Work, Energy and Power：練習問題

A conveyor belt in a factory transports parcels of mass \( 15 \text{ kg} \) each from the ground floor to a platform \( 4 \text{ m} \) above. It moves \( 8 \text{ parcels} \) every minute at a constant speed. If the electrical power supplied to the conveyor system is \( 250 \text{ W} \), what is the efficiency of the system? (Take \( g = 9.81 \text{ m s}^{-2} \))

A car of mass \( 1000 \text{ kg} \) accelerates from rest to \( 25 \text{ m s}^{-1} \) in \( 5 \text{ s} \) along a straight road. Assuming uniform acceleration, what is the instantaneous power developed by the engine at \( t = 2 \text{ s} \)?

An electric vehicle of mass \( 1200 \text{ kg} \) accelerates from rest to \( 20 \text{ m s}^{-1} \) in \( 4 \text{ s} \) along a straight path. Given the acceleration is uniform, determine the instantaneous power delivered by the motor at \( t = 3 \text{ s} \).

A boat of mass \( 500 \text{ kg} \) starts from rest and reaches a speed of \( 10 \text{ m s}^{-1} \) in \( 5 \text{ s} \) across a calm lake. If the engine provides a constant force, what is the instantaneous power output at \( t = 4 \text{ s} \)?

A racing car with a mass of \( 800 \text{ kg} \) accelerates from rest to \( 40 \text{ m s}^{-1} \) in \( 5 \text{ s} \) on a horizontal track. Assuming constant acceleration and neglecting air resistance, find the instantaneous power of the engine at \( t = 3 \text{ s} \).

Define power in terms of energy transfer and state its SI unit.

A student uses a 2.0-kW electric heater to warm a room. If the efficiency of the heater is 90%, calculate the electrical energy supplied by the heater in 600 seconds. Give your answer in kJ.

A small bead slides from rest down a smooth curved wire from point \( A \) to point \( B \). If the vertical height of \( A \) above \( B \) is \( h \), derive an expression for the speed of the bead at \( B \) in terms of \( g \) and \( h \) using the law of conservation of energy.

A toy car of mass \( 0.5 \text{ kg} \) is at rest on a smooth horizontal floor. A student applies a constant horizontal force of \( 2.0 \text{ N} \) to the car, pushing it over a distance of \( 1.5 \text{ m} \).

(a) Calculate the work done by the student on the toy car. (1 point)

(b) Using the work-energy theorem, determine the speed of the toy car after it has travelled the \( 1.5 \text{ m} \) distance. (2 points)

A hybrid car of mass \( 1200 \text{ kg} \) is traveling at a constant speed of \( 25 \text{ m s}^{-1} \) on a level road. The driver applies the regenerative braking system to bring the car to a complete stop. This system is able to recover \( 55\% \) of the car's initial kinetic energy and store it in the battery.

(a) Calculate the initial kinetic energy of the car before braking. (1 point)
(b) Calculate the amount of energy successfully stored in the battery during this stop. (1 point)
(c) If the stored energy from this single braking event is later used to lift the car vertically, what is the maximum height it could be raised? (2 points)
(d) If the braking process takes \( 8.0 \text{ s} \), calculate the average power at which energy is being recovered and stored in the battery. (2 points)