A Levels Physics

A metal cube of side l is placed in a vice and compressed elastically by two opposing forces F.
F-
F
metal cube
How will Al, the amount of compression, relate to 1?
A Aloc 1
12
1
B Alx !
C Δl
D Alc 12


Choice B is correct because:

Young modulus (E) = Stress (S) / Strain (ε)

Strain (ε) = Compression of the cube (Δl) / Original length of cube (L)

Stress (S) = Force applied on cube (F) / Cross-sectional area of cube (A)

Young Modulus (E) = [Force applied on cube (F) x Original length of cube (L)] / [Cross-sectional area of cube (A) x Compression of cube (Δl)]

Force applied on cube (F) = F N

Original length of the cube (L) = l m

Cross-sectional area of cube (A) = l2 m2

Compression of the cube (Δl) = Δl m

E = (F x l) / (l2 x  Δl)

E = F / (l x Δl)

Δl = F / (l x E)

Δl ∝ 1 / l (F & E are constant)

Choices A, C & D are incorrect because they do not correctly state the relationship between Δl & l as Δl ∝ 1 / l.

Young's Modulus | 2011 - O/N - 9702/11 | Q26