I always feel Stupid and Confused

I often get emails asking me about physicist questions.  Sometimes I can't resist answering, especially if it's a simple problem on a fundamental principle.  Try answering the question without looking at my solution, and then check my work to see if I got it right.

EMAIL TO ME:

Hello Professor -

My name is **** and I’m a WSU alum.  My daughter is taking honors science and we are a bit stumped on a question and I was wondering if you could help me.   

Scenario:

A 5 kg ball rolls at 4m/s and hits a fire hydrant.  The ball bounces off at 2 m/s. 

Question:

Which object has the greatest momentum.  The ball, hydrant, or is it the same? 

Answer?

Ball - I chose ball because of the definition of momentum.  The fire hydrant is not moving – the ball is.    And the question is not about force and gives no other information about the hydrant.

If you have a second I’d love to know if I’m correct, or if there is a different answer and explain it to me. 

Thanks,
MY ANSWER:

Hi ****,

I'm assuming that the question is asking for the momentum of the two objects just after the collision.  This problem is testing the concept of momentum conservation.  Momentum conservation ALWAYS holds even when mechanical energy is not conserved.  This is the principle to understand and apply.

Here is how I would solve the problem.  The initial moment of the ball is + 20 kg m/s and it's momentum just after the collision is - 10 kg m/s (assuming it bounced backwards).  Thus, the change of momentum is - 30 kg m/s.  But since momentum must be conserved, and it was initially 20 kg m/s, the ball must have imparted 30 kg m/s to the hydrant.  Now, momentum is conserved: 20 kg m/s (ball before collision) =  30 kg m/s (hydrant) - 10 kg m/s (ball after collision).  It seems strange because you can't see the hydrant moving but that is because it has so much mass.  So even though its velocity is near zero, the mass is so huge that the momentum is substantial.

The reason that I stipulate "just after the collision" is because the hydrant is attached to the earth, so while it might initially start to move one way, it will end up vibrating back and forth.  Probably more detail than you wanted to here, but just in case you were curious.  Another brain teaser: if the hydrant is oscillating after the collision, the momentum is oscillating too, so momentum seems not to be conserved.  The answer is that the hydrant is attached to the earth, so the earth and the hydrant will move in such a way that momentum is conserved.  It always needs to be conserved.

Don't let your daughter feel frustrated.  Applying physics concepts to problems is very difficult.  You only learn after making lots of mistakes, so have her learn from them.  When teaching any physics class, I give lots of problems of this sort, and some students get angry, accusing me of trying to trick them.  In attempting to do problems and then seeing the right way after struggling somehow results in it sinking in in a way that cannot be replicated by just giving the learner answers.

I don't want to undermine the teacher, who is probably giving the class a bunch of problems of this kind to train them to think, so I don't feel comfortable answering such questions in the future, because the struggle is an important part of learning and the teacher is, I hope, directing the struggles in a positive way.  Your daughter should attack problems by arguing with classmates, you, or whoever is up for a good fight.  My colleagues and I continue to do this even now as we learn new things.  Being able to thrive on being constantly confused in the quest to understand is the ticket for success.

I wish your daughter the best in her studies and tell her from a guy who is constantly confused and feeling stupid, this is the way it should be.  And don't give up!

(Pardon the typos, since I didn't have time to proof my email.)

Best,

Mark G. Kuzyk
Regents Professor of Physics
Meyer Distinguished Professor of Sciences
Washington State University
Pullman, WA 99164-2814

Phone: 509-335-4672
Fax: 509-335-7816

Web Page: www.NLOsource.com