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Set up the free-body diagram and the equations for Newton's 2 nd law for each object along each axis. Assume friction is present between all surfaces and the coefficient of friction is different between the different surfaces. (Note you should have 2 free body diagrams)

Set up the free-body diagram and the equations for Newton's 2 nd law for each object along each axis. Assume friction is present between all surfaces and the coefficient of friction is different between the different surfaces. (Note you should have 2 free body diagrams)

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Set up the free-body diagram and the equations for Newton's 2 nd law for each object along each axis. Assume friction is present between all surfaces and the coefficient of friction is different between the different surfaces. (Note you should have 2 free body diagrams)

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Consider two blocks M1 on top of M2 on a level table. There is no friction between block M2 and the table, but there is friction between block M1 and block M2. Denote the coefficients of static and kinetic friction between the blocks as μs and μk, respectively. The applied force F is applied to block M1 at an angle θ below the horizontal. The blocks start from rest. First, we will consider the situation where F is small enough that the two blocks stick together. (a) Draw free-body diagrams for the two masses. Be sure to label all forces and the direction of the accelerations. Also be sure to define an appropriate coordinate system for each free-body diagram. (b) Write down the Newton's second law equations for each block and each dimension (x and y). (c) Write down an inequality relating the force of friction and the normal force. (d) Identify the two Newton's third law pairs - i. e. the pairs of forces between the two blocks that are equal and opposite. (e) Find the acceleration of the blocks as a function of F, θ, M1, M2, g, μs, and μk. (You don't have to use all of these, but you will use at most these. ) (f) Find a condition on F such that the blocks stick together. i. e. Write an inequality in the form F ≤ Fmax for the blocks to stick together where Fmax is in terms of θ, M1, M2, g, μs, and μk.
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A small block of mass m rests on the rough, sloping side of a triangular block of block of mass M which itself rests on a horizontal frictionless table (see the figure). The rough incline surface has a coefficient of static friction μs. A) Suppose that you apply a horizontal force F to push the triangular block (see the figure). Explain what will happen to the small block if the applied force F is relatively small. You gradually increase force F, and explain what will eventually happen to the small block as the force is sufficiently large. B) Draw a free body diagram for each of the blocks m and M. What is the direction of acceleration of these two blocks when they stick and move together? How many forces act on each of the blocks m and M? How many Newton's 3rd law force pairs are there in these two free body diagrams? Set up a coordinate system fixed to the table. Is the block M an inertial frame? C) Determine the minimum horizontal force F such that the small block will start moving up the incline. Draw coordinate systems, and write down intermediate steps with equations.
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