# Frictional Force 1

1. Feb 17, 2007

### Peterson

INTRODUCTION:
This is a problem from my Introduction to Physical Science class using "Conceptual Physics" 10th Ed.by Paul G. Hewitt

EXACT PROBLEM:
"A 15-N cart rests in the isle of a jet airplane that is cruising horizontally at a constant velocity. The coefficient of static friction between the cart and the floor is 0.4, while the coefficient of kinetic friction is 0.2."

PROBLEMS FACED:
Determine the frictional force acting on the cart.

MY THOUGHTS:
I don't know what to do here really. I am not sure which formulas to use.

Last edited: Feb 17, 2007
2. Feb 17, 2007

### PhanthomJay

Think about Newton's 1st and 2nd law. Which one applies here?

3. Feb 17, 2007

### Peterson

Sorry for being ignorant, but I don't see how this helps.

4. Feb 17, 2007

### PhanthomJay

I'll narrow the field for you. Think about Newton's 1st law.

5. Feb 17, 2007

### Bitter

I'll add onto the hint. Newton first law, in a nutshell, says that if the net force is equal to zero then the body's velocity is not changing, so since the velocity isn't changing then accelaration isn't there.

So F=0

So draw a free body diagram. What forces are acting upon the cart? Do we have normal force, weight, etc etc. Define these and try again.

6. Feb 18, 2007

### Peterson

Here's what I have come up with:

Ffrictional = (Muk)(Fn) = (Muk)mg
F = (.2)(20)(9.8)
F = 39.2N

Am I even close?

Last edited: Feb 18, 2007
7. Feb 18, 2007

### gabee

Well, you only have a kinetic frictional force if the object is moving, and you only have a static frictional force if the object is still but something is trying to move it.

For example, try this: take a heavy book and place it on a table. Push it gently with the tip of your finger; it probably doesn't move. But you are applying a force to it. The force opposing your finger is the force of STATIC friction, because the object hasn't started moving yet. In fact, the force of static friction adjusts itself depending on how much force you apply to the book so that the two forces exactly cancel out! This happens until your force becomes larger than $f_{s\,max}$--then the object starts to move, and experiences a force of KINETIC friction, which depends on the normal force and OPPOSES the object's direction of motion (for example, when you drive your car forward, kinetic friction tries to push you backward).

So here's a question: in the airplane, which is traveling at constant velocity (acceleration = 0), which way is the cart moving? Is anything applying force to the cart? Is it moving at all?

Last edited: Feb 18, 2007
8. Feb 18, 2007

### Peterson

Ok, so is this question like an essay question then?

As in:
There is a static friction force acting on the cart. The plane is moving at a constant speed, and the only force action on the cart is gravity keeping it in place.

9. Feb 18, 2007

### gabee

The cart's vertical downward weight mg and the vertical upward normal force N cancel exactly. In order for there to be a static friction force, there must be something else trying to push horizontally on the cart (and the static friction force is opposing it, so that the cart is not moving). Can you tell me what is pushing on the cart horizontally?

Last edited: Feb 18, 2007
10. Feb 18, 2007

### Peterson

No. No I can not. It doesn't look like there is anything pushing the cart.

11. Feb 18, 2007

### gabee

Exactly! Then the cart is at rest, with NO forces pushing on it? What does that say about the friction?

12. Feb 18, 2007

### Peterson

The .4 static friction is greater than that .2 kinetic friction, so static friction is acting on the cart.

13. Feb 18, 2007

### Peach

Yes, static friction is acting on the object. I think gabee is trying to steer you towards the idea that if the cart is at rest, and the static friction which is the friction it takes to accelerate the object, then that must mean that the static friction is....?

14. Feb 18, 2007

### Peterson

one piece of a 500 piece puzzle and you don't have a picture to put it together with.:grumpy:

15. Feb 18, 2007

### gabee

First, make sure you understand when static friction acts.

If you have a block at rest on a horizontal surface, the only forces acting on it are mg downward and N upward. There is no force acting in the horizontal direction, not even static friction (yet!).

If you now start to apply a force to push the block to the right, NOW the block resists and there is a static frictional force to the left EXACTLY matching your own force, so that they cancel and it is still at rest. If you stop pushing again, the static friction force again drops to zero. Now you start to push again, slowly increasing your force. Static friction increases as your force increases so that they cancel exactly--UNTIL your force exceeds the maximum static friction, fs max.

Then the object will start to move, and is acted on by kinetic friction opposing the object's motion.

The key here is that you found that there is no force acting on your cart to begin with. So what force would static friction be matching and opposing??

16. Feb 18, 2007

### Peterson

I have a diagram of this. It's a block sitting on an inclined plane:

Let me try to word diagram this one:

pushing left force ---> =has to equal= <--- pushing force left

no pushing force = 0 static friction

[strong force =/= weaker force] = the cart moves

force of cart moving right is slowed by kinetic friction moving left

I don't know.

17. Feb 18, 2007

### gabee

First, a couple of things about the free body diagram:
Why is your gravity acting at a slant? Doesn't gravity usually pull things straight down..?
Your normal force is acting in the correct direction, perpendicular to the plane.

HOWEVER, this is not the correct free body diagram for this problem. The airplane is flying horizontally, which means the cart is sitting flat on the floor. The free body diagram should look like this:

I also changed your arrows to be the same size, since mg is equal in magnitude and opposite in direction to normal force.

Now, you've actually just said the answer in your last post. You've said before that there is no horizontal force pushing on the object. And you just told me
So...?

Last edited: Feb 18, 2007
18. Feb 18, 2007

### Peterson

I knew that this wasn't the correct diagram, because the plane was flying horizontally. I take it this one should look like this:

That's good to know.

Still not registering here.

So zero kinetic friction force since the cart is not moving (there's nothing kinetic to stop) and zero static friction force (nothing is pushing on the cart).

Last edited: Feb 18, 2007
19. Feb 18, 2007

### gabee

There is no horizontal force pushing on your cart.
If there is no force pushing on an object, static friction force is zero.

What is the static friction acting on your cart?

20. Feb 18, 2007

### Peterson

ok...

The problem states the is a static friction of 0.4 and a kinetic friction of 0.2. So there is something pushing the cart (a person maybe). BUt if the cart isn't moving, the forces exerted (from the person) are equal to the frictional forces.

My total frictional force is 0.6 then?