Question

# Two blocks of mass M and m slide along a horizontal table. A constant force F is applied to the block of mass M in a direction parallel to the table, as shown in the diagram below. The coefficient of static friction between the two blocks is µ, and there is no friction between the blocks and the table. The two blocks are not attached to each other, yet the block of mass m does not slide down the side of the block of mass M.

** a.) The diagram below is a free body diagram for the block of mass M. For each of the five arrows labeled on the diagram, clearly identify the corresponding force.(In other words, explain what each of the labels N, F, W, f, and N12 stands for.) Ifa force can come from multiple sources, identify which source the force comes from.

) Draw a free body diagram for the block of mass m. * c.) Using the free body diagrams in parts (a) and (b) and Newton's second law,write equations that relate the net force in the horizontal and vertical directions for each of the two blocks to the acceleration of the blocks in the corresponding direction(four independent equations in total). Write your answers in terms of the masses m and M, the acceleration due to gravity g, the magnitude of the acceleration of the blocks a, and the labels on the free body diagram in part (a).

d.) Write either a correct equation or a correct inequality that relates a normal force and a frictional force in this context of this problem. Write your answer in terms of u and the labels on the free body diagram in part (a).* ** e.) Using the equations from parts (c) and (d), solve for the minimum force F necessary for the block of mass m not to slide down the side of the block of mass M.Write your answer in terms of m, M, µ, and the acceleration due to gravity g.

** f.) In everyday non-physics language, and without including any computations or equations, explain why the block of mass m “levitates" alongside the block of mass M. ***g.) Explain why the answer you found in part (d) is the minimum force necessary and not the maximum force necessary.

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