Question

If a 24-kg mass stretches a spring 15 cm, what mass will stretch the spring 10 cm

Answer 1

16kg

Explanation:

This problem is borers on elasticity of materials.

according to Hooke's law, "provided the elastic limit of an elastic material is not exceeded the the extension e is directly proportional to the applied force."

`F= ke`

where F is the applied force in N

k is the spring constant N/m

e is the extension in meters

Given data

mass m= 24kg

extensnion=15cm in meters=
`(15)/(100)`=
`0.15m`

we can solve for the spring constant k

we also know that the force F = mg

assuming
`g=9.81m/s^(2)`

therefore

`24*9.81=k*0.15\\235.44=k*0.15\\k=(235.44)/(0.15) \\k=1569.6N/m\\`

We can use this value of k to solve for the mass that will cause an extension of
`10cm= 0.1m`

`x*9.81=1569.6*0.1\\\\x= (156.96)/(9.81) \\\x= 16kg`