Forces and energy：練習問題

A constant horizontal force of \(40\text{ N}\) is applied to push a box across a floor for a distance of \(5\text{ m}\) in the direction of the force.
Calculate the work done on the box.

A toy car of mass \(0.50\text{ kg}\) is travelling at a constant speed of \(6.0\text{ m/s}\).
What is the kinetic energy of the car?

A crane lifts a load of mass \(250\text{ kg}\) vertically upwards by a distance of \(8.0\text{ m}\).
Calculate the work done on the load.
(Gravitational field strength, \(g = 9.8\text{ N/kg}\))

A spring with a spring constant of \(150\text{ N/m}\) is compressed elastically by \(0.080\text{ m}\).
Calculate the elastic potential energy stored in the compressed spring.

A toy car of mass \(0.50\text{ kg}\) is pushed against a horizontal spring of spring constant \(k = 800\text{ N/m}\), compressing it by \(0.050\text{ m}\).
When released from rest, the spring transfers all of its stored elastic potential energy into kinetic energy of the car. The car then travels along a rough horizontal track where a constant frictional force of \(0.40\text{ N}\) acts on it until it comes to a stop.
Calculate the distance the car travels along the rough track before coming to rest.

A student uses an electric motor to lift a load of mass \(0.80\text{ kg}\) vertically upwards by a height of \(1.5\text{ m}\).
The gravitational field strength is \(g = 9.8\text{ N/kg}\).

(a) Calculate the increase in gravitational potential energy of the load.

(b) The motor takes \(4.0\text{ s}\) to lift the load. Calculate the useful power output of the motor.

(c) State what happens to the energy transferred by the motor that is not transferred to the gravitational potential energy store of the load.

A model car of mass \(1.2\text{ kg}\) is pushed against a horizontal spring, compressing the spring by \(0.15\text{ m}\).
The spring has a spring constant of \(320\text{ N/m}\).

(a) Calculate the elastic potential energy stored in the compressed spring.

(b) The spring is released and transfers all its stored elastic potential energy into kinetic energy of the car. Calculate the maximum speed reached by the car.

(c) After leaving the spring, the car travels along a rough horizontal track until it comes to rest. A constant frictional force of \(0.60\text{ N}\) acts against the motion of the car. Calculate the distance traveled by the car along the track before stopping.