能量—力作功：功、功率與效率：練習題

A machine transfers \(1500\text{ J}\) of energy in a time of \(30\text{ s}\).
Calculate the power of the machine.

A trolley with a mass of \(4.0\text{ kg}\) is pushed along a friction-free horizontal track by a constant force. The force does \(32\text{ J}\) of work on the trolley, which was initially at rest. Calculate the final speed of the trolley.

A box of mass \(5.0\text{ kg}\) is pulled \(10\text{ m}\) up a rough slope that is inclined at an angle to the horizontal. A constant pulling force of \(45\text{ N}\) is applied parallel to the slope. The vertical height gained by the box is \(6.0\text{ m}\). Calculate the energy dissipated as heat due to friction during this process. (Use \(g = 10\text{ N/kg}\))

A person pushes a box across a floor with a constant force of \(25\text{ N}\) over a distance of \(4.0\text{ m}\).
Calculate the work done on the box.

An electric motor is used to lift a mass of 50 kg through a vertical height of 12 m. The total energy supplied to the motor is 8.0 kJ. Calculate the energy dissipated as heat to the surroundings. (Use \(g = 10\text{ N/kg}\))

A weightlifter performs \(1,200\text{ J}\) of work to lift a barbell. If the lift takes \(1.5\text{ s}\) to complete, calculate the power output of the weightlifter in watts (\(\text{W}\)).

A crane is used to lift a container as shown in the diagram. If the crane performs \(160,000\text{ J}\) of work using a constant force of \(5,000\text{ N}\), calculate the vertical distance the container is moved.

A water pump lifts \(30\text{ kg}\) of water through a vertical height of \(20\text{ m}\) every minute, as illustrated in the diagram. Calculate the minimum power output of the pump. (Use gravitational field strength \(g = 10\text{ N/kg}\))

An electric winch is used to pull a boat up a ramp. The winch performs \(4500\text{ J}\) of useful work to move the boat. The total energy supplied to the winch during this process is \(6000\text{ J}\).

a) Calculate the efficiency of the winch.
b) Calculate how much energy is dissipated to the surroundings as heat and sound.
c) State the principle that explains why the total energy input must equal the sum of the useful energy and the wasted energy.

An electric motor in a lift (elevator) raises a load of mass \(400\text{ kg}\) vertically through a height of \(20\text{ m}\) at a constant speed. The journey takes \(10\text{ s}\). (Take \(g = 10\text{ N/kg}\))

a) Calculate the weight of the load.
b) Calculate the work done by the motor against gravity to lift the load.
c) Calculate the useful power output of the motor.
d) The motor is only \(75\%\) efficient. Calculate the total electrical power input required to operate the lift at this speed.