Work, energy and power：練習題

A car is traveling along a straight, horizontal road at a constant speed of \(25\text{ m s}^{-1}\). The total resistive force opposing the motion of the car is \(1200\text{ N}\).
What is the useful power output of the car's engine?

An electric motor is used to lift a weight. The motor has an efficiency of \(60\%\) and performs \(300\text{ J}\) of useful work in a time of \(5.0\text{ s}\).
What is the total electrical power input to the motor during this time?

A block of mass \(2.0\text{ kg}\) slides down a rough slope from point P to point Q. The distance along the slope PQ is \(5.0\text{ m}\) and the vertical height of P above Q is \(2.5\text{ m}\). The block starts from rest at P and reaches a speed of \(4.0\text{ m s}^{-1}\) at Q.
Taking the acceleration of free fall \(g = 9.81\text{ m s}^{-2}\), what is the work done against resistive forces during this motion?

A constant force of \(15\text{ N}\) acts on an object, causing it to move a distance of \(4.0\text{ m}\) in the same direction as the force.
What is the work done on the object by this force?

An electric motor is used to lift a crate of mass \(800\text{ kg}\) vertically through a height of \(15\text{ m}\) at a constant speed. The process takes \(20\text{ s}\) and the efficiency of the motor system is \(75\%\).
What is the total electrical power input to the motor?

A car is traveling at a constant velocity of \(22\text{ m s}^{-1}\) against a total resistive force of \(500\text{ N}\).
Calculate the power developed by the engine.

A sledge is pulled across horizontal snow by a force of \(80\text{ N}\) at an angle of \(25^\circ\) to the horizontal, as shown in the diagram.
Calculate the work done by the force in pulling the sledge a distance of \(15\text{ m}\).

A water pump lifts \(0.50\text{ kg}\) of water every second from a well \(10\text{ m}\) deep and discharges it at the surface with a speed of \(4.0\text{ m s}^{-1}\).
Determine the minimum useful power output required by the pump.

A car of mass \(950\text{ kg}\) is traveling at a constant speed of \(18\text{ m s}^{-1}\) when the driver sees an obstacle and applies the brakes, bringing the car to a stop.
(a) Calculate the kinetic energy of the car before the brakes are applied.
(b) The average braking force is \(5400\text{ N}\). Calculate the distance the car travels while braking, assuming all the kinetic energy is converted to internal energy in the brakes.

A cyclist of total mass \(80\text{ kg}\) (including the bicycle) travels up a road inclined at an angle of \(4.5^\circ\) to the horizontal. The cyclist maintains a constant speed of \(5.0\text{ m s}^{-1}\) against a constant resistive force of \(25\text{ N}\) due to air resistance and friction.
(a) Calculate the component of the weight of the cyclist and bicycle acting down the slope.
(b) Determine the total forward force that the cyclist must exert to maintain this speed.
(c) Calculate the useful power developed by the cyclist.