A 3-m long wire with a diameter of 1.5 mm has a Young's modulus of 9 $\times$ 10¹⁰N/m².What mass hung from the wire would extend it by 3 mm? A)159 kg B)5.20 kg C)16.2 kg D)64.8 kg E)None of the above

Question

Quizplus · Accepted Answer

The formula for the elongation of a wire is:

ΔL = (F * L) / (A * E)

where ΔL is the change in length, F is the force applied, L is the original length, A is the cross-sectional area of the wire, and E is the Young's modulus.

We can rearrange this formula to solve for the force:

F = (ΔL * A * E) / L

Plugging in the given values, we get:

F = (0.003 m * π * (0.0015 m/2)^2 * 9 * 10^10 N/m^2) / 3 m
F ≈ 210.7 N

To convert this force to mass, we can use the formula:

F = m * g

where m is the mass and g is the acceleration due to gravity (9.81 m/s^2).

Solving for m, we get:

m = F / g
m = 210.7 N / 9.81 m/s^2
m ≈ 21.5 kg

Therefore, the correct answer is closest to option C, which is 16.2 kg.

A 3-M Long Wire with a Diameter of 1 ×\times× 1010 N/m2

A 3-M Long Wire with a Diameter of 1 $\times$ 10¹⁰N/m²