# Free body diagram problem

1. Feb 27, 2013

### gullyb

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

An 82 kg couch is being pushed with a force of 56 N at an angle of 40 above horizontal. If the coefficient of friction between the couch and the floor is 0.051, what is the acceleration of the couch?

2. Relevant equations

3. The attempt at a solution

2. Feb 27, 2013

### SammyS

Staff Emeritus
Hello gullyb. Welcome to PF !

What have you tried?

Where are you stuck?

Before we can help you, you need to show some effort at solving this problem.

3. Feb 27, 2013

### SteamKing

Staff Emeritus
Merely stating a problem is not enough effort to obtain help.

4. Feb 27, 2013

### gullyb

ooh sorry,

okay i broke down the fa into its components which i get
fapph=56cos40
fapph=42.9

fappv=56sin40
fappv=36.0

then i found the fg to be 804.42
fg=mg
fg=(82)(9.81)
fg= 804.42

then i solved for fn by making fnet = 0 because the forces cancel out because there is no movement in the verticle direction.
fn=fnet-fg-fappv
fn=0-804.42-36.0
fn=840.42

then i find the force of friction which turns out to be the same as fapph this is where im stuck, because i dont think they should be the same
ff=uk*fn
=(0.051)(840.42)
=42.9

so if i try to find the acceleration it wont make sense
fnet=ff-faaph
fnet=0
fnet=ma
a=fnet/m

5. Feb 27, 2013

### PhanthomJay

Looks good, keep going, solve for a. What does that imply?

6. Feb 27, 2013

### gullyb

well this would mean that the acceleration is 0 so there is no acceleration? but i dont think that is right

7. Feb 27, 2013

### haruspex

I would have interpreted that as pushing upwards. Am I wrong?

8. Feb 27, 2013

### PhanthomJay

Why not? What does it mean if the couch is moving but not accelerating?

9. Feb 27, 2013

### gullyb

hmmm it means that its moving at a constant velocity. ooh okay yes that makes sense thank you! :D

10. Feb 27, 2013

### haruspex

Did you see my comment, post #7?

11. Feb 27, 2013

### gullyb

oooh sorry no, hmm that could be right because they didnt really give any direction to where the couch is going, but i kinda assumed that its moving forward so there wont be any displacement in the verticle direction?

12. Feb 27, 2013

### haruspex

There won't be any vertical displacement provided the upward component is insufficient overcome gravity. But it will reduce the normal force, and hence the friction.