• A child of mass m sits on top of a rectangular slab of mass M=40 kg, which in turn rests on a frictionless horizontal floor. The slab is attached to a horizontal spring with spring constant k=400 N/m (the other end is attached to the wall), as seen in the figure. The coefficient of static friction between the child and the top of the slab is μs=0.4. When the child and the slab are displaced from the equilibrium position, they oscillate together with simple harmonic motion, with amplitude of A=0.5 m. 
• a) What is the maximum acceleration (magnitude) of the SHM (slab and child) expressed in terms of m,M,k, and A ?
• b) Draw a FBD of the child only. 
• c) What is the minimum mass the child needs to have in order not to slip from the slab? Hint. The force of static friction needs to be larger than mass times maximum acceleration for the child. 
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X- A M 0 -A =0.40 k= 450 N/m www