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## Homework Statement

I believe that I have my answer. I would appreciate it if someone could check my work.

m

_{1}= 33 kg

m

_{2}= 14 kg

μ = 0.19

Angle is given by 5,12,23 triangle shown in figure.

Assume pulleys are massless.

What is the acceleration of mass m

_{2}on the incline plane? (Positive acceleration to be up ramp)

## Homework Equations

**Mass 2:**

T - m

_{2}g([itex]\frac{5}{13}[/itex]) - μm

_{2}g([itex]\frac{12}{13}[/itex]) = m

_{2}a

_{2}

**Mass 1:**

2T - m

_{1}g = m

_{1}a

_{1}

**Pulley System:**

a

_{2}= -2a

_{1}

## The Attempt at a Solution

Even though acceleration is assumed to be up the ramp, I drew my FBD with acceleration going down the ramp. I know that if my answer is negative it will be the opposite direction of what I assumed.

After I plugged the pulley equation into the mass 2 equation and then solved two equations with two unknowns:

T = 279.8 N

a

_{1}= 7.15 [itex]\frac{m}{s^2}[/itex]

a

_{2}= 14.30 [itex]\frac{m}{s^2}[/itex] (Initially this was a negative answer, which reversed my assumption of the direction)