Question

A marble column of cross-sectional area 1.3 m2 supports a mass of 21400 kg . The elastic modulus for marble is 5.0×1010N/m2. By how much is the column shortened if it is 7.9 m high? Express your answer to two significant figures and include the appropriate units.

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Mass supported by the marble column = M = 21400 kg

Weight supported by the marble column = W

W = Mg

W = (21400)(9.81)

W = 209934 N

Elastic modulus of marble = E = 5 x 10¹⁰ N/m²

Cross-sectional area of the marble column = A = 1.3 m²

Length of the marble column = L = 7.9 m

Amount the marble column is shortened by = L

Stress in the marble column = = W/A

Strain in the marble column = = L/L

L = 2.6 x 10^-5 m

Amount the marble column is shortened by = 2.6 x 10^-5 m