Question

A spring scale hung from the ceiling stretches by 5.2 cm when a 2.0 kg mass is hung from it. The 2.0 kg mass is removed and replaced with a 2.2 kg mass.
What is the stretch of the spring?

Answer 1

Physics - Damon, Wednesday, December 9, 2015 at 5:13am
F = k x

k = 2 g/6.1 cm

2.5g = (2g/6.1cm) x

x = 6.1 (2.5/2) cm

Answer 2

The ideal spring equation is

                               Stretch  =  K  times  Force  .

This says that the stretch is directly proportional to the force.
In simple English, that means that if you double the force, then
you double the stretch, and if you multiply the force by  π  or
any other number, you multiply the stretch by the same number.

So you can always write a proportion for a spring:

                 Stretch₁ / Force₁  =  Stretch₂ / Force₂ .

In this question, the force is increased to  (2.2 / 2.0) =  1.1 times .

So the stretch is also increased to  1.1 times .

                 (1.1) x (5.2 cm)  =  5.72 cm  .