2 Masses, Friction, Inclined Plane, Pulley problem

AI Thread Summary
The problem involves two masses connected by a massless rope over a frictionless pulley on an inclined plane that has friction. To solve for the tension in the rope and the acceleration of the blocks, Newton's 2nd Law is applied, allowing for the establishment of two dynamical equations. The frictional force can be calculated using the formula F_f = μN, where μ is the coefficient of friction and N is the normal force. With two equations and two unknowns—tension and acceleration—solving the system yields the desired results. This approach effectively simplifies the problem to find the answers.
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Here's a problem I've been having trouble with. I was hoping someone out there can give me some insight on it. Basically it's just two masses both coupled together with a massless rope on a frictionless and massless pulley on an inclined plane WITH friction. Here's the diagram. The problem is to figure out the tension in the rope and the acceleration of the blocks.
 

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Well, use Newton's 2nd Law, and pick a direction for the acceleration.

\sum_{i=1}^{n} \vec{F}_{i} = m \vec{a}

Also remember

F_{f} = \mu N
 
you get two dynamical equations... In which there are only two unknowns... Tension and acceleration... frictional force is known... Two equations two variables...Voila ! Theres your answer
 
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