Question

A block moving on a rough horizontal surface comes to rest after moving for a time To.the ratio of work done by force of friction in first half to that in next half time.

Answer 1

Answer:

Frictional force =μN=μmg=(μ

0

+αx)mg

W= work done by the frictional force

=−∫

0

x

(μ

0

+αx)mgdx=−mg(μ

0

.x+

2

αx

2

)

Applying work energy theorem

Work done =ΔK

−mg(μ

0

.x+

2

αx

2

)=

2

1

mv

2

−(

2

1

)mv

0

2

2

1

mv

2

=(

2

1

)mv

0

2

−mg(μ

0

.x+

2

αx

2

)