Chapter 4 - UCSB HEP

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WORK AND ENERGY 4.15 A particle of mass m moves in one dimension along the positive x axis. It is acted on by a constant force directed toward the origin with magnitude B, and an inverse square law repulsive force with magnitude d /x2. a. Find the potential energy function U(x). b. Sketch the energy diagram for the system when the maximum kinetic energy is KO = h vo2. c. Find the equilibrium position, xo. d, What is the frequency of small oscitlations about so 4.16 An 1,800-lb sportscar accelerates to 60 mi/h in 8 s. What is the average power that the engine delivers to the car's motion during thrs period 4.17 A snowmobile climbs a hill at 15 mi/hr. The hill has a grade of 1 ft rise for every 40 ft. The resistive force due to the snow is 5 percent of the vehicle's weight. How fast will the snowmobile move downhill, assuming its engine delivers the same power Ans. 45 mi/h 4.18 A 160-lb man leaps into the air from a crouching position. His center of gravity rises 1.5 ft before he leaves the ground, and it then rises 3 ft to the top of his leap. What power does he develop assuming that he pushes the ground with constant force Ans. clue, More than 1 hp, less than 10 hp 4.19 The man in the preceding problem again leaps into the air, but this time the force he applies decreases from a maximum at the beginning of the leap to zero at the moment he leaves the ground. As a reason- able approximation, take the force to be F = Fo cos wt, where FO is the peak farce, and contact with the ground ends when wt = a/2. Find the peak power the man develops during the jump. 4.20 Sand runs from a hopper at constant rate dm/dl onto a horizontal conveyor belt driven at constant speed V by a motor. a. Find the power needed to drive the belt. 6. Compare the answer to a with the rate of change of kinetic energy of the sand. Can you account for the difference 4.21 A uniform rape of mass X per unit length is coiled an a smooth horizontal table. One end is pulled straight up with constant speed VOW a. Find the force exerted on the end of the rope as a function of height y. b. Compare the power delivered to the rope with the rate of change of the rope's total mechanical energy. 4.22 A ball drops to the floor and bounces, eventually coming to rest. Collisions between the ball and floor are inelastic; the speed after each
PROBLEMS 199 collision is e times the speed before the collision where e < 1, (e is called the coefficient of restitution.) If the speed just before the first bounce is vo, find the time to come to rest. Ans. clue. If YO = 5 m/s, e = 0.5, then T =y 1 s 4.23 A small ball of mass m is placed on top of a "superball" of mass M, and the two balls are dropped to the floor from height h. How high does the small ball rise after the collision Assume that collisions with the superball are elastic, and that m
Page 1 and 2: WORM AND - ENERGY
Page 3 and 4: SEC. 4.2 INTEGRATING THE EQUATION O
Page 5 and 6: SEC. 4.2 INTEGRATING THE EQUATION O
Page 7 and 8: SEC. 4.3 TKE WORK-ENERGY THEOREM IN
Page 9 and 10: ' SEC. 4.4 INTEGRATING EQUATION OF
Page 11 and 12: SEC. 4.5 THE WORK-ENERGY THEOREM 16
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Page 19 and 20: SEC. 4.7 POTENTIAL ENERGY 169 venti
Page 21 and 22: SEC. 4.7 POTENTIAL ENERGY Example 4
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Page 35 and 36: SEC. 4.12 THE GENERAL LAW OF CONSER
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Page 45 and 46: PROBLEMS the top of the track (at a
Page 47: PROBLEMS 197 a. A lump of sticky pu

Chapter 4 - UCSB HEP

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