Question

A force `F` acts on an object (mass=1 kg) which is initially at rest as shown in the figure. Draw the graph showing the momentum of the object varying during the time for which the force acts.

Answer 1

Correct Answer - `F=100t" "0letle50ms`
`F=10-100t" "50msletle100ms`
Using `F=(dp)/(dt)`
For `0msletle50ms`
`rArr(dp)/(dt)=100t" "rArr" int_(0)^(p)dp=100int_(0)^(t)"t dt"`
`rArrp=50t^(2)` for `0letlems`
`rArrP_(50ms)=50((50)/(1000))^(2)=(50)/(400)=(1)/(8)=0.125Ns`
For `50msletle100ms`
`int_(0.125)^(p)dp=int_(0.125)^(p)(10-100)dt`
`p-0.125=10(t-(1)/(20))-50(t^(2)-(1)/(400))`
`p=0.125+10(t-(1)/(20))-50(t^(2)-(1)/(400))`
`P_(100ms)=0.25Ns`