Energy changes in a system, and the ways energy is stored before and after such changes：練習問題

Which of the following defines internal energy within a system?

A spring with a spring constant of \(k = 150\text{ N/m}\) is compressed by \(0.04\text{ m}\). Calculate the elastic potential energy stored in the spring.

An object is projected upwards with an initial kinetic energy of \(100\text{ J}\). At a certain height, it has \(40\text{ J}\) of kinetic energy. Assuming no energy is dissipated to the surroundings, what is the gravitational potential energy gained at this point?

A student carries a 5 kg box up a flight of stairs to a height of 4 m. Calculate the increase in the gravitational potential energy store of the box. (Assume gravitational field strength \( g = 9.8 \, \text{N/kg} \))

A car of mass 1200 kg is travelling at a speed of 10 m/s. The driver applies the brakes, and the car comes to a stop. Calculate the amount of work done by the braking force to stop the car.

An electric kettle is used to boil water. Describe the energy transfer that occurs when the current flows through the heating element of the kettle.

A car of mass \(1200\text{ kg}\) is travelling at a speed of \(20\text{ m/s}\). Calculate the kinetic energy stored in the moving car using the formula \(E_k = \frac{1}{2}mv^2\).

A student investigates the specific heat capacity of a copper block. If \(4600\text{ J}\) of energy is supplied to a \(1\text{ kg}\) block and the temperature rises by \(12\text{ °C}\), calculate the specific heat capacity and explain one reason why the calculated value might be higher than the true value.

A student investigates the energy transfers for a small electric motor lifting a load. The motor is connected to a power supply and used to lift a weight of mass \(0.25\text{ kg}\) through a vertical height of \(1.2\text{ m}\).

(a) Calculate the gravitational potential energy gained by the load. (Assume \(g = 9.8\text{ N/kg}\)).

(b) The motor is connected to a \(6.0\text{ V}\) supply and a constant current of \(0.80\text{ A}\) flows through it. It takes \(5.0\text{ seconds}\) to lift the weight. Calculate the total electrical energy supplied to the motor during this time.

(c) Calculate the efficiency of the motor for this lift. Give your answer as a percentage.

(d) In reality, the motor is less than \(100\%\) efficient. Explain the energy store changes that occur in the motor and why some energy is dissipated during this process.