Learning Goal:

To be able to set up and analyze the free$-$body diagrams and equations of motion for a system of particles.

Consider the mass and pulley system shown. Mass $m_1=36kg$ and mass $m_2=10kg.$ The angle of the inclined plane is given, and the coefficient of kinetic friction between mass $m_2$ and the inclined plane is ${}_k=0\mathrm{.}12.$ Assume the pulleys are massless and frictionless.

$($Figure $1)$

Part A $-$ Finding the acceleration of the mass on the inclined plane

What is the acceleration of mass $m_2$ on the inclined plane? Take positive acceleration to be up the ramp.

Express your answer to three significant figures and include the appropriate units.

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Part B $-$ Finding the speed of the mass moving up the ramp after a given time

If the system is released from rest, what is the speed of mass $m_2$ after $4$ s $?$

Express your answer to three significant figures and include the appropriate units.

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Part C $-$ Finding the distance moved by the hanging mass

When mass $m_2$ moves a distance $2\mathrm{.}18$ m up the ramp, how far downward does mass $m_1$ move?

Express your answer to three significant figures and include the appropriate units.

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