Hiroshima was equivalent to 13 kilotons of TNT. To how many Hiroshima bombs would the meteorite impact have been equivalent? Answer: (a) 5 1014 J; (b) 0.1 megaton TNT; (c) 8 bombs 4 A bead with mass 1.8 10-2 kg is moving along a wire in the positive direction of an x axis. Beginning at time t = 0, when the bead passes through x = 0 with speed 12 m/s, a constant force acts on the bead. Figure 7-22 indicates the bead's position at these four times: t0 = 0, t1 = 1.0 s, t2 = 2.0 s, and t3 = 3.0 s. The bead momentarily stops at t = 3.0 s. What is the kinetic energy of the bead at t = 10 s? Figure 7-22 Problem 4. 5 A father racing his son has half the kinetic energy of the son, who has half the mass of the father. The father speeds up by 1.0 m/s and then has the same kinetic energy as the son. What are the original speeds of (a) the father and (b) the son? Answer: (a) 2.4 m/s; (b) 4.8 m/s 6 A force is applied to a bead as the bead is moved along a straight wire through displacement +5.0 cm. The magnitude of is set at a certain value, but the angle between be chosen. Figure 7-23 gives the work W done by much work is done by and the bead's displacement can on the bead for a range of values; W0 = 25 J. How if is (a) 64 and (b) 147? Figure 7-23 Problem 6. sec. 7-5 Work and Kinetic Energy 7 A 3.0 kg body is at rest on a frictionless horizontal air track when a constant horizontal force acting in the positive direction of an x axis along the track is applied to the body. A stroboscopic graph of the position of the body as it slides to the right is shown in Fig. 7-24. The force is applied to the body at t = 0, and the graph records the position of the body at 0.50 s intervals. How much work is done on the body by the applied force between t = 0 and t = 2.0 s? Figure 7-24 Problem 7. Answer: 0.96 J 8 A ice block floating in a river is pushed through a displacement embankment by rushing water, which exerts a force work does the force do on the block during the displacement? along a straight on the block. How much 9 The only force acting on a 2.0 kg canister that is moving in an xy plane has a magnitude of 5.0 N. The canister initially has a velocity of 4.0 m/s in the positive x direction and some time later has a velocity of 6.0 m/s in the positive y direction. How much work is done on the canister by the 5.0 N force during this time? Answer: 20 J 10 A coin slides over a frictionless plane and across an xy coordinate system from the origin to a point with xy coordinates (3.0 m, 4.0 m) while a constant force acts on it. The force has magnitude 2.0 N and is directed at a counterclockwise angle of 100 from the positive direction of the x axis. How much work is done by the force on the coin during the displacement? 11 A 12.0 N force with a fixed orientation does work on a particle as the particle moves through the threedimensional displacement m. What is the angle between the force and the displacement if the change in the particle's kinetic energy is (a) +30.0 J and (b) -30.0 J? Answer: (a) 62.3; (b) 118 12 A can of bolts and nuts is pushed 2.00 m along an x axis by a broom along the greasy (frictionless) floor of a car repair shop in a version of shuffleboard. Figure 7-25 gives the work W done on the can by the constant horizontal force from the broom, versus the can's position x. The scale of the figure's vertical axis is set by Ws = 6.0 J. (a) What is the magnitude of that force? (b) If the can had an initial kinetic energy of 3.00 J, moving in the positive direction of the x axis, what is its kinetic energy at the end of the 2.00 m? Figure 7-25 Problem 12. 13 A luge and its rider, with a total mass of 85 kg, emerge from a downhill track onto a horizontal straight track with an initial speed of 37 m/s. If a force slows them to a stop at a constant rate of 2.0 m/s2, (a) what magnitude F is required for the force, (b) what distance d do they travel while slowing, and (c) what work W is done on them by the force? What are (d) F, (e) d, and (f) W if they, instead, slow at 4.0 m/s2? Answer: (a) 1.7 102 N; (b) 3.4 102 m; (c) - 5.8 104 J; (d) 3.4 102 N; (e) 1.7 102 m; (f) - 5.8 104 J 14 Figure 7-26 shows an overhead view of three horizontal forces acting on a cargo canister that was initially stationary but now moves across a frictionless floor. The force magnitudes are F1 = 3.00 N, F2 = 4.00 N, and F3 = 10.0 N, and the indicated angles are 2 = 50.0 and 3 = 35.0. What is the net work done on the canister by the three forces during the first 4.00 m of displacement? Figure 7-26 Problem 14. 15 Figure 7-27 shows three forces applied to a trunk that moves leftward by 3.00 m over a frictionless floor. The force magnitudes are F1 = 5.00 N, F2 = 9.00 N, and F3 = 3.00 N, and the indicated angle is = 60.0. During the displacement, (a) what is the net work done on the trunk by the three forces and (b) does the kinetic energy of the trunk increase or decrease? Figure 7-27 Problem 15. Answer: (a) 1.50 J; (b) increases 16 An 8.0 kg object is moving in the positive direction of an x axis. When it passes through x = 0, a constant force directed along the axis begins to act on it. Figure 7-28 gives its kinetic energy K versus position x as it moves from x = 0 to x = 5.0 m; K0 = 30.0 J. The force continues to act. What is v when the object moves back through x = -3.0 m? Figure 7-28 Problem 16. sec. 7-6 Work Done by the Gravitational Force 17 A helicopter lifts a 72 kg astronaut 15 m vertically from the ocean by means of a cable. The acceleration of the astronaut is g/10. How much work is done on the astronaut by (a) the force from the helicopter and (b) the gravitational force on her? Just before she reaches the helicopter, what are her (c) kinetic energy and (d) speed? Answer: (a) 12 kJ; (b) - 11 kJ; (c) 1.1 kJ; (d) 5.4 m/s 18 (a) In 1975 the roof of Montreal's Velodrome, with a weight of 360 kN, was lifted by 10 cm so that it could be centered. How much work was done on the roof by the forces making the lift? (b) In 1960 a Tampa, Florida, mother reportedly raised one end of a car that had fallen onto her son when a jack failed. If her panic lift effectively raised 4000 N (about force do on the car? 19 of the car's weight) by 5.0 cm, how much work did her In Fig. 7-29, a block of ice slides down a frictionless ramp at angle = 50 while an ice worker pulls on the block (via a rope) with a force that has a magnitude of 50 N and is directed up the ramp. As the block slides through distance d = 0.50 m along the ramp, its kinetic energy increases by 80 J. How much greater would its kinetic energy have been if the rope had not been attached to the block? Figure 7-29 Problem 19. Answer: 25 J 20 A block is sent up a frictionless ramp along which an x axis extends upward. Figure 7-30 gives the kinetic energy of the block as a function of position x; the scale of the figure's vertical axis is set by Ks = 40.0 J. If the block's initial speed is 4.00 m/s, what is the normal force on the block? Figure 7-30 Problem 20. 21 A cord is used to vertically lower an initially stationary block of mass M at a constant downward acceleration of g/4. When the block has fallen a distance d, find (a) the work done by the cord's force on the block, (b) the work done by the gravitational force on the block, (c) the kinetic energy of the block, and (d) the speed of the block. Answer: (a) - 3Mgd/4; (b) Mgd; (c) Mgd/4; (d) (gd/2)0.5 22 A cave rescue team lifts an injured spelunker directly upward and out of a sinkhole by means of a motordriven cable. The lift is performed in three stages, each requiring a vertical distance of 10.0 m: (a) the initially stationary spelunker is accelerated to a speed of 5.00 m/s; (b) he is then lifted at the constant speed of 5.00 m/s; (c) finally he is decelerated to zero speed. How much work is done on the 80.0 kg rescuee by the force lifting him during each stage? 23 In Fig. 7-31, a constant force of magnitude 82.0 N is applied to a 3.00 kg shoe box at angle = 53.0, causing the box to move up a frictionless ramp at constant speed. How much work is done on the box by when the box has moved through vertical distance h = 0.150 m? Figure 7-31 Problem 23. Answer: 4.41 J 24 In Fig. 7-32, a horizontal force of magnitude 20.0 N is applied to a 3.00 kg psychology book as the book slides a distance d = 0.500 m up a frictionless ramp at angle = 30.0. (a) During the displacement, what is the net work done on the book by , the gravitational force on the book, and the normal force on the book? (b) If the book has zero kinetic energy at the start of the displacement, what is its speed at the end of the displacement? Figure 7-32 Problem 24. 25 In Fig. 7-33, a 0.250 kg block of cheese lies on the floor of a 900 kg elevator cab that is being pulled upward by a cable through distance d1 = 2.40 m and then through distance d2 = 10.5 m. (a) Through d1, if the normal force on the block from the floor has constant magnitude FN = 3.00 N, how much work is done on the cab by the force from the cable? (b) Through d2, if the work done on the cab by the (constant) force from the cable is 92.61 kJ, what is the magnitude of FN? Figure 7-33 Problem 25. Answer: (a) 25.9 kJ; (b) 2.45 N sec. 7-7 Work Done by a Spring Force 26 In Fig. 7-9, we must apply a force of magnitude 80 N to hold the block stationary at x = -2.0 cm. From that position, we then slowly move the block so that our force does +4.0 J of work on the springblock system; the block is then again stationary. What is the block's position? ( Hint: There are two answers.) 27 A spring and block are in the arrangement of Fig. 7-9. When the block is pulled out to x = +4.0 cm, we must apply a force of magnitude 360 N to hold it there. We pull the block to x = 11 cm and then release it. How much work does the spring do on the block as the block moves from xi = +5.0 cm to (a) x = +3.0 cm, (b) x = -3.0 cm, (c) x = -5.0 cm, and (d) x = -9.0 cm? Answer: (a) 7.2 J; (b) 7.2 J; (c) 0; (d) - 25 J 28 During spring semester at MIT, residents of the parallel buildings of the East Campus dorms battle one another with large catapults that are made with surgical hose mounted on a window frame. A balloon filled with dyed water is placed in a pouch attached to the hose, which is then stretched through the width of the room. Assume that the stretching of the hose obeys Hooke's law with a spring constant of 100 N/m. If the hose is stretched by 5.00 m and then released, how much work does the force from the hose do on the balloon in the pouch by the time the hose reaches its relaxed length? 29 In the arrangement of Fig. 7-9, we gradually pull the block from x = 0 to x = +3.0 cm, where it is stationary. Figure 7-34 gives the work that our force does on the block. The scale of the figure's vertical axis is set by Ws = 1.0 J. We then pull the block out to x = +5.0 cm and release it from rest. How much work does the spring do on the block when the block moves from xi = +5.0 cm to (a) x = +4.0 cm, (b) x = -2.0 cm, and (c) x = -5.0 cm? Figure 7-34 Problem 29. Answer: (a) 0.90 J; (b) 2.1 J; (c) 0 30 In Fig. 7-9a, a block of mass m lies on a horizontal frictionless surface and is attached to one end of a horizontal spring (spring constant k) whose other end is fixed. The block is initially at rest at the position where the spring is unstretched (x = 0) when a constant horizontal force in the positive direction of the x axis is applied to it. A plot of the resulting kinetic energy of the block versus its position x is shown in Fig. 7-35. The scale of the figure's vertical axis is set by Ks = 4.0 J. (a) What is the magnitude of What is the value of k? ? (b) Figure 7-35 Problem 30. 31 The only force acting on a 2.0 kg body as it moves along a positive x axis has an x component Fx = -6x N, with x in meters. The velocity at x = 3.0 m is 8.0 m/s. (a) What is the velocity of the body at x = 4.0 m? (b) At what positive value of x will the body have a velocity of 5.0 m/s? Answer: (a) 6.6 m/s; (b) 4.7 m 32 Figure 7-36 gives spring force Fx versus position x for the springblock arrangement of Fig. 7-9. The scale is set by Fs = 160.0 N. We release the block at x = 12 cm. How much work does the spring do on the block when the block moves from xi = +8.0 cm to (a) x = +5.0 cm, (b) x = -5.0 cm, (c) x = -8.0 cm, and (d) x = -10.0 cm? Figure 7-36 Problem 32. 33 The block in Fig. 7-9a lies on a horizontal frictionless surface, and the spring constant is 50 N/m. Initially, the spring is at its relaxed length and the block is stationary at position x = 0. Then an applied force with a constant magnitude of 3.0 N pulls the block in the positive direction of the x axis, stretching the spring until the block stops. When that stopping point is reached, what are (a) the position of the block, (b) the work that has been done on the block by the applied force, and (c) the work that has been done on the block by the spring force? During the block's displacement, what are (d) the block's position when its kinetic energy is maximum and (e) the value of that maximum kinetic energy? Answer: (a) 0.12 m; (b) 0.36 J; (c) - 0.36 J; (d) 0.060 m; (e) 0.090 J sec. 7-8 Work Done by a General Variable Force 34 A 10 kg brick moves along an x axis. Its acceleration as a function of its position is shown in Fig. 737. The scale of the figure's vertical axis is set by as = 20.0 m/s2. What is the net work performed on the brick by the force causing the acceleration as the brick moves x from = 0 to x = 8.0 m? Figure 7-37 Problem 34. 35 The force on a particle is directed along an x axis and given by F = F0(x/x0 - 1). Find the work done by the force in moving the particle from x = 0 to x = 2x0 by (a) plotting F(x) and measuring the work from the graph and (b) integrating F(x). Answer: (a) 0; (b) 0 36 A 5.0 kg block moves in a straight line on a horizontal frictionless surface under the influence of a force that varies with position as shown in Fig. 7-38. Figure 7-38 Problem 36. The scale of the figure's vertical axis is set by Fs = 10.0 N. How much work is done by the force as the block moves from the origin to x = 8.0 m? 37 Figure 7-39 gives the acceleration of a 2.00 kg particle as an applied force moves it from rest along an x axis from x = 0 to x = 9.0 m. The scale of the figure's vertical axis is set by as = 6.0 m/s2. How much work has the force done on the particle when the particle reaches (a) x = 4.0 m, (b) x = 7.0 m, and (c) x = 9.0 m? What is the particle's speed and direction of travel when it reaches (d) x = 4.0 m, (e) x = 7.0 m, and (f) x = 9.0 m? Figure 7-39 Problem 37. Answer: (a) 42 J; (b) 30 J; (c) 12 J; (d) 6.5 m/s, + x axis; (e) 5.5 m/s, + x axis; (f) 3.5 m/s, + x axis 38 A 1.5 kg block is initially at rest on a horizontal frictionless surface when a horizontal force along an x axis is applied to the block. The force is given by N, where x is in meters and the initial position of the block is x = 0. (a) What is the kinetic energy of the block as it passes through x = 2.0 m? (b) What is the maximum kinetic energy of the block between x = 0 and x = 2.0 m? 39 A force acts on a particle as the particle moves along an x axis, with in newtons, x in meters, and c a constant. At x = 0, the particle's kinetic energy is 20.0 J; at x = 3.00 m, it is 11.0 J. Find c. Answer: 4.00 N/m 40 A can of sardines is made to move along an x axis from x = 0.25 m to x = 1.25 m by a force with a magnitude given by F = exp(-4x2), with x in meters and F in newtons. (Here exp is the exponential function.) How much work is done on the can by the force? 41 A single force acts on a 3.0 kg particle-like object whose position is given by x = 3.0t - 4.0t2 + 1.0t3, with x in meters and t in seconds. Find the work done on the object by the force from t = 0 to t = 4.0 s. Answer: 5.3 102 J 42 Figure 7-40 shows a cord attached to a cart that can slide along a frictionless horizontal rail aligned along an x axis. The left end of the cord is pulled over a pulley, of negligible mass and friction and at cord height h = 1.20 m, so the cart slides from x1 = 3.00 m to x2 = 1.00 m. During the move, the tension in the cord is a constant 25.0 N. What is the change in the kinetic energy of the cart during the move? Figure 7-40 Problem 42. sec. 7-9 Power 43 A force of 5.0 N acts on a 15 kg body initially at rest. Compute the work done by the force in (a) the first, (b) the second, and (c) the third seconds and (d) the instantaneous power due to the force at the end of the third second. Answer: (a) 0.83 J; (b) 2.5 J; (c) 4.2 J; (d) 5.0 W 44 A skier is pulled by a towrope up a frictionless ski slope that makes an angle of 12 with the horizontal. The rope moves parallel to the slope with a constant speed of 1.0 m/s. The force of the rope does 900 J of work on the skier as the skier moves a distance of 8.0 m up the incline. (a) If the rope moved with a constant speed of 2.0 m/s, how much work would the force of the rope do on the skier as the skier moved a distance of 8.0 m up the incline? At what rate is the force of the rope doing work on the skier when the rope moves with a speed of (b) 1.0 m/s and (c) 2.0 m/s? 45 A 100 kg block is pulled at a constant speed of 5.0 m/s across a horizontal floor by an applied force of 122 N directed 37 above the horizontal. What is the rate at which the force does work on the block? Answer: 4.9 102 W 46 The loaded cab of an elevator has a mass of 3.0 103 kg and moves 210 m up the shaft in 23 s at constant speed. At what average rate does the force from the cable do work on the cab? 47 A machine carries a 4.0 kg package from an initial position of at t = 0 to a final position of at t = 12 s. The constant force applied by the machine on the package is For that displacement, find (a) the work done on the package by the machine's force and (b) the average power of the machine's force on the package. Answer: (a) 1.0 102 J; (b) 8.4 W 48 A 0.30 kg ladle sliding on a horizontal frictionless surface is attached to one end of a horizontal spring ( k = N/m) whose other end is fixed. The ladle has a kinetic energy of 10 J as it passes through its equilibrium position (the point at which the spring force is zero). (a) At what rate is the spring doing work on the ladle as the ladle passes through its equilibrium position? (b) At what rate is the spring doing work on the ladle when the spring is compressed 0.10 m and the ladle is moving away from the equilibrium position? 49 A fully loaded, slow-moving freight elevator has a cab with a total mass of 1200 kg, which is required to travel upward 54 m in 3.0 min, starting and ending at rest. The elevator's counter-weight has a mass of only 950 kg, and so the elevator motor must help. What average power is required of the force the motor exerts on the cab via the cable? Answer: 7.4 102 W 50 (a) At a certain instant, a particle-like object is acted on by a force while the object's velocity is What is the instantaneous rate at which the force does work on the object? (b) At some other time, the velocity consists of only a y component. If the force is unchanged and the instantaneous power is -12 W, what is the velocity of the object? 51 A force initial position of acts on a 2.00 kg mobile object that moves from an to a final position of in 4.00 s. Find (a) the work done on the object by the force in the 4.00 s interval, (b) the average power due to the force during that interval, and (c) the angle between vectors and . Answer: (a) 32.0 J; (b) 8.00 W; (c) 78.2 52 A funny car accelerates from rest through a measured track distance in time T with the engine operating at a constant power P. If the track crew can increase the engine power by a differential amount dP, what is the change in the time required for the run? Additional Problems 53 Figure 7-41 shows a cold package of hot dogs sliding right-ward across a frictionless floor through a distance d = 20.0 cm while three forces act on the package. Two of them are horizontal and have the magnitudes F1 = 5.00 N and F2 = 1.00 N; the third is angled down by = 60.0 and has the magnitude F3 = 4.00 N. (a) For the 20.0 cm displacement, what is the net work done on the package by the three applied forces, the gravitational force on the package, and the normal force on the package? (b) If the package has a mass of 2.0 kg and an initial kinetic energy of 0, what is its speed at the end of the displacement? Figure 7-41 Problem 53. Answer: (a) 1.20 J; (b) 1.10 m/s 54 The only force acting on a 2.0 kg body as the body moves along an x axis varies as shown in Fig. 7-42. The scale of the figure's vertical axis is set by Fs = 4.0 N. The velocity of the body at x = 0 is 4.0 m/s. (a) What is the kinetic energy of the body at x = 3.0 m? (b) At what value of x will the body have a kinetic energy of 8.0 J? (c) What is the maximum kinetic energy of the body between x = 0 and x = 5.0 m? Figure 7-42 Problem 54. 55 A horse pulls a cart with a force of 40 lb at an angle of 30 above the horizontal and moves along at a speed of 6.0 mi/h. (a) How much work does the force do in 10 min? (b) What is the average power (in horsepower) of the force? Answer: (a) 1.8 105 ft lb; (b) 0.55 hp 56 An initially stationary 2.0 kg object accelerates horizontally and uniformly to a speed of 10 m/s in 3.0 s. (a) In that 3.0 s interval, how much work is done on the object by the force accelerating it? What is the instantaneous power due to that force (b) at the end of the interval and (c) at the end of the first half of the interval? 57 A 230 kg crate hangs from the end of a rope of length L = 12.0 m. You push horizontally on the crate with a varying force to move it distance d = 4.00 m to the side (Fig. 7-43). (a) What is the magnitude of when the crate is in this final position? During the crate's displacement, what are (b) the total work done on it, (c) the work done by the gravitational force on the crate, and (d) the work done by the pull on the crate from the rope? (e) Knowing that the crate is motionless before and after its displacement, use the answers to (b), (c), and (d) to find the work your force does on the crate. (f) Why is the work of your force not equal to the product of the horizontal displacement and the answer to (a)? Figure 7-43 Problem 57. Answer: (a) 797 N; (b) 0; (c) - 1.55 kJ; (d) 0; (e) 1.55 kJ; (f) F varies during displacement 58 To pull a 50 kg crate across a horizontal frictionless floor, a worker applies a force of 210 N, directed 20 above the horizontal. As the crate moves 3.0 m, what work is done on the crate by (a) the worker's force, (b) the gravitational force on the crate, and (c) the normal force on the crate from the floor? (d) What is the total work done on the crate? 59 An explosion at ground level leaves a crater with a diameter that is proportional to the energy of the explosion raised to the power; an explosion of 1 megaton of TNT leaves a crater with a 1 km diameter. Below Lake Huron in Michigan there appears to be an ancient impact crater with a 50 km diameter. What was the kinetic energy associated with that impact, in terms of (a) megatons of TNT (1 megaton yields 4.2 1015 J) and (b) Hiroshima bomb equivalents (13 kilotons of TNT each)? (Ancient meteorite or comet impacts may have significantly altered Earth's climate and contributed to the extinction of the dinosaurs and other life-forms.) Answer: (a) 1 105 megatons TNT; (b) 1 107 bombs 60 A frightened child is restrained by her mother as the child slides down a frictionless playground slide. If the force on the child from the mother is 100 N up the slide, the child's kinetic energy increases by 30 J as she moves down the slide a distance of 1.8 m. (a) How much work is done on the child by the gravitational force during the 1.8 m descent? (b) If the child is not restrained by her mother, how much will the child's kinetic energy increase as she comes down the slide that same distance of 1.8 m? 61 How much work is done by a force a position to a position Answer: -6J with x in meters, that moves a particle from to a position ? 62 A 250 g block is dropped onto a relaxed vertical spring that has a spring constant of k = 2.5 N/cm (Fig. 744). The block becomes attached to the spring and compresses the spring 12 cm before momentarily stopping. While the spring is being compressed, what work is done on the block by (a) the gravitational force on it and (b) the spring force? (c) What is the speed of the block just before it hits the spring? (Assume that friction is negligible.) (d) If the speed at impact is doubled, what is the maximum compression of the spring? Figure 7-44 Problem 62. 63 To push a 25.0 kg crate up a frictionless incline, angled at 25.0 to the horizontal, a worker exerts a force of 209 N parallel to the incline. As the crate slides 1.50 m, how much work is done on the crate by (a) the worker's applied force, (b) the gravitational force on the crate, and (c) the normal force exerted by the incline on the crate? (d) What is the total work done on the crate? Answer: (a) 314 J; (b) - 155 J; (c) 0; (d) 158 J 64 Boxes are transported from one location to another in a ware-house by means of a conveyor belt that moves with a constant speed of 0.50 m/s. At a certain location the conveyor belt moves for 2.0 m up an incline that makes an angle of 10 with the horizontal, then for 2.0 m horizontally, and finally for 2.0 m down an incline that makes an angle of 10 with the horizontal. Assume that a 2.0 kg box rides on the belt without slipping. At what rate is the force of the conveyor belt doing work on the box as the box moves (a) up the 10 incline, (b) horizontally, and (c) down the 10 incline? 65 In Fig. 7-45, a cord runs around two massless, frictionless pulleys. A canister with mass m = 20 kg hangs from one pulley, and you exert a force on the free end of the cord. (a) What must be the magnitude of if you are to lift the canister at a constant speed? (b) To lift the canister by 2.0 cm, how far must you pull the free end of the cord? During that lift, what is the work done on the canister by (c) your force (via the cord) and (d) the gravitational force? (Hint: When a cord loops around a pulley as shown, it pulls on the pulley with a net force that is twice the tension in the cord.) Figure 7-45 Problem 65. Answer: (a) 98 N; (b) 4.0 cm; (c) 3.9 J; (d) - 3.9 J 66 If a car of mass 1200 kg is moving along a highway at 120 km/h, what is the car's kinetic energy as determined by someone standing alongside the highway? 67 A spring with a pointer attached is hanging next to a scale marked in millimeters. Three different packages are hung from the spring, in turn, as shown in Fig. 7-46. (a) Which mark on the scale will the pointer indicate when no package is hung from the spring? (b) What is the weight W of the third package? Figure 7-46 Problem 67. Answer: (a) 23 mm; (b) 45 N 68 An iceboat is at rest on a frictionless frozen lake when a sudden wind exerts a constant force of 200 N, toward the east, on the boat. Due to the angle of the sail, the wind causes the boat to slide in a straight line for a distance of 8.0 m in a direction 20 north of east. What is the kinetic energy of the iceboat at the end of that 8.0 m? 69 If a ski lift raises 100 passengers averaging 660 N in weight to a height of 150 m in 60.0 s, at constant speed, what average power is required of the force making the lift? Answer: 165 kW 70 A force acts on a particle as the particle goes through displacement (Other forces also act on the particle.) What is c if the work done on the particle by force is is (a) 0, (b) 17 J, and (c) -18 J? 71 A constant force of magnitude 10 N makes an angle of 150 (measured counterclockwise) with the positive x direction as it acts on a 2.0 kg object moving in an xy plane. How much work is done on the object by the force as the object moves from the origin to the point having position vector Answer: - 37 J ? 72 In Fig. 7-47a, a 2.0 N force is applied to a 4.0 kg block at a downward angle as the block moves rightward through 1.0 m across a frictionless floor. Find an expression for the speed vf of the block at the end of that distance if the block's initial velocity is (a) 0 and (b) 1.0 m/s to the right. (c) The situation in Fig. 7-47b is similar in that the block is initially moving at 1.0 m/s to the right, but now the 2.0 N force is directed downward to the left. Find an expression for the speed vf of the block at the end of the 1.0 m distance. (d) Graph all three expressions for vf versus downward angle for = 0 to = 90. Interpret the graphs. Figure 7-47 Problem 72. 73 A force in the positive direction of an x axis acts on an object moving along the axis. If the magnitude of the force is F = 10e-x/2.0 N, with x in meters, find the work done by as the object moves from x = 0 to x = 2.0 m by (a) plotting F(x) and estimating the area under the curve and (b) integrating to find the work analytically. Answer: (a) 13 J; (b) 13 J 74 A particle moves along a straight path through displacement while force acts on it. (Other forces also act on the particle.) What is the value of c if the work done by 75 on the particle is (a) zero, (b) positive, and (c) negative? An elevator cab has a mass of 4500 kg and can carry a maximum load of 1800 kg. If the cab is moving upward at full load at 3.80 m/s, what power is required of the force moving the cab to maintain that speed? Answer: 235 kW 76 A 45 kg block of ice slides down a frictionless incline 1.5 m long and 0.91 m high. A worker pushes up against the ice, parallel to the incline, so that the block slides down at constant speed. (a) Find the magnitude of the worker's force. How much work is done on the block by (b) the worker's force, (c) the gravitational force on the block, (d) the normal force on the block from the surface of the incline, and (e) the net force on the block? 77 As a particle moves along an x axis, a force in the positive direction of the axis acts on it. Figure 7-48 shows the magnitude F of the force versus position x of the particle. The curve is given by F = a/x2, with a = 9.0 N m2. Find the work done on the particle by the force as the particle moves from x = 1.0 m to x = 3.0 m by (a) estimating the work from the graph and (b) integrating the force function. Figure 7-48 Problem 77. Answer: (a) 6 J; (b) 6.0 J 78 A CD case slides along a floor in the positive direction of an x axis while an applied force acts on the case. The force is directed along the x axis and has the x component Fax = 9x-3x2 with x in meters and Fax in newtons. The case starts at rest at the position x = 0, and it moves until it is again at rest. (a) Plot the work does on the case as a function of x. (b) At what position is the work maximum, and (c) what is that maximum value? (d) At what position has the work decreased to zero? (e) At what position is the case again at rest? 79 A 2.0 kg lunchbox is sent sliding over a frictionless surface, in the positive direction of an x axis along the surface. Beginning at time t = 0, a steady wind pushes on the lunchbox in the negative direction of the x axis. Figure 7-49 shows the position x of the lunchbox as a function of time t as the wind pushes on the lunch-box. From the graph, estimate the kinetic energy of the lunchbox at (a) t = 1.0 s and (b) t = 5.0 s. (c) How much work does the force from the wind do on the lunchbox from t = 1.0 s to t = 5.0 s? Figure 7-49 Problem 79. Answer: (a) 0.6 J; (b) 0; (c) - 0.6 J 80 Numerical integration. A breadbox is made to move along an x axis from x = 0.15 m to x = 1.20 m by a force with a magnitude given by F = exp(-2x2), with x in meters and F in newtons. (Here exp is the exponential function.) How much work is done on the breadbox by the force? Copyright2011JohnWiley&Sons,Inc.Allrightsreserved.
MOST POPULAR MATERIALS FROM PHYSICS phy 280
MOST POPULAR MATERIALS FROM PHYSICS
MOST POPULAR MATERIALS FROM Bergen Community College