What Force Prevents a Skater from Rolling Down an Incline?

[cwong24]

Homework Statement

A skateboarder + skateboard has a combined mass of 70 kg.
How much force is required to prevent them from rolling down a 15 degree incline?

Homework Equations

Weight = 70kg * 9.81m/s^2
Normal = cos 15 * W
Friction = sin 15 * W

The Attempt at a Solution

I solved for friction but my instructor says that I should solve for the Normal force because that is the largest force that must be overcome to get the mass rolling.
I do not understand why exactly since the Normal force isn't a force acting in same direction as the rolling direction.
My instructor said that this isn't just a mass sliding down but that the mass is on wheels so once the Normal force is overcome, the skater will start rolling down.
Am I just mixing up/missing some basic concept?

 

[Doc Al]

Weight = 70kg * 9.81m/s^2

I understand this.

Normal = cos 15 * W

And this.

Friction = sin 15 * W

But not this. That's not how you find friction, but who says there's friction in this problem anyway? Perhaps you just mislabeled this?

What force must you counter to stop the rolling? (What force causes them to roll in the first place?)

No, you don't need the normal force.

 

[cwong24]

OK if there is no friction, I don't know if there is or not since the problem did not say there is or not.
The portion of the Weight force directed down the incline would be sin 15* W.
Since the skater isn't moving, then the force that must be overcome to get this mass rolling should be equal to sin 15*W.
Is that how a mass on wheels is suppose to work?
The normal force doesn't in any way keep the skater from rolling down?

 

[Doc Al]

OK if there is no friction, I don't know if there is or not since the problem did not say there is or not.

Assume there isn't any.

The portion of the Weight force directed down the incline would be sin 15* W.
Since the skater isn't moving, then the force that must be overcome to get this mass rolling should be equal to sin 15*W.

Good. (That's the force that must be exerted to prevent rolling. You want to balance out the force of gravity acting down the incline so that the net force is zero.)

Is that how a mass on wheels is suppose to work?

Yes.

The normal force doesn't in any way keep the skater from rolling down?

Correct.

 

[FireStorm000]

The problem is wrong on account of your FBD. Without drawing in the normal/restoring force the diagram is technically wrong, as it doesn't show all of the forces. I believe you got the problem wrong because the answer they wanted was N + F = mg, yielding an answer of b ~ mg

In short, it was supposed to be a conceptual question seeing if you understand the concept of static equilibrium; that is, all forces must cancel for the object to remain at rest. Since the only known force acting is mg, the opposing force must be equal in magnitude to mg, and opposite in direction (Newton III)

Feel free to tell the teacher that the problem would be better write if it made reference to "the sum of forces required to keep the object at rest"

And lastly: The answer isn't E. Ever.

 

[Doc Al]

I believe you got the problem wrong because the answer they wanted was N + F = mg, yielding an answer of b ~ mg

Interesting. Given the wording of the problem, I would have assumed that they meant what additional applied force must be used to prevent rolling. None of the answers match that choice. It's a strangely worded problem indeed if they wanted an answer of mg! (You don't need a diagram to get that answer!)

 

[cwong24]

I can get answer B if I only calculate the y component of the Weight force. But that leaves the x component of the Weight force unaccounted for.

Can the x component just not contribute to keeping the mass on the incline?

(I drew a FBD as I understand you are saying)

 

[FireStorm000]

Not quite, now F is missing from the diagram.

You are however right that the only way to get the "right" answer is wrong. This problem is so convoluted I'm not sure anyone can help you. 'B' is the magnitude of N. Which leaves us wondering what on Earth happened to F. The only thing I can think of is that this problem is flat out wrong, because that question is not asking for the magnitude of the normal force.