[Physics] Velocity and acceleration question

Question

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?

Answer 1

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?

2. 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.