Question

What is the distance a spring of stiffness `k` must be depressed if it supports an object of mass `m` on a friction-less inclined plane at an angle `theta`?

Answer 1

`\frac{mg\sin\theta}{k}`

Explanation:

The force `F` acting against the spring supporting an object of mass `m` on a plane inclined at an angle `\theta` with the horizontal, is given as

`F=\text{component of weight mg down the inclined plane}`

`F=mg\sin\theta`

Now, the depression in the spring due to a compressive force `F`

`\frac{\text{force}}{\text{stiffness}}`

`=\frac{F}{k}`

`=\frac{mg\sin\theta}{k}`