Dynamics Question: Skier Sliding Distance

[MemoIhad]

[SOLVED] Dynamics Question

Homework Statement

A skier on a slope inclined at 4.7(degrees) to the horizontal pushes on ski poles and starts down the slope. The initial speed is 2.7m/s. The coefficient of kinetic friction between skis and snow is 0.11. Determine how far the skier will slide before coming to rest.

Homework Equations

Fnet=ma
Fg=mg
v2=v1+2ad
Ff(force of friction)=uk(coefficiant of kinetic friction)xFn(normal force)

The Attempt at a Solution

Well after drawing a free body diagram, I concluded that Fnet=fg+fappcos4.7-(force of friction) after subbing in:
ma=mg+fappcos4.7-uk(Fn)
mass cancels out so:
a=g+fappcos4.7-uk(Fn)

but now I have no fapp value. I also tried solving it without a Fapp and subbing my acceleration answer into the relevant equation to get the distance, but my answer was wayyyyy of the right answer, which is 13m

I wish I could explain more or show that I tired more, but these type of questions always confuse me, I've yet to solve one.

 

[Shooting Star]

Resolve the forces along and normal to the slope. Along the slope, what is the component of gravity?

(What are you denoting by Fapp?)

 

[Doc Al]

There's no additional "applied" force. The only forces acting on the skier are: gravity, friction, and the normal force.

What's the normal force equal to? What's the component of gravity acting down the slope?

 

[MemoIhad]

Resolve the forces along and normal to the slope. Along the slope, what is the component of gravity?

(What are you denoting by Fapp?)

Fapp is meant to denote the force applied.

There's no additional "applied" force. The only forces acting on the skier are: gravity, friction, and the normal force.

What's the normal force equal to? What's the component of gravity acting down the slope?

Normally, I'd say that the normal force would equal the force of gravity, but since its at an angle the normal force equal something else.

Maybe this will help: http://img167.imageshack.us/img167/4996/answer2ux1.th.jpg
This is the solution I found, but I looked at it and I don't understand much of anything they're doing. Maybe explaining the steps or how the formula is initially set up will be easier to help me with then figuring the whole question from scratch. Thanks for the time and help!

 

[Shooting Star]

It says exactly the same thing as we do. By x, they mean along and down the plane, and y is normal to the plane.

Which portion are you not able to understand ?

 

[MemoIhad]

^^ Well, to start, I don't really understand how they set up the formula for x and the formula for y. What does it mean in English? I also don't understand why they put mgsin(angle), I was taught that its always fappcos(angle).

 

[Shooting Star]

Do you know how to resolve, i.e., break up a force into two mutually perpendicular directions?

 

[MemoIhad]

I'm not sure what you mean by that, I think I know it by another name. What I have been taught is too draw a free body diagram, then draw all the forces acting on the object. So for this question, the FBD would look like this: http://img144.imageshack.us/img144/7971/fbdtl9.th.jpg
Hope this is what you mean.

 

[Shooting Star]

Right. Now notice that two of the forces are along the plane, and one is normal to the plane, but the mg is pointing down. We want that force of gravity to be broken up so that the components are either along or normal to the plane. Then we can add up all the forces directly as x or y forces.

The inclination theta of the plane is given. Can you do what I said?

 

[MemoIhad]

Ok, I see what your saying. So mg needs to be broken up into x an y. Now how would you do this? Would you say that the x component is mgsin4(degrees) and the y is mgcos4(degrees). My reasoning for putting the sine and cos where they are is that I remember the teacher saying that cos always goes to the angle opposite of...something..I forgot the exact word. Is this what you're trying to show me? Am I on the right path?

 

[Shooting Star]

That's good enough. (Stop writing the whole sin4(degrees); I'll use 'b' for the angle.)

Now write down the x and y forces and sum them. Refer to the solution you had attached. If stuck, get back here.

You have to know that force of friction is kN. Think for some time.

 

[MemoIhad]

ALright, thanks a lot for the patience and help. If I do have more questions, I'll post back. Thanks.