Question

A solid steel cylinder is standing (on one of its ends) vertically on the floor. The length of the cylinder is 4.0 m and its radius is 67 cm. When an object is placed on top of the cylinder, the cylinder compresses by an amount of 5.1 10-7 m. What is the weight of the object?

Answer 1

Answer:

W=35955 N

Explanation:

In an elastic material like steel when deformation takes place then the stress ( σ ) produced in the material is directly proportional to the strain ( ∈

therefore young  modulus=stress/strain

y=σ/∈

y$y=\frac{f/a}{e/l}$

f=external force

A is the cross-sectional area

L is the original length

Δ L  is the elongation

young modulus of steel 200 Gpa

$200*10^{9} =\frac{f/\pi *r^2}{e/dl}$

$200*10^{9} =\frac{f/\pi *.67^2}{5.1*10^-7/4}$

200*10^9=f/1.41/(5.1*10^-7/4)

f=200*10^9*1.41*(5.1*10^-7/4)

f=35955 N

which is equal to the weight of the body