Question

Can someone help with a friction problem in mechanics?

Answer 1

What do you need help with?

Answer 2

A small box rests on top of a large box. The two boxes accelerate forward at 2.5 m/s^2. There is no slippage between the two boxes. What is the minimun value of the coefficient of static friction between the boxes? (No forces or masses are given.)

Answer 3

If there's no slippage with the acceleration, then the friction force between the small box and the large box has to at least equal the force on the small box generated by the acceleration. The force of acceleration on the small box is:\[F=m _{s}a=(2.5\frac{ m }{ s ^{2} })m _{s}\]The frictional force exerted by the small box is:\[F _{f}=\mu _{k}m _{s}g=\mu _{k}F _{n}\]Equate F andFf and solve for μk:\[F=F _{f}\]\[2.5m _{s}=\mu _{k}m _{s}g\]\[\mu _{k}=\frac{ 2.5m _{s} }{ m _{s} g}\]\[\mu _{k}=\frac{ 2.5 }{ g }=\frac{ 2.5 }{ 9.8 }=0.255\]

Answer 4

Nice. Thank you.