Finding the Value of the Rolling Friction Force

[realslow]

Homework Statement

What is the value of the rolling friction force given 1)Fnet=0.24N (deceleration up the ramp) and 2)Fnet=0.21N (acceleration down the ramp)?

Homework Equations

Fnet = Fgravity - Ffriction (?)

The Attempt at a Solution

Somehow I need to combine these values to find the frictional force...
So I tried this:
0.24 = 5.0 - Ffric
0.21 = 5.0 - (-Ffric)
elimination
0.03 = -2Ffric
Ffric = 0.015 (disregarding the negative?)
Does this work?

 

[JaredJames]

Are you given the mass of the object in the question? It's not relevant, but you've used a value for it.

 

[realslow]

Yes, sorry, the mass was 0.510 kg.

 

[JaredJames]

Up Ramp:
F_a = F_gravity + F_friction
F_gravity = F_a - F_friction

Down Ramp:
F_b = F_gravity - F_friction
F_gravity = F_b + F_friction

F_gravity is equal in both instances so:
F_a - F_friction = F_b + F_friction
F_a - F_b = F_friction + F_friction
F_a - F_b = 2F_friction
F_friction = (F_a - F_b) / 2

Based on that, I'd say I agree with your answer of 0.015.

You don't need the mass of the object for this.

 

[realslow]

Yay! Thank you :)
I just wanted to clarify, gravity + friction make up the net force for the cart going up the ramp because gravity and friction are working in the same direction?

 

[JaredJames]

Yay! Thank you :)
I just wanted to clarify, gravity + friction make up the net force for the cart going up the ramp because gravity and friction are working in the same direction?

Correct. Both are acting against the direction of motion.

 

[realslow]

Okay! :D
Sorry, I just had one question relating to this one, if you could help me again.
I need to state whether my answer is reasonable.
I said it is reasonable because it is 6.8% of the average net force.. and at first I was thinking 0.068 was also the coefficient of friction, but then I calculated friction divided by average net force. It isn't the coefficient.. is it?
I'm also not sure if I was correct in using the average net force.

 

[JaredJames]

Okay! :D
Sorry, I just had one question relating to this one, if you could help me again.
I need to state whether my answer is reasonable.
I said it is reasonable because it is 6.8% of the average net force.. and at first I was thinking 0.068 was also the coefficient of friction, but then I calculated friction divided by average net force. It isn't the coefficient.. is it?
I'm also not sure if I was correct in using the average net force.

For this question, assume everything is acting down the slope to avoid any nasty angles in there.

So everything lines up and cancels out nicely.

Yes, you used it correctly.

Is your answer reasonable? Well do you expect the rolling resistance to be high or low?

 

[realslow]

Sorry, if you could clarify what you mean when you say, "So everything lines up and cancels out nicely."

I'm not too sure.. I don't think the rolling resistance would be high though.

 

[JaredJames]

Sorry, if you could clarify what you mean when you say, "So everything lines up and cancels out nicely."

It's all acting down the slope. Assume net, gravity and friction all refer specifically to those forces acting down the ramp.

I'm not too sure.. I don't think the rolling resistance would be high though.

Correct, is your value high?

 

[realslow]

Oh, okay!

Nope, it isn't high.

Thank you again for your troubles :)