A steel wire is used to lift heavy object. The cable has a diameter of 14.25 mm and an initial length of 33.5 m. If the cable stretches 2.50 mm, what is the mass of the heavy object? Use 20.0 x 10^10 Pa for Young’s modulus for steel. Give your answer in kg and with 3 significant figures.

20E10=(9.8*Mass)33.5/(.0025*PI(.001425/2)^2)

solving for mass
mass=20E10*(.0025*PI(.001425/2)^2)/33.5*9.8) kg
I get about 233kg
check my work

To calculate the mass of the heavy object, we first need to determine the strain in the steel wire. Strain is defined as the change in length divided by the original length. In this case, the strain (ε) is given by:

ε = (change in length) / (original length)

Given that the cable stretches 2.50 mm and the initial length is 33.5 m (which is equal to 33,500 mm), we can calculate the strain as:

ε = (2.50 mm) / (33,500 mm)

Next, we need to find the stress in the steel wire. Stress (σ) is defined as the force applied divided by the cross-sectional area. The force applied is the weight of the heavy object, and the cross-sectional area is related to the diameter of the wire.

The cross-sectional area (A) of a wire with diameter (d) is given by:

A = (π/4) * d^2

Substituting the given diameter of 14.25 mm into the equation, we can calculate the cross-sectional area of the wire:

A = (π/4) * (14.25 mm)^2

Now, we can determine the stress using the Young's modulus (E) of the steel wire. Stress is given by:

σ = ε * E

Substituting the known values, we get:

σ = (2.50 mm / 33,500 mm) * (20.0 x 10^10 Pa)

Finally, we can calculate the force applied to the wire by multiplying the stress by the cross-sectional area:

Force = σ * A

Once we have the force, we can determine the mass (m) of the heavy object using the equation:

m = Force / g

where g is the acceleration due to gravity.

Solving for the mass using the provided information will give us the answer to the question.