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Two masses are connected to one another with a massless rope that passes over a massless...

Two masses are connected to one another with a massless rope that passes over a massless and frictionless pulley as shown in the figure below. When the two mass system is released from rest, the hanging mass m2 = 31.5 kg accelerates upward at a rate of 2.3 m/s2. The coefficient of kinetic friction between m1 and the incline is 0.08, and the angle of inclination of the ramp is 57 degrees. For the entirety of this problem, air resistance can be neglected


  • a. (7.5 points) Draw a free-body diagram of m2. Label the different types of forces acting on this mass along with their directions. Calculate the value(s) for any force(s) that has/have an explicit equation.
  • b. (10 points) Use your free-body diagram from part a and one of Newton's Laws to determine the magnitude of the tension in the rope.
  • c. (7.5 points) Draw a free-body diagram of m1. Label the different types of forces acting on this mass along with their directions.
  • d. (10 points) Use your free-body diagram from part c and one of Newton's Laws to construct an equation that relates the magnitude of the normal force acting on m1to its mass.
  • e. (15 points) Use your free-body diagram from part c, one of Newton's Laws in a different direction, and your answer to part d to solve for the mass of m1.
  • f. (20 point) If the two mass system is released from rest, how far does m1 have to slide down the incline for the the centripetal acceleration on the rim of the pulley to be equal to three times the acceleration due to gravity on Earth. You can assume that there is no slipping between the rope and the pulley. Take the radius of the pulley to be 0.15 m.



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Answer #1

Since the figure isn't given, I will try to draw the figure based on the description.

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