Homework H5.H - Fa22

Problem statement
Solution video


Discussion and hints:

Recall the following four-step plan outline in the lecture book and discussed in lecture:

Step 1: FBDs
Draw a single free body diagram for the system made up of block A, the disk and the pulley combined.

Step 2: Kinetics (work/energy)

  • Write down the kinetic expressions for the block, disk and pulley individually, and then add those together to find the total KE for the system of your FBD. For each KE expression, recall that your reference point for the rotational component needs to be either the center of mass of the body, or a fixed point on the rigid body. You might consider using the no-slip, rolling contact point C as your reference point for the disk.
  • Do the same for the potential energies: write down the PEs for each body individually and add together.
  • Also, based on your FBD above, which, if any force, does nonconservative work on the system in your FBD? Determine work for such a force.

Step 3: Kinematics
Note that the instant center (IC) for the disk is the no-slip contact point C. (Carefully study either the animation above - you can actually see the IC from this!) Locating this IC is critical for you in setting up and using the kinematics for this problem. What is the speed of point B on the disk as compared to the disk's center E? (Refer back to C being the IC for the disk.) See the freeze-frame image below, and compare the speed of B with that of A.

Step 4: Solve
Solve your equations above for the speed of block A.

Any questions?

5 thoughts on “Homework H5.H - Fa22”

  1. How do I determine the motion of block A on release? Can I use the overall FBD of the system to do that or should I use individual FBDs? Or is there a different way to do it?

    1. I think we are supposed to use Newton/Eulers first to determine the rotation of the pulley and thus the direction of block A. Then you can solve for speed with the work-energy equations.

    1. I am not entirely sure but looking at the simulation they have under hints it looks like the point directly above B and to the right of O has a different velocity vector compared to at B.

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