Solve Newtons 2nd Law for Friction Coefficient: 4kg School Bag, 20N Force

[purplelgnd18]

Homework Statement

While walking down the hallway, a student drags his 4kg school bag. The force on the bag is 20N [60 degrees above the horizontal]. If the bag moves at a constant speed, what is the coefficient of friction?

Homework Equations

Fn = Fg-Fasintheta

Ff = u(Fn).

The Attempt at a Solution

Well, I found Fg to be aprrox. 39.2N, then I found Fn to be approx. 21.9N. Now I'm stumped. Any help would be appreciated.

 

[Delphi51]

Welcome to PF, Purplelgnd!
Looks like you have the vertical part all figured out correctly. You just need the horizontal applied force and then you can write F = ma for the horizontal. There will, of course, be two horizontal forces to add or subtract and one of them will have the μ you are looking for in its expression.

 

[purplelgnd18]

Welcome to PF, Purplelgnd!
Looks like you have the vertical part all figured out correctly. You just need the horizontal applied force and then you can write F = ma for the horizontal. There will, of course, be two horizontal forces to add or subtract and one of them will have the μ you are looking for in its expression.

Thanks for the welcome! Purplelgnd is actually a name I made up for a Minnesota Vikings forum that I post on (not a proud day today to be a fan I admit).

OK but sadly, I'm still stumped. I'm actually about to break down into tears right now, LOL.

 

[purplelgnd18]

Ok so I plugged in a few numbers and tried this.

Ff = -Facos60
Ff = -(20N)cos60
Ff = 10N

Then:

u = Ff/Fn
u= 10N / 21.9 N
u = ~0.49

Is this correct?

 

[Delphi51]

Start by finding the horizontal part of the 20 N force at angle 60 degrees.

Pardon my offering unsolicited advice, but it really, really helps you, me and your poorly paid marker if you get in the habit of writing things out nicely. For the part you already did finding Fn = 21.9, you should have a diagram showing the 20 N at an angle of 60 degrees. Then show it replaced by a vertical plus a horizontal vector.

Next step, find Fx.

 

[Delphi51]

Okay, you beat me to it. But check that 10/21.9 calc again - I don't get .49.

 

[purplelgnd18]

I think I was reading the numbers off wrong.

~0.46?

 

[Delphi51]

That's it!
Good luck on the next one.

 

[purplelgnd18]

haha, Thank you so much!

My dad is a Physics Prof. over at the University of Waterloo (in Ontario), and he didn't have time to help me with this homework. LOL, oh well.

Thanks again!