What is the minimum mass m that will stick and not slip?

  • Thread starter mugzieee
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  • #1
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a block of mass m is resting on a 20degree slope. The block has coefficients of friction mu_s =0.80 and mu_k =0.50 with the surface. It is connected via a massless string over a massless, frictionless pulley to a hanging block of mass 2.0 kg. (sorry didnt know of a way to distribute a picture)
what is the minimum mass m that will stick and not slip?

i drew 1 free body diagrams of the mass m and mass 2.
For the FBD of m1:
I have normal force, kinetic friction,static friction, the weight components of the mass, and the force of the second mass acting on the first one.

For the FBD of m2:
I have just the force acting on ms from m1, and the weight of m2.

im not quite sure if the block is accelerating kuz it says resting, but then again im given coefficients of frictional forces. also can i equate the 2 tension forces of the ropes from the third law?
im pretty stumped, im not sure how to proceed after drawing the FBD's.
 

Answers and Replies

  • #2
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The block is not accelerating, the coefficient of kinetic friction is not required and is likely only given to see if you understand that it is not needed. The coefficient of static friction will be required to calculate the minimum mass.

Because there will be no acceleration for the mass you are calculating, all the force component equations from your FBD's will equal zero, and the tensions in each diagram are equal.

Remember that the maxium frictional force (while the block is still at rest) is mu_s*N.
 

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