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 μ _{k} **for which the system has

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:

- Draw
**free body diagrams (FBDs)**for the objects of interest - Apply
**Newton's 2nd Law**(**∑***F*=)**ma** **Solve**for the target variable

The kinetic friction force is calculated using

$\overline{){{\mathit{f}}}_{{\mathit{k}}}{\mathbf{=}}{{\mathit{\mu}}}_{{\mathit{k}}}{\mathit{N}}}$

Also, remember that when we use tilted coordinate axes for inclined plane problems like this, the weight * mg* makes a

$\overline{){\mathit{m}}{{\mathit{g}}}_{{\mathit{x}}}{\mathbf{=}}{\mathit{m}}{\mathit{g}}{\mathbf{}}{\mathbf{sin}}{\mathit{\theta}}\phantom{\rule{0ex}{0ex}}{\mathit{m}}{{\mathit{g}}}_{{\mathit{y}}}{\mathbf{=}}{\mathit{m}}{\mathit{g}}{\mathbf{}}{\mathbf{cos}}{\mathit{\theta}}}$

Suppose the coefficient of kinetic friction between *m*_{A} and the plane in the figure is *μ _{k}* = 0.13, and that

(*a*) As *m*_{B} moves down, determine the magnitude of the acceleration of *m*_{A} and *m*_{B}, given *θ *= 33°.

(*b*) What value of *μ*_{k} 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.