Question

A 0.38 kg mass is attached to a spring with a spring constant 106 N/m so that the mass is allowed to move on a horizontal frictionless surface. The mass is released from rest when the spring is compressed 0.109 m. Find the maximum force on the mass. Answer in units of N.

Answer 1

Answer:11.55 N

Step-by-step explanation:

Given

mass
`m=0.38 kg`

Spring constant
`k=106 N/m`

initial compression
`x=0.109 m`

mass will perform simple harmonic motion with general equation of motion given by

`x=A\sin \omega t`

where
`x=Position\ of\ Mass`

`A=maximum\ Amplitude`

`\omega =Natural\ frequency\ of\ oscillation=\sqrt{(k)/(m)}`

`\omega =16.70 rad/s`

`t=time`

therefore acceleration is given by

`a=-A\omega ^2\sin \omega t`

`a_(max)=A\omega ^2`

initial compression is equivalent to max amplitude

thus
`A=0.109 m`

`a_(max)=A\omega ^2=0.109* (16.70)^2=30.405 m/s^2`

therefore Maximum Force
`F=ma_(max)`

`F=0.38* 30.405=11.55 N`