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A block of mass m=1kg moving on a horizo...

A block of mass `m=1kg` moving on a horizontal surface with speed `v_(i)=2ms^(-1)` enters a rough patch ranging from `x0.10m to x=2.01m`. The retarding force `F_(r)` on the block in this range ins inversely proportional to x over this range
`F_(r)=-(k)/(x) fo r 0.1 lt xlt 2.01m`
`=0` for `lt 0.1m` and `x gt 2.01m` where `k=0.5J`. What is the final K.E. and speed `v_(f)` of the block as it crosses the patch?

Text Solution

Verified by Experts

The correct Answer is:
1
`W=int f_(r)dx=-kIn(2/(0.1))=-1.5 J` `therefore W = Delta K`
`(1)/(2)xx 1 xx v^(2)-(1)/(2) xx 1 xx 4 =-1.5 implies v=1 " ms"^(-1)`
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