Acceleration on Inclined Plane and Pulley System

[aaronfue]

Homework Statement

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

m₁ = 33 kg
m₂ = 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 m₂ on the incline plane? (Positive acceleration to be up ramp)

Homework Equations

Mass 2:
T - m₂g($\frac{5}{13}$) - μm₂g($\frac{12}{13}$) = m₂a₂

Mass 1:
2T - m₁g = m₁a₁

Pulley System:
a₂ = -2a₁

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

a₁ = 7.15 $\frac{m}{s^2}$

a₂ = 14.30 $\frac{m}{s^2}$ (Initially this was a negative answer, which reversed my assumption of the direction)

 

[aaronfue]

Homework Statement

I thought that my answers were correct but they are not. I would appreciate it if someone could check my work. I can't seem to find where I made my mistake!

I have also attached a scan of my free body diagrams and the equations that I came up with.

m₁ = 33 kg
m₂ = 14 kg
μ = 0.19
Angle is given by 5,12,13 triangle shown in figure.
Assume pulleys are massless.

What is the acceleration of mass m₂ on the incline plane?

Homework Equations

These are the equations that I came up with from my free body diagrams:

Mass 2:
T - m₂g($\frac{5}{13}$) - μm₂g($\frac{12}{13}$) = m₂a₂

Mass 1:
2T - m₁g = m₁a₁

Pulley System:
a₂ = -2a₁

The Attempt at a Solution

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

T = 121.43 N

a₁ = 2.45 $\frac{m}{s^2}$

a₂ = 4.90 $\frac{m}{s^2}$ (Initially this was a negative answer, which reversed my assumption of the direction)

 

[Simon Bridge]

What makes you think the answer is incorrect? Do you have answers provided: perhaps they hold a clue?

You could check by simplifying the system - the pulley system offers a mechanical advantage in one direction ... which, and what does that mean?