Question

a 150 kg person stands on a compression spring with spring constant 10000 n/m and nominal length of 0.50 what is the total length​

Answer 1

The total length is 0.65m.

Step-by-step explanation:

The total length
`x_(tot)` of the spring is equal to its length
`x_0` right now (0.50 m ) plus the amount
`x` by which it is compressed due to weight of the man:

`x_(tot) = x_0+x`

The spring compression is given by Hooke's law:

`F = -kx`

which in our case gives

`-Mg = -kx`

solving for
`x` we get:

`x= (Mg)/(k )`

putting in
`M = 150kg, g= 10m/s^2` and
`k = 10,000N/m` we get:

`x= ((150kg)(10m/s^2))/(10,000N/m^2)`

`x = 0.15m`

Hence, the total length of the spring is

`x_(tot) = 0.50m+0.15m`

`\boxed{x_(tot) = 0.65m.}`