# Inclined plane and pulley

## 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)

#### Attachments

• inclined plane.JPG
4.9 KB · Views: 375

## 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)

#### Attachments

• FBD-Inclined plane.pdf
293.3 KB · Views: 144
Simon Bridge