Energy, work and power：練習題

Which energy store increases when a box is lifted vertically from the floor onto a high shelf?

An electric motor with an efficiency of \(75\%\) is supplied with \(2000\text{ J}\) of electrical energy. What is the useful work done by the motor?

A crane lifts a load of mass \( 1200 \text{ kg} \) vertically through a height of \( 15 \text{ m} \) in \( 30 \text{ s} \). If the total electrical energy input to the crane during this time is \( 300 \text{ kJ} \), what is the efficiency of the crane? (Take gravitational field strength \( g = 10 \text{ N/kg} \)).

Which of these energy resources does not have the Sun as its original source?

A stone of mass \(0.20\text{ kg}\) is dropped from rest down a well. After falling for \(3.0\text{ s}\), it hits the water surface. Assuming air resistance is negligible, what is the kinetic energy of the stone just before it hits the water? (Take \(g = 9.8\text{ m/s}^2\))

A worker applies a constant horizontal force of \(60\text{ N}\) to push a box across a floor for a distance of \(12\text{ m}\) in a time of \(8.0\text{ s}\). Calculate the power developed by the worker.

A motor with an efficiency of \(75\%\) is used to lift a \(60\text{ kg}\) load vertically at a constant speed of \(0.50\text{ m/s}\). Calculate the electrical power input to the motor. (Use \(g = 9.8\text{ N/kg}\))

A wooden block of mass \(3.0\text{ kg}\) slides down a rough slope from a vertical height of \(1.5\text{ m}\). When it reaches the bottom of the slope, its speed is \(4.0\text{ m/s}\).

Calculate the amount of energy dissipated as thermal energy due to friction as the block slides down the slope. (Take \(g = 9.8\text{ N/kg}\)).

A crane lifts a building material of mass \(500 \text{ kg}\) from the ground to a height of \(20 \text{ m}\) in \(40 \text{ s}\).

(a) Calculate the gravitational potential energy gained by the building material.

(b) Determine the useful power output of the crane.

(c) If the crane's motor has an efficiency of \(60\%\), calculate the total electrical power input to the crane.

(d) Explain, in terms of energy stores and transfers, how the building material gains gravitational potential energy.

An electric motor is used to pull a block of mass \(20 \text{ kg}\) up a ramp at a constant speed. The ramp is \(10 \text{ m}\) long and reaches a vertical height of \(3.0 \text{ m}\). The motor takes \(15 \text{ s}\) to pull the mass from the bottom to the top. The electrical power input to the motor is \(80 \text{ W}\). Assume \(g = 9.8 \text{ N/kg}\).

(a) Calculate the gain in gravitational potential energy of the block.

(b) Determine the useful power output of the motor.

(c) Calculate the efficiency of the motor system.

(d) The constant tension in the rope pulling the block up the ramp is \(95 \text{ N}\). Calculate the total work done by the rope on the block and account for the difference between this value and your answer in part (a).