Work and power：練習問題

A car of mass \( 800\text{ kg} \) accelerates from rest to a speed of \( 15\text{ m/s} \) in a time of \( 5.0\text{ s} \). Calculate the average useful power output of the car engine during this period, assuming no energy is lost to the surroundings.

An electric motor is used to lift a load of total mass \( 1200\text{ kg} \) vertically at a constant speed of \( 1.5\text{ m/s} \). If the motor is \( 60\% \) efficient, calculate the electrical power input required by the motor. (Take \( g = 10\text{ N/kg} \))

A crate of mass \( 50\text{ kg} \) is pushed \( 10\text{ m} \) up a slope to a vertical height of \( 4.0\text{ m} \). A constant frictional force of \( 120\text{ N} \) acts against the motion along the slope. Calculate the total work done in moving the crate to the top of the slope. (Take \( g = 10\text{ N/kg} \))

A car with a mass of \( 1500 \text{ kg} \) is travelling at a constant speed of \( 20 \text{ m/s} \). Calculate the average braking force required to bring the car to a complete stop over a distance of \( 50 \text{ m} \).

An electric motor with an efficiency of \( 75\% \) is used to lift a \( 20\text{ kg} \) load vertically through a height of \( 12\text{ m} \) in \( 20\text{ seconds} \). Calculate the electrical power input required by the motor. (Take \( g = 10\text{ N/kg} \))

A student uses an electric motor to lift a load of weight 5.0 N through a vertical height of 2.0 m. The motor is connected to a 12 V battery and takes 4.0 seconds to lift the load. The current in the circuit is 0.50 A.

(a) Calculate the useful work done by the motor in lifting the load.

(b) Calculate the total electrical energy supplied to the motor by the battery during these 4.0 seconds.

(c) Determine the efficiency of the motor system.

A crate of mass 120 kg is pushed up a rough ramp that is 15 m long to a platform 4.0 m above the ground. A constant force of 400 N is applied parallel to the ramp to move the crate at a constant speed.

(a) Calculate the work done by the 400 N force in moving the crate to the top of the ramp.

(b) Calculate the gain in gravitational potential energy of the crate. (Take \( g = 10 \text{ N/kg} \))

(c) Calculate the work done against friction during this process.

(d) Calculate the average power required if the task takes 10 seconds to complete.

(e) State the energy transfer that occurs due to the work done against friction.