Find acceleration

Question

A 60 kg block slides along the top of a 100 kg block. The lighter block has an acceleration of 3.4 m/s² when a horizontal force F= 400 N is applied. Assuming there is no friction between the bottom 100 kg block and the horizontal frictionless surface but there is friction between the blocks. Find the acceleration of the 100 kg block during the time the 60 kg block remains in contact.

Answer 1

Since 400/3.4 = 117.6 Kg and NOT 60 Kg it must be assumed that some of the 400 N force is used to accelerate the 100 Kg block as well but not both equally. Also, the top block will sense a frictional force and it doesn't matter if the bottom block moves or not. So, make a free body diagram and recognize that the friction between the two blocks opposes the 400 N force and the resulting equation will be ma=friction or 60*3.4= f (frictional force) = 204 N. This same frictional force will accelerate the lower block and the equation becomes 100a=204 N. Solving to find a= 2.04 m/s^2 for the 100 Kg block.