GCSE Questions - Hooke's Law
Q3. Cordelia hangs a length of copper wire from the ceiling.
She adds weights to the bottom of the wire and measures the extension of the wire.
Look at a table of some of her results.
Weight (N) |
Extension (m) |
0 |
0 |
2 |
0.01 |
4 |
0.02 |
6 |
0.03 |
8 |
0.04 |
10 |
0.08 |
12 |
0.16 |
(a)
(i) Plot the values from Cordelia's experiment on the graph paper below.
(Some have been done for you).
All three points correctly plotted ![](../../../../graphics/symbols/nuclides/ticksmall.png)
OR two points correctly plotted ![](../../../../graphics/symbols/nuclides/ticksmall.png)
(2 marks)
![](../graphics/graph34ANS.png)
(ii) Draw a line of best-fit on the graph.
You should draw a straight line up to 0.04, 8 (using a ruler to do so!) and continue the line with a curved line consistent with points plotted past this point. ![](../../../../graphics/symbols/nuclides/ticksmall.png)
[1 mark]
(iii) Describe and explain the shape of the graph.
Initially the extension increases steadily/linearly/uniformly - it exhibits direct proportionally.
This corresponds to elastic behaviour in the wire and it is obeying Hooke's Law. ![](../../../../graphics/symbols/nuclides/ticksmall.png)
Then after the wire reaches its elastic limit
the extension increases plastically and Hooke's Law is no longer obeyed.
It stretches by a greater amount for each 2N weight added past this point.
[4 marks]
(b) Calculate the spring constant for the 0 – 6N part of the graph.
The spring constant is the gradient of the straight line part of the graph.
k = F/x ![](../../../../graphics/symbols/nuclides/ticksmall.png)
k = 6/0.03
k = 200
N/m ![](../../../../graphics/symbols/nuclides/ticksmall.png)
[3 marks]
(c) Calculate the work done in stretching the wire to 0.04m.
work done = area under the graph line up to that point
½ x 8 x 0.04
= 0.16
J![](../../../../graphics/symbols/nuclides/ticksmall.png)
OR using
E = ½FΔx
E = ½ x 200 x 0.042 ![](../../../../graphics/symbols/nuclides/ticksmall.png)
E = 0.16
J![](../../../../graphics/symbols/nuclides/ticksmall.png)
[3 marks]
(Total 13 marks)