Question

masses m1 and m2 are stacked together on a level surface that has friction. The blocks are accelerating together to the right. There is static friction between the two blocks. Analyze the forces on each block

Answer 1

let mass m1 is on the bottom and mass m2 is on the top.

as no friction coefficient values are provided, assume that all surfaces have kinetic friction coefficient mu.

let pulling/pushing force is horizontal and of magnitude F.

then total friction force offered to both the blocks=friction coefficient*normal force

=mu*(m1+m2)*g

assuming F is greater than this friction force value,

net force on the blocks=F-mu*(m1+m2)*g

then acceleration of the blocks=total force/total mass

=(F-mu*(m1+m2)*g)/(m1+m2)

now, for the top block, the only force acting on it is friction force due to contact with mass m1

hence friction force=m2*acceleration

=m2*(F-mu*(m1+m2)*g)/(m1+m2)

so the key points are:

acceleration is determined by (force acting on the blocks -friction force on the blocks)/combined mass

friction force between the blocks is keeping the block m2 in contact with m1 and acts in the direction of motion

this friction force is responsible for driving mass m2

and friction force value is given by m2*acceleration of the blocks