In these lessons, we will

• Describe what is meant by power.

• Calculate power using either energy or work done.

Example:

When a car stops, 40000J of work is done by the brakes in a time of 5s. Calculate the power of the brakes.

1. (a) How much work is done in lifting an object that weighs 250N to a height of 4m?

(b) At what rate is work done if the 250N object is lifted to a height 4m in 4s?

2. A block of stone weighs 500 newtons. It is 20m pushed up a slope.

(a) Neglecting friction, how much force is needed to push it up the incline at constant velocity?

(b)(i) How much work is done to push it up the incline?

(ii) How much work is done in lifting the block vertically 4m?

3. Someone takes 11 minutes to walk up a hill 120m high. His weight is 550N.

(a) How much work did he do in climbing the hill?

(b) How many seconds did he take to climb the hill?

(c) What power is developed by his muscles as he climbs?

(d) If he runs up the hill his muscles can exert 500 Watts. How long will it take him to get to the top of the hill?

4. An electric motor is 75% efficient. It is used to raise a weight of 1000N a vertical distance of 5m in 10s.

(a) How much work muset the motor do in raising the weight?

(b) What is the power developed by the motor as it raises the weight?

(c) Given its efficiency, at what rate must power be supplied to the motor.

(d) What happens to the energy used to raise the weight?

5. The escalator at Highgate underground station transports people up and sown a vertical height of 30m in one minute.

(a) How much work was done by the motor of the escalator in taking someone with weight 750N from the bottom to the top?

(b) Calculate the power exerted by the motor in raising each traveler.

At busy times, the escalator moves more than 120 people up the stairs every minute.

(c) What is the minimum amount of power required from the electric motors that drive the escalators. (Assume that each passenger has an average weight of 750N)

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