功、能量與功率：練習題

A crate of mass 45 kg is pulled a distance of 12 m across a horizontal floor by a constant force of 150 N acting at an angle of 25° to the horizontal. Calculate the work done on the crate by the 150 N force.

A block of mass 2.0 kg is pushed against a horizontal spring, compressing it by 0.15 m. The spring has a stiffness of \( 800 \text{ N m}^{-1} \). When released, the block moves across a rough horizontal surface and comes to rest after travelling a total distance of 1.2 m from the point of release. Calculate the average frictional force acting on the block.

An electric car of mass 1200 kg travels at a constant speed of \( 25 \text{ m s}^{-1} \) along a level road. The total resistive force opposing the motion is 850 N. What is the output power of the car's motor?

A car of mass \( M \) is accelerating along a horizontal road. At the instant its speed is \( v \), its engine provides a constant power \( P \). If the total resistive force at this speed is \( R \), which expression represents the instantaneous acceleration \( a \) of the car?

A winch is used to lift a load of 200 kg vertically through a height of 15 m in a time of 25 s. If the electrical power input to the winch is 2.5 kW, what is the efficiency of the winch?

An electric motor with an efficiency of 65% is used to lift a mass of \(4.0 \text{ kg}\) through a vertical height of \(3.0 \text{ m}\) in a time of \(5.0 \text{ s}\). Calculate the electrical input power required by the motor, assuming \(g = 9.81 \text{ m s}^{-2}\).

A car of mass \(1100 \text{ kg}\) is travelling at a constant speed of \(20 \text{ m s}^{-1}\) on a level road where the total resistive force is \(650 \text{ N}\). Calculate the power developed by the car's engine to maintain this speed.

A box is pulled a distance of \(8.0 \text{ m}\) along a horizontal floor by a force of \(25 \text{ N}\) acting at an angle of \(35^\circ\) above the horizontal. Calculate the work done on the box by this force.

A car of mass \(1200\text{ kg}\) travels at a constant speed of \(20\text{ m s}^{-1}\) up a hill inclined at an angle of \(6.0^{\circ}\) to the horizontal. The total resistive force opposing the motion is \(500\text{ N}\).

(a) Calculate the component of the car's weight acting down the slope.
(b) Determine the useful power output developed by the car's engine to maintain this speed.

An electric motor is used to lift a load of \(250\text{ kg}\) through a vertical height of \(15\text{ m}\). The motor is connected to a \(230\text{ V}\) supply and draws a constant current of \(4.0\text{ A}\) for a duration of \(50\text{ s}\).

(a) Calculate the work done in lifting the load.
(b) Calculate the electrical energy input to the motor.
(c) Determine the efficiency of the motor system.