# Frictional Force 1

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.

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PhanthomJay
Homework Helper
Gold Member
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.
Think about Newton's 1st and 2nd law. Which one applies here?

Think about Newton's 1st and 2nd law. Which one applies here?
Sorry for being ignorant, but I don't see how this helps. PhanthomJay
Homework Helper
Gold Member
Sorry for being ignorant, but I don't see how this helps. I'll narrow the field for you. Think about Newton's 1st law.

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.

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?

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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?

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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?
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.

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?

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

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

Exactly! Then the cart is at rest, with NO forces pushing on it? What does that say about the friction?
The .4 static friction is greater than that .2 kinetic friction, so static friction is acting on the cart.

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....?

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

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??

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

Then the object will start to move, and is acted on by kinetic friction opposing the object's motion.
force of cart moving right is slowed by kinetic friction moving left

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??
I don't know.

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:

http://img250.imageshack.us/img250/9730/hw1cj7.jpg [Broken]

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
no pushing force = 0 static friction
So...?

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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:

http://img250.imageshack.us/img250/9730/hw1cj7.jpg [Broken]
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I knew that this wasn't the correct diagram, because the plane was flying horizontally. I take it this one 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.
That's good to know.

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...?
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).

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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?

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?
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?

This appears to be more of a conceptual question that tests your knowledge of when there is a frictional force acting on an object, rather than giving you numbers to plug into an equation. Just because they throw in some numbers doesn't mean that all of a sudden there's a cocktail waitress pushing on the cart! That information is there to throw you off track to see if you understand that there is actually no static friction acting on the object.

The question asks for the force of friction acting on the object--not what fs max or fk would be if the object WERE to move. Since the object is not moving, and is not trying to move, there is no force of friction acting on it.

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This appears to be more of a conceptual question that tests your knowledge of when there is a frictional force acting on an object, rather than giving you numbers to plug into an equation. Just because they throw in some numbers doesn't mean that all of a sudden there's a cocktail waitress pushing on the cart! That information is there to throw you off track to see if you understand that there is actually no static friction acting on the object.

The question asks for the force of friction acting on the object--not fs max or fk. Since the object is not moving, and is not trying to move, there is no force of friction acting on it.
Didn't I say that before?

Peterson said:
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).

lol, when I started replying you hadn't edited to put that in yet, I didn't see it. Yes, it should be zero!

Also, yes, your new diagram for the inclined plane is correct. :)

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Doc Al
Mentor
The problem states the is a static friction of 0.4 and a kinetic friction of 0.2.
Those are coefficients of friction that describe the properties of the surfaces--they may or may not be useful in answering the question. (As gabee explains, in this case not. )

Those are coefficients of friction that describe the properties of the surfaces--they may or may not be useful in answering the question. (As gabee explains, in this case not. )
Shoot the professor and his useless information! Once again, thanks for the help. I can see that this is going to be a long semester, and I'll be back for sure, lol.

Regards,
Matt P