10. Conservation of Energy

(II) In the high jump, the kinetic energy of an athlete is transformed into gravitational potential energy without the aid of a pole. With what minimum speed must the athlete leave the ground in order to lift his center of mass 2.10 m and cross the bar with a speed of 0.50 m/s?

(I) A novice skier, starting from rest, slides down an icy frictionless 8.0° incline whose vertical height is 115 m. How fast is she going when she reaches the bottom?

(II) A sled is initially given a shove up a frictionless 18.0° incline. It reaches a maximum vertical height 1.22 m higher than where it started at the bottom. What was its initial speed?

(II) A 62-kg trampoline artist jumps upward from the top of a platform with a vertical speed of 4.5 m/s. (a) How fast is he going as he lands on the trampoline, 2.0 m below (Fig. 8–32)? <IMAGE>

(I) A 16.0-kg child descends a slide 2.20 m high and, starting from rest, reaches the bottom with a speed of 1.15 m/s. How much thermal energy due to friction was generated in this process?

(a) A 3.0-g locust reaches a speed of 3.0 m/s during its jump. What is its kinetic energy at this speed?

(b) If the locust transforms energy with 35% efficiency, how much energy is required for the jump?

Proper design of automobile braking systems must account for heat buildup under heavy braking. Calculate the thermal energy dissipated from brakes in a 1500-kg car that descends a 17° hill. The car begins braking when its speed is 95 km/h and slows to a speed of 35 km/h in a distance of 0.30 km measured along the road.

(II) A 62-kg trampoline artist jumps upward from the top of a platform with a vertical speed of 4.5 m/s. (b) If the trampoline behaves like a spring of spring constant 5.8 x 10⁴ N/m, how far does he depress it?

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(II) Consider the track shown in Fig. 8–39. The section AB is one quadrant of a circle of radius 2.0 m and is frictionless. B to C is a horizontal span 3.0 m long with a coefficient of kinetic friction μₖ = 0.25 . The section CD under the spring is frictionless. A block of mass 1.0 kg is released from rest at A. After sliding on the track, it compresses the spring by 0.20 m. Determine:

(a) the velocity of the block at point B ;

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(II) Consider the track shown in Fig. 8–39. The section AB is one quadrant of a circle of radius 2.0 m and is frictionless. B to C is a horizontal span 3.0 m long with a coefficient of kinetic friction μₖ = 0.25 . The section CD under the spring is frictionless. A block of mass 1.0 kg is released from rest at A. After sliding on the track, it compresses the spring by 0.20 m. Determine:

(b) the thermal energy produced as the block slides from B to C ;

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(II) Consider the track shown in Fig. 8–39. The section AB is one quadrant of a circle of radius 2.0 m and is frictionless. B to C is a horizontal span 3.0 m long with a coefficient of kinetic friction μₖ = 0.25 . The section CD under the spring is frictionless. A block of mass 1.0 kg is released from rest at A. After sliding on the track, it compresses the spring by 0.20 m. Determine:

(c) the velocity of the block at point C ;

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(II) Consider the track shown in Fig. 8–39. The section AB is one quadrant of a circle of radius 2.0 m and is frictionless. B to C is a horizontal span 3.0 m long with a coefficient of kinetic friction μₖ = 0.25 . The section CD under the spring is frictionless. A block of mass 1.0 kg is released from rest at A. After sliding on the track, it compresses the spring by 0.20 m. Determine:

(d) the stiffness constant k for the spring.

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In one day, a 75-kg mountain climber ascends from the 1500-m level on a vertical cliff to the top at 2400 m. The next day, she descends from the top to the base of the cliff, which is at an elevation of 1350 m. What is her change in gravitational potential energy (a) on the first day?