Topic Menu

Cyber-chess a chess instruction site

GCSE Questions: Hooke's Law

Q2. The diagram shows an exercise device called a chest expander. The three springs are identical.

A person pulls outwards on the handles and does work to stretch the springs.

(a) What type of energy is stored in the springs when the springs are stretched?

Elastic potential energy

[1 mark]

(b) The following graph shows how the extension of a single spring from the chest expander
depends on the force acting on the spring.

(i) How can you tell, from the graph, that the limit of proportionality of the spring has not been exceeded?

The line is straight

[1 mark]

(ii) Use data from the graph to calculate the spring constant of the spring. Give the unit.

k = F/e

k = 160/0.4 = 400 N/m

[3 marks]

(iii) Three identical resistors joined in parallel in an electrical circuit share the total current in the circuit. In a similar way, the three springs in the chest expander share the total force exerted.

By considering this similarity, use the graph to determine the total force exerted on the chest expander when each spring is stretched by 0.25 m.

Force of one spring stretched by 0.25m = 100 N (see graph)

Therefore three springs would have a force of 3 x 100 N = 300 N

[2 marks]

(c) Barry is doing an exercise called a chin-up.

Each time he does one chin-up Barry lifts his body 0.40 m vertically upwards. His mass is 65 kg.

Barry is able to do 12 chin-ups in 60 seconds. Calculate the power he developes when doing this exercise.

Gravitational field strength = 10 N/kg

 

Barry's weight = mg = 65 x 10 = 650 N

Work done in one chin up = weight x vertical distance raised

Work done = 650 x 0.40 = 260 J

Work done in doing 12 chin ups = 12 x 260 = 3120 J

Power = work done/time taken

P = 3120/60 = 52 W

[3 marks]

[10 Marks TOTAL]