Homework H5.B - Fa22

Problem statement
Solution video

DISCUSSION THREAD

Any questions??


For Part (a), the coefficient of static friction between the sphere and the ramp is sufficiently large that the sphere does not slip as it rolls. Here f ≠ μkN.

For Part (b), the coefficient of friction is reduced such that slipping does occur. Here f = μkN.

Can you see the difference in rotational motion of the sphere between the no-slip and slipping cases?

Four-step plan:

Step 1 - FBD: Draw a free body diagram of the sphere. Take care in getting the direction of the friction force on the sphere correct.

Step 2 - Kinetics: Write down the Newton/Euler equations for the sphere. Be careful with your moment equation - it is recommended that you use a moment equation about the center of mass of the sphere.

Step 3 - Kinematics: For Part (a), C is a no-slip point. Relate the angular acceleration of the sphere to the acceleration of G. For part (b), C is NOT a no-slip point. You cannot relate the angular acceleration back to the acceleration of G through kinematics. Instead you need to use: f = μkN.

Step 4 - Solve

 

One thought on “Homework H5.B - Fa22”

  1. For part b, how are we supposed to relate the angular acceleration with the acceleration of the center of gravity without using kinematics and using friction ?

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