Problem: Suppose the coefficient of kinetic friction between mA and the plane in the figure is μk = 0.13, and that mA = mB = 2.7 kg.(a) As mB moves down, determine the magnitude of the acceleration of mA and mB, given  θ = 33°.(b) What value of μk will keep the system from accelerating?

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This problem asks us to determine the magnitude of acceleration of the system for a given coefficient of kinetic friction, then the smallest value of μk for which the system has zero acceleration.

This is a system of objects, inclined planes with friction kind of problem. Just as forces problems, we'll follow the same series of steps:

  1. Draw free body diagrams (FBDs) for the objects of interest
  2. Apply Newton's 2nd Law (Fma )
  3. Solve for the target variable

The kinetic friction force is calculated using

fk=μkN

Also, remember that when we use tilted coordinate axes for inclined plane problems like this, the weight mg makes a known angle with the y-axis, not the x-axis. That means we'll decompose block A's weight vector like this:

mgx=mg sinθmgy=mg cosθ

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Problem Details

Suppose the coefficient of kinetic friction between mA and the plane in the figure is μk = 0.13, and that mA = mB = 2.7 kg.

(a) As mB moves down, determine the magnitude of the acceleration of mA and mB, given  θ = 33°.

(b) What value of μk will keep the system from accelerating?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Systems of Objects: Inclined Planes + Friction concept. If you need more Systems of Objects: Inclined Planes + Friction practice, you can also practice Systems of Objects: Inclined Planes + Friction practice problems.