Question

Two circular rods, one steel and the other copper, are both 0.760 m long and 1.50 cm in diameter. Each is subjected to a force with magnitude 3850 N that compresses the rod.

Part A

What is the difference in the length of the two rods when compressed?

Express your answer in meters to two significant figures.

Δℓ =

nothing

  m  

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Answer 1

Young's modulus of steel = 200 GPa = 200e9 Pa

Young's modulus of copper = 130 GPa = 130e9 Pa

Note , 1 Pa =  ‎kg⋅m⁻¹⋅s⁻²

We know that

young's modulus = stress / strain

For steel,

stress = F/A = 3850 / 1.767e-4 = 2.178e7 N/m²

For copper also,

stress = 2.178e7 N/m²

Now,

For steel

200e9   = 2.178e7 * 0.760 m / L

L = 8.2764e-5 m

For copper

130e9 =  2.178e7 * 0.760 m / L

L = 1.273e-4 m

difference in length is 4.453e-5 m ( please check this) the method is absolutely correct.