Friction, Mass, and Incline angles. Calling wizards

[hellocubed]

A woman is sidestepping up a hill. It is well known that her weight will not affect the steepness of the incline she climbs.
μ(mg)= (mg)cosθ
μ= cosθ
Mass cancels right out and the Only factor that affects the steepness of the hill is the Coefficient of Static friction.

Now a different scenario:

A rectangular block is placed on an incline, and the threshold angle is found (before it slips off). No matter what side you put the block on the incline, the threshold angle is the same. Why?
A.) Friction depends on contact area of the object
B.) Friction depends on the position of the center of mass
C.) Friction depends on the total surface area
D.) Friction depends on the mass of the object.

The answer is D...
What? Did we not establish in the top that the Threshold angle of an independent object on an incline is ONLY dependent on μ= cosθ?
Changing mass has no effect on cosθ, and hence mass is completely irrelevant.


Am I correct in saying this problem is incorrect?

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[dmf2682]

Suggest you go back and look at your example question. Friction force is mu N where N is the normal force. If you're on an incline then your normal force has an angle component to it. (Read, not just mg ) Draw a picture and you'll see.

Good luck!

 

[milski]

The friction force does depend on the mass, the threshold angle does not - these are two different things.

 

[hellocubed]

Suggest you go back and look at your example question. Friction force is mu N where N is the normal force. If you're on an incline then your normal force has an angle component to it. (Read, not just mg ) Draw a picture and you'll see.

Good luck!

you are correct. the actual formula is

μ(mg)cosθ=(mg)sinθ
μ= tanθ

Still, same thing. Mass does not affect the incline angle.

The friction force does depend on the mass, the threshold angle does not - these are two different things.

Yes I am aware of this, but the question is asking about "why the angle of the incline is immutable," which mass obviously has nothing to do with. The answer choice might as well talk about how elephants are not pink, which would also be a true statement. It just doesn't answer the question.

 

[dmf2682]

you are correct. the actual formula is

μ(mg)cosθ=(mg)sinθ
μ= tanθ

Still, same thing. Mass does not affect the incline angle.



Yes I am aware of this, but the question is asking about "why the angle of the incline is immutable," which mass obviously has nothing to do with. The answer choice might as well talk about how elephants are not pink, which would also be a true statement. It just doesn't answer the question.

As you wrote above the angle is a function of mu

That's not what the question is asking. It's asking why if you rotate the block so a different side is down the angle doesn't change. It's really asking what friction force is. And d is the best answer.

 

[EnginrTheFuture]

The angle does not depend on mass for these reasons (as you know):

1) As the mass increases, the force on the block down the slope due to gravity does increase....
2) BUT as you increase the mass, the frictional force N x mu increases proportionally as well

For this reason, because the force down and force against are based on the same mass and proportional, the angle stays the same. Ask yourself what would happen if this choice wasn't rue...

If the frictional force did not depend on mass, but rather surface area or area of contact... if the mass increased but the area of contact didn't the angle of inclination WOULD decrease because the force down increased but force against did not (since area stayed same). We know this isn't true and this is why we know that the reason mass doesn't matter is because it DOES contribute. It just contributes equally which is why you see the phenomona. The sole reason mass looks like it doesn't matter to angle of inclination is because friction depends on mass.

 

[MedPR]

My physics 1 final is on Wednesday, then I'll never ever ever click on another physics MCAT thread.

 

[hellocubed]

As you wrote above the angle is a function of mu

That's not what the question is asking. It's asking why if you rotate the block so a different side is down the angle doesn't change. It's really asking what friction force is. And d is the best answer.

The frictional force has nothing to do with the incline angle.
If the frictional force changes from 10000000N to 1N, the incline angle would not change. And the mass can be changed from infinity to 1, the incline angle would not change.

The question is asking why the incline angle doesn't change when you rotate the block
The answer is because the Coefficient of Friction Does Not Change

It has nothing to do with mass, or the Frictional force.

 

[hellocubed]

The angle does not depend on mass for these reasons (as you know):

1) As the mass increases, the force on the block down the slope due to gravity does increase....
2) BUT as you increase the mass, the frictional force N x mu increases proportionally as well

For this reason, because the force down and force against are based on the same mass and proportional, the angle stays the same. Ask yourself what would happen if this choice wasn't rue...

If the frictional force did not depend on mass, but rather surface area or area of contact... if the mass increased but the area of contact didn't the angle of inclination WOULD decrease because the force down increased but force against did not (since area stayed same). We know this isn't true and this is why we know that the reason mass doesn't matter is because it DOES contribute. It just contributes equally which is why you see the phenomona. The sole reason mass looks like it doesn't matter to angle of inclination is because friction depends on mass.

Err, I understand what you are saying.

I do not like the question, but I suppose the answer choice is saying "because frictional force and gravitational force increase proportionally at a ratio of 1:1"
😡

 

[dmf2682]

The frictional force has nothing to do with the incline angle.
If the frictional force changes from 10000000N to 1N, the incline angle would not change. And the mass can be changed from infinity to 1, the incline angle would not change.

The question is asking why the incline angle doesn't change when you rotate the block
The answer is because the Coefficient of Friction Does Not Change

It has nothing to do with mass, or the Frictional force.

Is that an answer choice?

So let's role play here. You're hello cubed. I'm the mcat.

Me: question question question, a b c or d?
You: well, I understand the question but here's a completely different answer.
Me: ???
You: I choose e.
Me: ???
You: (I choose e)^3
Me: ???

 

[johnwandering]

Is that an answer choice?

So let's role play here. You're hello cubed. I'm the mcat.

Me: question question question, a b c or d?
You: well, I understand the question but here's a completely different answer.
Me: ???
You: I choose e.
Me: ???
You: (I choose e)^3
Me: ???

You can't just lay over and accept a 3rd company's practice question answer and incorporate it into your knowledge base. You have to challenge why the answer is correct, because the next time you see it it will most likely Not be accompanied with 3 floozies.

The point of these practice tests is not to get the most correct answers correct. But to understand why the answer choice is true.


That is my approach, and I think OP's as well.

 

[hellocubed]

I noted that I did not understand the question. Choice D was no more correct than the other 3.

I was pretty darn sure that BR just screwed up the question, which they have done plenty of times. It was in my best interest to understand why they were not wrong thoroughly.


But now it's all straightened out.

 

[dmf2682]

You can't just lay over and accept a 3rd company's practice question answer and incorporate it into your knowledge base. You have to challenge why the answer is correct, because the next time you see it it will most likely Not be accompanied with 3 floozies.

The point of these practice tests is not to get the most correct answers correct. But to understand why the answer choice is true.


That is my approach, and I think OP's as well.

OK. Now that I'm home and can type better (than on my phone) I'll give you my reasoning for getting D, out of what I would call a very reasonable question.

I'll preface by saying that the MCAT has as much to do with problem solving skills as it does background material. Do you think physicians really need to know about orbital mechanics? How about the details of a grignard mechanism? Problem solving skills. Includes cutting out bad answers and keeping the good.

My approach for this problem:

A rectangular block is placed on an incline, and the threshold angle is found (before it slips off). No matter what side you put the block on the incline, the threshold angle is the same. Why?
A.) Friction depends on contact area of the object
B.) Friction depends on the position of the center of mass
C.) Friction depends on the total surface area
D.) Friction depends on the mass of the object.

Not to beat a dead horse here but we're talking about threshold angle being the same. We know that because the force due to gravity parallel to the incline surface (call it Fparallel) is constant and the thing isn't going anywhere, the force due to friction (which counteracts Fparallel) is also constant. So friction doesn't change.

Here's where the problem solving comes in.
A is eliminated because the contact area can change depending on how the block is rotated. We can get rid of A because we said friction's constant.
B is eliminated because friction doesn't depend on center of mass (I think we can agree that this choice is just wrong without debate)
C is eliminated because it's even more wrong than B. Nonsensical.
which leads us to....

D! It's the only one that makes at least some sense. Arguable or not, it's better than everything else.

 

[Morsetlis]

The threshold angle is just a fancy way of calculating the inflection point at which the normal force x friction coefficient is less than the acceleration due to gravity down the incline.

Initially, all the weight of the object is used for the normal force, on a flat incline.

As the incline gains angle, the weight of the object is split between a normal force, and an accelerational force down the incline.

The normal force x friction coefficient opposes this accelerational force down the incline.

At a certain angle, the normal force x friction coefficient is less than the acceleration due to gravity down the incline. Then the object slips down the incline. This angle is where

Frictional force holding the object in place --> &#956;(mg)cos&#952; = (mg)sin&#952; <--Accelerational force down the incline

As you have deduced, the Threshold angle &#952; does not depend on the weight of the object, however... the question poses a disturbance to equilibrium: flipping the object on different sides. It is really asking, with this action ALONE, why did the equation not change?

-The frictional force is not dependent on center of mass. Likewise, flipping the object on different sides, without moving parts or changing densities or morphology, will not change the center of mass.

-Friction does not depend on contact area, because there will be more pressure (matter column on top of a discrete, constant area) to counteract less area... leading to the same force. You can see a counterexample with Velcro: friction with Velcro is dependent on surface area, not the matter column on top of a discrete constant area as in classical physics.

-Friction does not depend on the total surface area of the object because surfaces that are not in contact with the surface are not participating in the creation of friction.

Therefore, while changing the mass would not change the threshold angle, flipping the object on different sides does NOT change the mass, the center of mass, or the total surface area. Friction does NOT depend on total surface area, or surface area in contact with the normal plane. Therefore, the only TRUE answer, which is NOT changed by the action of flipping the object on different sides, is D.

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An even simpler explanation:

The action of flipping the object on different sides changes A, but not B, C, or D.
Changing A does not change the threshold angle, therefore A is false. If it did, the experiment would be invalid.
Changing B, C, or D will not change the threshold angle, therefore the experiment is still valid.
Amongst B, C, and D, only D is true. Therefore the experiment proves D.

Friction is the item being discussed, not the threshold angle!

This tests both your knowledge of an incline plane, and your ability to make a differential diagnosis based on a given investigation.

 

[Morsetlis]

The frictional force has nothing to do with the incline angle.
If the frictional force changes from 10000000N to 1N, the incline angle would not change. And the mass can be changed from infinity to 1, the incline angle would not change.

The question is asking why the incline angle doesn't change when you rotate the block
The answer is because the Coefficient of Friction Does Not Change

It has nothing to do with mass, or the Frictional force.

It doesn't matter what the experiment is, the answer choices are what you have to pick. You are not doing this experiment to save the world, or even to find out how incline angles change. Based on the responses you can possibly give, you are actually caring about the Frictional force.

If the question were:

You put a 4x4x4 block (96 units of SA) on an incline and a 2x4x8 block (112 units of SA) of equal densities on the same incline. They slip off at the same threshold angle, why?
A.) Friction depends on contact area of the object
B.) Friction depends on the position of the center of mass
C.) Friction depends on the total surface area
D.) Friction depends on the mass of the object.

The answer would still be D.

If the question were:

You put a dense 2x4x4 block on top of a 2x4x4 block with half the density, on an inclined plane, and record the threshold angle. Then you reverse the stacking of the blocks, but the stack still slip off at the same threshold angle, why?
A.) Friction depends on contact area of the object
B.) Friction depends on the position of the center of mass
C.) Friction depends on the total surface area
D.) Friction depends on the mass of the object.

The answer would still be D.

If the question were:

A 4x4x4 block and a 4x4x4 block with twice the density were placed on an incline plane. The threshold angles are the same, why?
A.) Friction depends on contact area of the object
B.) Friction depends on the position of the center of mass
C.) Friction depends on the total surface area
D.) Friction depends on the mass of the object.

The answer would still be D. But it would be a terrible question. That's because D is the only true statement, but the experiment does not falsify any other choices.