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 1010 Pa for Young’s modulus for steel. Give your answer in kg and with 3 significant figures.

To find the mass of the heavy object, we need to apply Hooke's law, which relates the force applied to a spring or elastic material to the displacement it undergoes. In this case, the cable stretches due to the weight of the object hanging from it.

First, let's find the amount by which the cable has stretched relative to its original length. We know that the initial length of the cable is 33.5 m, and it stretches 2.50 mm. So, the change in length, ΔL, is given by:

ΔL = 2.50 mm = 2.50 x 10^(-3) m

Next, we can calculate the strain (ε) using the formula:

ε = ΔL / L

Where L is the initial length of the cable.

ε = (2.50 x 10^(-3) m) / (33.5 m)

Now, to calculate the stress (σ) on the cable, we use the formula:

σ = Y * ε

Where Y is the Young's modulus of the material.

Y = 20.0 x 10^10 Pa

σ = (20.0 x 10^10 Pa) * [(2.50 x 10^(-3) m) / (33.5 m)]

Finally, we can use the stress to find the force applied to the cable using the formula:

F = A * σ

Where A is the cross-sectional area of the cable.

The diameter of the cable is given as 14.25 mm, so the radius (r) is half of the diameter:

r = 14.25 mm / 2 = 7.125 mm = 7.125 x 10^(-3) m

The area (A) of a cylindrical cable is given by:

A = π * r^2

A = π * (7.125 x 10^(-3) m)^2

With the area calculated, you can now find the force (F) applied to the cable.

Once you know the force acting on the cable, you can determine the mass of the heavy object by dividing the force by the acceleration due to gravity (9.8 m/s^2).

The mass (m) of the object is given by:

m = F / g

Where g is the acceleration due to gravity.

Substituting the appropriate values and performing the calculations will give you the mass of the heavy object.