10. Conservation of Energy

A sled starts from rest at the top of the frictionless, hemispherical, snow-covered hill shown in FIGURE P10.56. a. Find an expression for the sled's speed when it is at angle ϕ .

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?

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?

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?

A 62-kg trampoline artist jumps upward from the top of a platform with a vertical speed of 4.5 m/s. 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.

A 1.0 kg mass that can move along the x-axis experiences the potential energy U = (x²−x) J, where x is in m. The mass has velocity v_x = 3.0 m/s at position x = 1.0 m. At what position has it slowed to 1.0 m/s?

FIGURE 10.23 showed the potential-energy curve for the O₂ molecule. Consider a molecule with the energy E₁ shown in the figure. a. What is the maximum speed of an oxygen atom as it oscillates back and forth? Don't forget that the kinetic energy is the total kinetic energy of the system. The mass of an oxygen atom is 16 u, where 1u=1 atomic mass unit =1.66×10⁻²⁷ kg .

The spring shown in FIGURE P10.54 is compressed 50 cm and used to launch a 100 kg physics student. The track is frictionless until it starts up the incline. The student's coefficient of kinetic friction on the 30° incline is 0.15. What is the student's speed just after losing contact with the spring?

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Two blocks with masses m_A and m_B are connected by a massless string over a massless, frictionless pulley. Block B, which is more massive than block A, is released from height h and falls. A 1.0 kg block and a 2.0 kg block are connected by a massless string over a massless, frictionless pulley. The impact speed of the heavier block, after falling, is 1.8 m/s. From how high did it fall?

Two blocks with masses m_A and m_B are connected by a massless string over a massless, frictionless pulley. Block B, which is more massive than block A, is released from height h and falls. Write an expression for the speed of the blocks just as block B reaches the ground.