Solving the Conceptual Fnet=ma Problem for Bill & Susan

[saralsaigh]

sorry i got one more question, its conceptual and i have a little problem with it,
1. The problem:
Bill and Susan are both standing on identical skateboards (with really good ball bearings) initally at rest. Bill weighs three times as much as susan. Bill pushes horizontally on Susan's back, causing susan to start moving away from Bill. Immediately after Bill stops moving.
We are give many choices and asked to pick the correct statement, the two that i have a problem with are:
a) Susan is is moving away from Bill, and Bill is stationary
b) Susan and bill are moving away from each other, and susan's speed is three times larger than that of Bill.

Homework Equations

Ok i think Newton's thrid law applies here and Fnet=ma

The Attempt at a Solution

The correct answer is (b) however i have a problem with that, ok i know that the force Bill is exerting on susan is equal and opposite to the force susan is exerting on Bill however it is possible that susan starts moving while bill is stationary because the static friction of bill is larger than that of susan because his weight is more and therefore his normal force is larger. however i don't think its correct to say that if they both overcame their static friction that susan's SPEED would be three times larger shouldn't it be her ACCELERATION that is three times larger not her speed? because of Fnet=ma?

 

[berkeman]

The wording of your problem statement must not be 100% accurate. What does this statement mean? "Immediately after Bill stops moving."

That makes no sense. Are you missing some words or punctuation marks in your problem statement? If Bill is not moving (v=0), then Susan is moving infinitely faster than Bill, not 3x.

 

[saralsaigh]

yea sry its "Immediately after Bill stops moving, "

 

[Doc Al]

1. The problem:
Bill and Susan are both standing on identical skateboards (with really good ball bearings) initally at rest. Bill weighs three times as much as susan. Bill pushes horizontally on Susan's back, causing susan to start moving away from Bill. Immediately after Bill stops moving.

I assume this last sentence is a typo, and should have read something like: Immediately after Bill stops pushing.

The correct answer is (b) however i have a problem with that, ok i know that the force Bill is exerting on susan is equal and opposite to the force susan is exerting on Bill

Right, they exert equal and opposite forces on each other.

however it is possible that susan starts moving while bill is stationary because the static friction of bill is larger than that of susan because his weight is more and therefore his normal force is larger.

I'm sure you are expected to ignore any effects of static friction. They have excellent, low-friction skateboards.

however i don't think its correct to say that if they both overcame their static friction that susan's SPEED would be three times larger shouldn't it be her ACCELERATION that is three times larger not her speed?

You are correct that her acceleration will be three times greater than Bill's, from Newton's 2nd law. But since the force acts for the same amount of time on each, her resultant speed will also be three times greater than Bill's.

 

[neutrino]

First, Newton's third law does not, at least explicitly, say Fnet = ma. It's the one with action and reaction, remember?

What you say regarding static friction is right. A greater force would be need to push Bill than Susan, but I think the problem assumes that there is no friction between the skateboards and the ground.

To the speed/acceleration: You need to use the Fnet = ma, which happens to be Newton's second law, here. A body is accelerated as long as there is a net force acting on it. Once Bill stops pushing Susan, she starts moving with the constant velocity to which she was accelerated to, and this velocity turns out to be three times Bill's velocity.(as measured by someone "fixed" to the ground) When you start learning a bit more in mechanics, you'd realize that this is a consequence of the law of conservation of linear momentum.

 

[saralsaigh]

Thanks guys for ur help i think i can sort of picture it now