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GCSE Questions: Hooke's Law

Q1. Katrina carried out an investigation to determine the spring constant of a spring.

Here is her results table:

Force /N
Extension/cm
0.0
0.0
2.0
3.5
4.0
8.0
6.0
12.5
8.0
16.0
10.0
20.0

 

Describe a method she could have used to obtain this data.

Your answer should include any cause of inaccuracy in the data.

Your answer may include a labelled diagram.

This type of question is marked in two ways:

- the examiner looks for relevant instructions

- but also for the correct order - and any opposing instructions make you lose marks!

It is not just a 'tick fest' - but a marker does look to see how many relevant points you have made, then considers how you have strung them together to put your answer into a 'level'

Level 3:

The method would lead to the production of a valid outcome. All key steps are identified and logically sequenced.

5 - 6 marks
Level 2: The method would not necessarily lead to a valid outcome. Most steps are identified, but the method is not fully logically sequenced.
3 - 4 marks
Level 1: The method would not lead to a valid outcome. Some relevant steps are identified, but links are not made clear.
1 - 2 marks
Level 0: No relevant content.
0 marks

 

Indicative content they looked for:

set up a clamp stand with a clamp
hang the spring from the clamp
use a second clamp and boss to fix a (half) metre ruler alongside the spring
record the metre ruler reading that is level with the bottom of the spring
hang a 2 N weight from the bottom of the spring
record the new position of the bottom of the spring
calculate the extension of the spring
measure the extension of the spring
add further weights to the spring so the force increases 2 N at a time up to 10 N
for each new force record the position of the bottom of the spring and calculate / measure the extension


possible source of inaccuracy:
not fixing the ruler in position but simply holding the ruler next to the spring
not clamping the ruler vertical
misjudging the position of the bottom of the spring
parallax error
allow any other sensible suggestion that could reasonably lead to inaccuracy in the data
allow a description that would increase accuracy
repeating the measurements is insufficient

[6 marks]

(b) Katrina measured the extension for five different forces rather than just measuring the extension for one force. Suggest why.

It was 'to identify any anomalous results' or 'to reduce the effect of random error'.

'to obtain an average' or 'to be able to draw a graph' was considered insufficient to get you a mark.

[1 mark]

(c) This graph has some of the data obtained by Katrina already plotted.

Complete the graph by plotting the missing data and draw in the line of best fit.

[2 marks]

(d) Write down the equation that links extension, force and spring constant.

Force = spring constant x extension

F = ke

[1 mark]

(e) Calculate the spring constant of the spring that Katrina used.

Give your answer in newtons per metre.

You can use any points on the graph that are on the line for the calculation.

k = F/e

k = 10 N/20 cm

But you are asked to do it in N/m

k = 10 N/ 0.20 m = 50 N/m

[4 marks]

(f) Hooke's Law states that:

'The extension of an elastic object is directly proportional to the force applied, provided the limit of proportionality is not exceeded.'

Katrina concluded that over the range of force used, the spring obeyed Hooke's Law.

Explain how the data supports her conclusion.

The line is straight and passes through the origin- this shows it is directly proportional.

[2 marks]

[16 Marks TOTAL]