Energy：練習問題

Which of the following equations correctly represents the relationship between work done (\(W\)), force (\(F\)), and distance moved in the direction of the force (\(d\))?

An electric motor is supplied with \(4000\text{ J}\) of total energy. If \(3000\text{ J}\) is transferred into useful kinetic energy, what is the efficiency of the motor?

A ball with a mass of \(0.5\text{ kg}\) is raised to a height of \(10\text{ m}\) above the ground. It is then released. What is its kinetic energy just before it hits the ground, assuming air resistance is negligible? (Use \(g = 9.8\text{ N/kg}\))

Which of the following energy resources is classified as a renewable way to provide energy?

A machine has a power rating of \(50\text{ W}\). How much energy does it transfer in \(2\text{ minutes}\)?

State the Law of Conservation of Energy as defined in the Oxford AQA syllabus.

An electric motor performs \(150\text{ J}\) of work over a period of \(10\text{ seconds}\). Calculate the power output of the motor.

A spring with a spring constant (\(k\)) of \(200\text{ N/m}\) stores \(4\text{ J}\) of elastic potential energy. Calculate the extension of the spring in meters.

A crane is used to lift a shipping container from a dock. The provided Sankey diagram represents the energy transfers occurring in the crane motor during a single lift.
The motor receives a total electrical energy input of \(25,000\text{ J}\). During the operation, the crane successfully lifts a load of \(200\text{ kg}\) to a vertical height of \(10\text{ m}\). (Assume the gravitational field strength \(g = 10\text{ N/kg}\))
(a) Calculate the useful work done by the crane in lifting the container.
(b) Use the efficiency formula to calculate the efficiency of the motor as a percentage.
(c) Determine the total amount of energy dissipated to the surroundings as heat and sound.
(d) Suggest one practical modification to the crane mechanism that would improve its efficiency.

A safety test vehicle with a mass of \(800\text{ kg}\) is accelerated from rest to a speed of \(20\text{ m/s}\) by an engine providing a constant forward force of \(1600\text{ N}\).
(a) Calculate the kinetic energy of the vehicle when it reaches the speed of \(20\text{ m/s}\).
(b) Assuming that no energy is lost to the surroundings through friction or air resistance, calculate the theoretical distance the vehicle must travel to reach this speed.
(c) In a real-world test, the vehicle actually travels a distance of \(125\text{ m}\) to reach the speed of \(20\text{ m/s}\). Calculate the total work done against resistive forces (friction and air resistance) during this acceleration.
(d) Explain, using the relationship between work done and kinetic energy, why the stopping distance of a vehicle increases significantly when the road surface is wet or icy.