10. Conservation of Energy

(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.

A block of mass m slides down a frictionless track, then around the inside of a circular loop-the-loop of radius R . From what minimum height h must the block start to make it around without falling off? Give your answer as a multiple of R.

A 50 g mass is attached to a light, rigid, 75-cm-long rod. The other end of the rod is pivoted so that the mass can rotate in a vertical circle. What speed does the mass need at the bottom of the circle to barely make it over the top of the circle?

How much work is done by the environment in the process shown in FIGURE EX10.39? Is energy transferred from the environment to the system or from the system to the environment?

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

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 the thermal energy produced as the block slides from B to C.

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 the velocity of the block at point C.

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 the stiffness constant k for the spring.