In this problem, we'll use Newton's second law of motion:

$\overline{){{\mathbf{F}}}_{\mathbf{n}\mathbf{e}\mathbf{t}}{\mathbf{=}}{\mathbf{m}}{\mathbf{a}}}$, where F_{net} is the net force, m is mass, and a is acceleration.

The frictional force is expressed as:

$\overline{){\mathbf{f}}{\mathbf{=}}{\mathbf{\mu}}{\mathbf{N}}}$, where is the coefficient of friction and N is the normal force.

Weight:

$\overline{){\mathit{w}}{\mathbf{=}}{\mathit{m}}{\mathit{g}}}$

The total force acting on m_{1} is:

m_{1}g - T = m_{1}a ................... (1)

Block 1, of mass m_{1}, is connected over an ideal (massless and frictionless) pully to block 2, of mass m_{2}, as shown. Assume that the blocks accelerate as shown with an acceleration of magnitude a and that the coefficient of kinetic friction between block 2 and the plane is µ

Find the ratio of the masses m_{1}/m_{2}.

Express your answer in terms of some or all of the variables a, µ, and θ, as well as the magnitude of the acceleration due to gravity g.

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Our tutors have indicated that to solve this problem you will need to apply the Inclined Planes with Friction concept. You can view video lessons to learn Inclined Planes with Friction. Or if you need more Inclined Planes with Friction practice, you can also practice Inclined Planes with Friction practice problems.