When a 125-kg piece of equipment is hung from a steel wire of length 75 cm,it stretches the wire by 4.00 mm.If instead the wire had a length of 150 cm,but all else were the same,by what distance would the same equipment stretch the wire?
A)16.0 mm
B)8.00 mm
C)4.00 mm
D)2.00 mm
E)1.00 mm

Question

Quizplus · Accepted Answer

The change in length of the wire, ΔL, is proportional to the original length of the wire, L, and the weight hanging from it, F: ΔL ∝ FL. Therefore, we can write:

ΔL = kFL

where k is a constant of proportionality that depends on the wire's material, cross-sectional area, and other properties.

We can use the given data to find k:

4.00 mm = k(125 kg)(0.75 m)

k = 7.11 × 10^-3 N/m

Now we can use this value of k to find the new elongation when the wire is longer:

ΔL' = kFL' = (7.11 × 10^-3 N/m)(125 kg)(1.50 m) = 1.69 mm

Therefore, the equipment would stretch the longer wire by 1.69 mm (choice B).

When a 125-Kg Piece of Equipment Is Hung from a Steel