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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