Inclined plane and pulley

  • Thread starter aaronfue
  • Start date
  • #1
122
0

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([itex]\frac{5}{13}[/itex]) - μm2g([itex]\frac{12}{13}[/itex]) = 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 [itex]\frac{m}{s^2}[/itex]

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

Attachments

  • inclined plane.JPG
    inclined plane.JPG
    4.9 KB · Views: 375

Answers and Replies

  • #2
122
0

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([itex]\frac{5}{13}[/itex]) - μm2g([itex]\frac{12}{13}[/itex]) = 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 [itex]\frac{m}{s^2}[/itex]

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

Attachments

  • FBD-Inclined plane.pdf
    293.3 KB · Views: 144
  • #3
Simon Bridge
Science Advisor
Homework Helper
17,874
1,655
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?
 

Related Threads on Inclined plane and pulley

  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
7
Views
5K
  • Last Post
2
Replies
39
Views
9K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
5
Views
3K
  • Last Post
Replies
1
Views
4K
Replies
12
Views
6K
Replies
0
Views
9K
  • Last Post
Replies
19
Views
5K
Replies
2
Views
2K
Top