HOOKE'S LAW
3 marks · NormalA metal wire is stretched by attaching weights. The original length of the wire is 50.0 cm. With a 10 N force, the length becomes 50.8 cm.
Calculate the extension of the wire.
If the extension is proportional to the force for this wire, what would its length be when a 25 N force is applied?
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(a) 0.8 cm
(b) 52.0 cm
Common mistakes: Reversing subtraction when finding extension; Incorrect use of ratio for proportionality
Show mark scheme and worked solution
Marking points
A1 (a) · 1 mark · Correct calculation of extension: 50.8 cm – 50.0 cm = 0.8 cm.
M1 (b) · 1 mark · Finds extension for 25 N using proportionality (sets up correct ratio/calculation). (follow-through)
A2 (b) · 1 mark · Gives correct new length: 52.0 cm (adds calculated extension to original length). (follow-through)
Worked solution
(a) Extension = 50.8 cm – 50.0 cm = 0.8 cm.
(b) 10 N causes 0.8 cm extension. Force and extension are proportional.
x = (0.8 / 10) × 25 = 2.0 cm extension.
So, new length = 50.0 cm + 2.0 cm = 52.0 cm.