Question

a spring of spring constant k=12.5N/m is hung vertically. a 0.500kg mass is then suspended from the spring. what is the displacement of the end of the spring due to the wieght of the 0.500 kg mass?

Answer 1

The displacement of one end of the spring due to weight = 0.4 m.

Step-by-step explanation:

Given :

Spring constant
`(k) = 12.5 (N)/(m)`

Mass
`(m) = 0.5 kg`

From the hooke's law,

Force is proportional to the negative of the displacement.

`F` ∝
`-x`

`F = -kx`

Where minus sign represent that, the force is always directed toward mean position.

Now one force is gravity
`mg` acts as a downward. so we write,

`mg = kx`

Here we take only magnitude.

`x = (mg)/(k)`

Where
`x =` displacement of one end of spring,
`g = 10 (m)/(s^(2) )`

`x = (0.5* 10)/(12.5)`

`x = 0.4` m