A cart of mass M on frictionless wheels will be pushed with a constant force F.

Question

A cart of mass M on frictionless wheels will be pushed with a constant force F. A block of mass m is placed on top of the cart. There is friction between the cart and the block.

If the block does not slide against the cart

a. What is the maximum acceleration of the block?

b. What is the maximum force the can be applied to the cart? If the block does slide against the cart,

c.What is the acceleration of the block?

d. What force is required to accelerate the cart at twice the acceleration of the block if the cart mass is twice that of the block?

Explanation / Answer

a) The maximum frictional force between cart and block with out slipping is µmg

therfore max acceleration of block is µmg/m = µg

b) the force applied to the cart is µ(m+M)g

c) acceleration of the block is (F + µmg) / m

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