Question

The 200g mass is replaced with 100g mass. What is the new length of the spring?

Answer 1

Answer on Question #42205

Physics - Mechanics | Kinematics | Dynamics

Question:

The 200g mass is replaced with 100g mass. What is the new length of the spring?

Solution:

The Hook's law for a spring is

$$F = k \Delta x.$$

In our case extension of a spring is caused by gravity. So, if $m_{1} = 200g$, the initial length of a spring can be determined by the following procedure:

$$k \Delta x _ {1} = m _ {1} g \Rightarrow \Delta x _ {1} = \frac {m _ {1} g}{k}.$$

The same for the second mass $m_{2} = 100g$:

$$\Delta x _ {2} = \frac {m _ {2} g}{k}.$$

So, one conclude that

$$\frac {\Delta x _ {2}}{\Delta x _ {1}} = \frac {m _ {2} g / k}{m _ {1} g / k} = \frac {m _ {2}}{m _ {1}} = 0.5.$$

Answer:

The length of a spring is a half of the initial length.