Work, energy and power：練習問題

A crate of mass \( 50 \text{ kg} \) is pushed at a constant speed of \( 1.2 \text{ m s}^{-1} \) across a horizontal floor. The force of friction acting on the crate is \( 200 \text{ N} \). What is the power required to maintain this motion?

A car of mass \( 1200 \text{ kg} \) accelerates from rest to a speed of \( 20 \text{ m s}^{-1} \) in \( 8.0 \text{ s} \). Assuming the acceleration is uniform and air resistance is negligible, what is the average power developed by the engine?

An electric pump raises \( 600 \text{ kg} \) of water per minute from a well of depth \( 15 \text{ m} \). The water is ejected from the pump through a nozzle with a speed of \( 10 \text{ m s}^{-1} \). What is the useful power output of the pump? (Take \( g = 9.81 \text{ m s}^{-2} \))

A ball is dropped from a height \( h \) above the ground. If air resistance is negligible, which expression represents the speed \( v \) of the ball just before it hits the ground?

An object of mass \( m \) moves with a constant velocity \( v \) against a resistive force \( F \). Which expression represents the work done by the object against the resistive force in a time interval \( t \)?

An object is moved at a constant speed along a horizontal surface by a force of \( 12 \text{ N} \) acting at an angle of \( 30^{\circ} \) to the horizontal. Calculate the work done by this force as the object is displaced by \( 5.0 \text{ m} \) along the surface.

A motor with an efficiency of \( 75\% \) is used to lift a mass of \( 40 \text{ kg} \) vertically through a height of \( 15 \text{ m} \) in a time of \( 10 \text{ s} \). Determine the total electrical power input required by the motor. Assume \( g = 9.81 \text{ m s}^{-2} \).

(a) Define work done by a force.
(b) A crate of mass \( 45 \text{ kg} \) is pulled at a constant speed of \( 1.2 \text{ m s}^{-1} \) along a horizontal floor by a rope. The rope makes an angle of \( 30^{\circ} \) with the horizontal. The tension in the rope is \( 140 \text{ N} \).
(i) Calculate the work done by the tension force as the crate moves a distance of \( 5.0 \text{ m} \).
(ii) Determine the power developed by the tension force.

A small object of mass \( m \) is released from rest at point A and slides down a frictionless curved track to point B, which is at a vertical distance \( h \) below A. At point B, the object enters a rough horizontal surface and travels a distance \( d \) before coming to rest at point C.

(a) Show that the speed of the object at point B is given by \( v = \sqrt{2gh} \).
(b) The object has a mass of \( 0.25 \text{ kg} \) and the height \( h \) is \( 0.80 \text{ m} \). Calculate the kinetic energy of the object at point B.
(c) A constant frictional force of \( 0.50 \text{ N} \) acts on the object between B and C. Use energy considerations to calculate the distance \( d \).
(d) Describe the energy transformation that occurs as the object moves from B to C.