Note: You can do these problems on paper if you wish!

  1. Two blocks, A and B, are tied together with a rope of mass M. Block B is being pushed with a constant horizontal force as shown in the figure below.

    Assume that there is no friction between the blocks and the table and that the blocks have already been moving for a while at the instant shown.

    1. Describe the motions of block A, block B, and the rope.

    2. Draw a separate free-body diagram for each block and for the rope. Describe your free-body diagram in words by specifying the type of force, the object on which the force is exerted, and the object exerting the force.

    3. Identify all the Newton's Third Law (action-reaction) force pairs in your diagrams.

    4. Compare the magnitudes of the horizontal components of all forces on your diagrams. Identify those forces which have the same magnitude. Explain your reasoning in arriving at this comparison.

    5. Consider the horizontal components of the forces exerted on the rope by blocks A and B. Is your answer above for the relative magnitude of these components consistent with your knowledge of the net force on the rope?

  2. Assume the blocks for problem 1 are now connected by a very light, flexible, and inextensible string of mass m where m < M.
    1. If the motion of the blocks is the same as in problem 1, how does the net force on the string compare to the net force on the rope?

    2. Determine whether the net force on the following objects is greater than, less than, or equal to the net force on them in problem 1:
      1. block A
      2. block B
      3. and the system composed of the blocks and the connecting rope or string.
      Explain your answers to the above.

    3. Compare the horizontal components of the following pairs of forces:
      • the force on the string by block A and the force on on the rope by block A. Explain.
      • the force on the string by block B and the force on the rope by block B. Explain.

    4. Suppose the mass of the string that connects blocks A and B becomes smaller and smaller, but the motion remains the same as in problem 1. What happens to:
      • the magnitude of the net force on that connecting string?
      • the magnitude of the forces exerted on that connecting string by blocks A and B?

    5. A string exerts a force on each of the two objects to which it is attached. For a massless string, the magnitudes of both forces are often referred to as the ``tension in the string''.

      Justify the use of this terminology, in which a single value is assumed for the magnitudes of both forces.

    6. If you know that the net force on a massless string is zero, what can you infer about its motion?