Forces and Motion
6 marks · NormalYou investigate how the extension of a metal spring varies with the force applied. The table shows your results.
| Force/N | Extension/cm |
|---|---|
| 0.0 | 0.0 |
| 2.0 | 1.5 |
| 4.0 | 3.0 |
| 6.0 | 4.5 |
| 8.0 | 6.0 |
State the SI unit for extension in this experiment.
Plot a graph of force (vertical axis) against extension (horizontal axis). Draw the best-fit straight line and label axes with correct units.
Explain why the graph is a straight line that passes through the origin.
Describe what will happen if the force applied is increased well beyond 8.0 N.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) metre (m) · must show 'metre' or 'm' accepted, accept 'cm' if justified by table, but SI unit is m
(b) Straight line graph through origin; axes: Force (N), Extension (cm or m) · must show axes correct units and scale, data points correctly plotted, best-fit straight line, starts at origin
(c) The direct proportionality between force and extension in the initial region shows the spring obeys Hooke’s law: extension is proportional to force when within the elastic limit. No force, no extension, so line goes through origin. · must show mentions proportionality/Hooke's law, refers to extension and force being directly proportional, states line passes through origin (no force means no extension)
(d) The spring will go beyond its elastic limit: the extension will increase rapidly, not proportional to force, and the spring may not return to its original length (plastic or permanent deformation). · must show description of elastic limit or plastic deformation, reference to non-linear relationship beyond limit
Must show: axes labelled: Force (N), Extension (cm or m), origin included, straight line through points
Show mark scheme and worked solution
Marking points
B1 (a) · 1 mark · States correct SI unit for extension: metre (m).
P1 (b) · 1 mark · Axes labelled with correct quantities and units; correct scale; points correctly plotted.
P2 (b) · 1 mark · Best-fit straight line through the origin drawn.
B2 (c) · 1 mark · Correctly explains that force is proportional to extension (Hooke's law) in initial region.
B3 (c) · 1 mark · Refers to the graph passing through the origin: no force means no extension.
B4 (d) · 1 mark · Mentions loss of proportionality or plastic deformation if limit is exceeded.
Worked solution
a) The SI unit for extension is metre (m).
b) The correct axes are: Vertical axis: Force (N); Horizontal axis: Extension (cm or m). Points (0,0), (1.5,2.0), (3.0,4.0), (4.5,6.0), (6.0,8.0) plotted. Draw a straight line of best fit through the origin.
c) The graph is a straight line through the origin because, for a metal spring in the elastic region, force is directly proportional to extension. This is Hooke’s law. When no force is applied, there is no extension. (F = kx)
d) If the force is increased well beyond 8.0 N, the spring will pass its elastic limit. The extension will increase disproportionately, the line will curve, and the spring will not return to its original length when the force is removed (plastic deformation).