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1.The magnitude of the total force acting on a ball rolling without slipping down a ramp is greater than the magnitude of the total force acting on the same ball if it slides down the ramp without friction. True or false?

I chose true for this one, as I figured that if our force has to oppose friction, then it must be greater than that force without friction. However the correct answer is false.

2.The magnitude of the velocity of an object must change if the magnitude of its acceleration is a constant. True or false?

I chose true for this one too. If acceleration is constant, then velocity is linear. This turned out to be false as well.

Can anyone explain to me why I was wrong for both of these?

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It's good that you stated your reasoning, but it would be even better if you could isolate the difficult ideas and ask a conceptual question rather than restating your homework. For example, "What forces act on a ball that rolls without slipping, and what are their relative magnitudes? –  Mark Eichenlaub Dec 4 '10 at 19:52
    
Why the downvote? –  maq Dec 4 '10 at 19:52
    
If I got the wrong answer obviously I dont know what I'm looking for. This is why I'm asking. –  maq Dec 4 '10 at 19:54
1  
The down vote was already explained. Don't just post your homework. Figure out what you don't understand, and ask that instead. In my first comment, I gave an example of a more appropriate question on the same material. –  Mark Eichenlaub Dec 4 '10 at 22:40

3 Answers 3

up vote 3 down vote accepted

Mark I liked his approach very much, by he stating his reasoning I had enough information to figure out where the flaws on his rationale were. Which for he to do it by himself would be much more difficult. The things I did not like in his question were, the vague title question, and that two question were asked in a single thread. fprime, to set an example, would split te two questions and reformulate it. I will put the proper answer after.

The second question you could have asked more directly.

Does the magnitude of the velocity of an object must change if the magnitude of its acceleration is a constant?

Then put your answer and rationale below.

Now lets go for the answers.

  1. It seems to me that you got the concept of "total force acting on an object" wrong. When it says force acting it does not mean that we are going to apply a force to it. I it means, list all the forces that are applied on it and sum everything vectorially. In this case there is only the weight, normal and friction force. Check the picture below, and try to do the vectorial sum. Remember that in one of the cases the friction force is absent, so just imagine the picture without it. Did I get it right? I mean does the answer make sense now?

alt text

  1. That is a very common misconception of acceleration, that I struggled myself with when I was learning it. Problem lies on the missmatch of the popular definition of acceleration and the formal definition of acceleration.

The definition you are working with is probably. "Acceleration is the rate by which the magnitude of the velocity changes". While the formal definition of acceleration is "Acceleration is the rate by which the velocity is changes". Now because velocity has the direction property it can change its direction without changing its magnitude. Changing direction IS a change in velocity.

We actually use the wrong definition all around in our daily life. When we say do not accelerate while turning in a curve. We mean do not step the gas. But by the formal definition, it is impossible to turn without accelerating. So when we hear this phrase we know the person is not using the formal acceleration concept.

So you must understand that in the question the formal definition is to be assumed. For it is this definition that is used in professional setting. So take care with it, all physics and engineering books and articles assume this the formal definition of acceleration.

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The solution to 2. can be found also for the informal definition of acceleration (or acceleration in 1D). Namely, the acceleration being equal to zero. It's quite possible that this is an accidental solution that wasn't intended for that question. In that case it's a wrongly formulated question. –  Marek Dec 5 '10 at 12:25
    
Bernardo: How do you include the diagram in the answers, or questions? –  Pupil Dec 9 '10 at 4:32
    
@Bernado.. just click on the image button right to curly braces. –  Sreekanth Karumanaghat Apr 12 '13 at 4:17

I'll just give you (very obvious) hints because I don't want to solve the problem completely for you (it's better to solve it on your own).

Hint for 1: just think what kind of forces are there in both cases.

Hint for 2: think about all the possible values the constant might have.

Hint for 2 for a different solution: think in more dimensions.

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Well this is not homework I'm reviewing for a test and I already know the answers so I dont know the point of hints its just a conceptual question –  maq Dec 4 '10 at 20:52
    
Hint for 1 (part 2): the total force is the vectorial sum of all the forces... –  Ebenezer Sklivvze Dec 4 '10 at 20:53
    
Hint for 2b: the velocity of an object is not the same as the magnitude of the velocity (a.k.a. the speed). –  Ebenezer Sklivvze Dec 4 '10 at 20:54
    
@fprime: knowing answers is nothing without understanding them. I just gave you hints because I think it'll be good for you to think on your own for some more (then you can ask more specific questions). We can always give you complete answers later but when you'll see them, you'll lose the chance to solve the problem on your own. It's mainly through the actual solving (as opposed to reading) that the physical (or indeed any) intuition develops. –  Marek Dec 4 '10 at 20:57
    
@Sklivvz: that's what I first thought too, but then I realized that problem could have been meant for one dimension where the two notions agree (except for the sign). And then I realized that another (strange) solution exists. –  Marek Dec 4 '10 at 21:00

I am going to comment on the first question only. The sum of the forces is equal to acceleration, so I guess this poorly worded question boils down to which ball is accelerating more: a) With friction and angular acceleration, or b) Without friction and zero angular acceleration.

From an energy perspective you can suspect that with friction some of the work done goes towards rotating the ball and thus will be less left to move it linearly.

The math also supports this argument if you work out all the forces/moments, as well required rotational motion for each scenario.

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