young's modulus a level physics

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#1
Could someone please solve this (it's from an mcq paper 970_m16_qp_12 question 19):
A 50 cm length of copper wire of diameter 2.0 mm is joined to a 50
cm length of steel wire of diameter 1.0 mm, making a combination wire of length 1.0 m (copper above steel)
The combination of wire is stretched by a weight added to it's end. both copper and steel obey hooke's law. what is the ratio of extension of steel to extension of copper.
The answer is 2 but how?
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1 year ago
#2
(Original post by simplysuga)
Could someone please solve this (it's from an mcq paper 970_m16_qp_12 question 19):
A 50 cm length of copper wire of diameter 2.0 mm is joined to a 50
cm length of steel wire of diameter 1.0 mm, making a combination wire of length 1.0 m (copper above steel)
The combination of wire is stretched by a weight added to it's end. both copper and steel obey hooke's law. what is the ratio of extension of steel to extension of copper.
The answer is 2 but how?
The questions says the young modulus of steel is twice the young modulus of copper. You didnt add this very important detail.

Young modulus = f × l / A × e

L and f for both the materials is common.

(E of steel) = 2 × (E of copper)

f × l / A of steel × e (steel) = 2 × f × l / A of copper × e (copper)

f × 50 / A × e (steel) = 2 × f × 50 / A × e (copper)

1 / A of steel × e (steel) = 2 / A of copper × e (copper)

A of copper / A of steel × 2 = e (steel) ÷ e (copper)

(π ÷ 4 × 2^2) / 2 × (π ÷ 4 × 1^2) = e (steel) ÷ e (copper)

4 / 2 = e (steel) / e (copper)

e (steel) / e (copper) = 2
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