A block of mass m = 4 kg is placed on top of a block of mass M = 2 kg. The lower block M rests on a frictionless horizontal surface. A horizontal spring of spring constant k = 120 N/m is attached to the UPPER block m and a rigid wall. The coefficient of static friction between the two blocks is = 0.3 . If the system is set into oscillation, what is the maximum amplitude (in cm) for which the lower block does not slip

Step-by-step solution

When the two blocks oscillate together without slipping, they move with a common acceleration. The angular frequency of the system is: ^2 = k M+m = 120 2+4 = 120 6 = 20 rad/s ^2 Since the spring is attached to the upper block, the only horizontal force acting on the lower block M is the static friction between the two blocks. For the lower block to not slip, the required frictional force must be less than or equal to the limiting static friction. The limiting static friction depends on the normal force between the