What is the Acceleration of a Couch Being Pushed at an Angle with Friction?

[gullyb]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

 

[SammyS]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

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[SteamKing]

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[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 vertical 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 I am stuck, because i don't think they should be the same
ff=uk*fn
=(0.051)(840.42)
=42.9

so if i try to find the acceleration it won't make sense
fnet=ff-faaph
fnet=0
fnet=ma
a=fnet/m

idk what i did wrong please help ?

 

[PhanthomJay]

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

 

[gullyb]

well this would mean that the acceleration is 0 so there is no acceleration? but i don't think that is right

 

[haruspex]

a force of 56 N at an angle of 40 above horizontal

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

 

[PhanthomJay]

well this would mean that the acceleration is 0 so there is no acceleration? but i don't think that is right

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

 

[gullyb]

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

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

 

[haruspex]

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

Did you see my comment, post #7?

 

[gullyb]

Did you see my comment, post #7?

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 won't be any displacement in the vertical direction?

 

[haruspex]

i kinda assumed that its moving forward so there won't be any displacement in the vertical direction?

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.