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Nov 3, 2008

Homework Problem 6/79

Suggestions:
  1. FBD: The free body diagram will include friction force (up the incline), normal force and weight force. Recommend x-axis along incline.
  2. Newton-Euler: Write down Newton equation for x- and y-components. For Euler equation use center of mass G for summation of moments.
  3. Kinematics: The problem does NOT say if the cylinder slips as it rolls. You will need to make an assumption one way or the other. Then check your assumption. Recommend that you assume NO SLIP. Use kinematics equation between G and the no-slip contact point C to relate aG to alpha.
  4. Solve: Solve kinetics and kinematics equations for normal and friction froces as well as aG. CHECK your no-slip assumption above (compare the friction force found with mus*N). If you find that the cylinder slips (f > mus*N), then the no-slip kinematics is not valid. Resolve with friction = muk*N.
Any questions?

4 comments:

kyle brooks said...

i dont really understand teh kinematic steps we need to take to get tehe solution on this problem, anyone with any advice it would be greatly appreciated.

CMK said...

Recall that you do not know at the beginning if the cylinder rolls without slipping or slips as it rolls down the incline.

If NO SLIP:
In this case the contact point C does not slip as the cylinder rolls. This says that aC = aC*j (j is the unit vector perpendicular to the incline). Also, you know that G moves only along x, or aG = aG*i. From this, you can write:

aG = aC + alpha x rG/C - omega^2*rG/C

OR

aG*i = aC*j + (alpha*k) x (R*j) - omega^2*(R*j)

Using the x-components:
aG = - alpha*R


If the cylinder SLIPS:
In this case, there are no usable kinematics from the cylinder (aG is NOT equal to -R*alpha). However, you use f = muk*N to solve.

Good question.


Does this help?

Nick Powell said...

so assuming no slip is it correct to have N -mgcos = 0 since Agy is 0?

nour said...

Nick i think that u can write N-mgcos40=0 anyway because the disk is only sliding on the ramp supposedly.
If i m wrong please someone correct me.