# Inclined plane and pulley

1. Feb 14, 2013

### aaronfue

1. The problem statement, all variables and given/known data

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)

2. Relevant equations

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

Mass 1:
2T - m1g = m1a1

Pulley System:
a2 = -2a1

3. 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)

#### Attached Files:

• ###### inclined plane.JPG
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2. Feb 15, 2013

### aaronfue

1. The problem statement, all variables and given/known data

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?

2. Relevant 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

3. 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)

#### Attached Files:

• ###### FBD-Inclined plane.pdf
File size:
293.3 KB
Views:
69
3. Feb 15, 2013

### 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?