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Re: [Phys-l] block sliding on a skateboard

Thanks for doing this. One of my colleagues has IP on his laptop and we are playing with it right now at a department meeting. Cool.

Bob at PC

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of Philip Keller
Sent: Monday, February 06, 2012 10:25 AM
To: 'Forum for Physics Educators'
Subject: Re: [Phys-l] block sliding on a skateboard

I have made some interactive physics simulations about these questions. If I
may recap and add some notes...

On 2012, Feb 03, , at 15:58, LaMontagne, Bob wrote:

Here is a simple problem I proposed to my general physics students that
has generated a lot of discussion by them despite the problem's simplicity. I
will throw it out here for your amusement.

Lock the wheels of a long skateboard so it won't move. Now take a 1 kg
mass and drop it from a short distance onto the skateboard with a horizontal
speed of 2 m/s. The mass slides along the surface of the board and stops
after a half meter.

Now unlock the wheels and repeat the experiment. How far does the mass
now slide relative to the surface of the skateboard before it stops sliding?
Take the mass of the skateboard to be 10 kg. How far does it slide relative to
the ground?

Bob at PC

As BC and others have noted, this can be solved (with some necessary 1st
year physics assumptions) with conservation of momentum followed by an
energy analysis. But it can also be solved directly with dynamics methods and
it is interesting to do it that way. You find the friction force, then the
accelerations, and then use kinematics to see when the mass and the board
reach the same velocity.

This problem is the topic of the first of the two simulations I have posted on
my website. I changed the skateboard to a sled on frictionless ice and I
release the box from just above the sled. The box has a mass of 1 kg and
there are slider controls that let you vary the initial horizontal speed of the
box, the mass of the sled and the coefficient of sliding friction. (And you will
see that some combinations cause the box to slide right off the far end! So
even with the safe assumptions of 1st year physics, the problem is more
complex than it seems.)

I also include a graph of the velocities. It is interesting to look at. The two
objects have constant acceleration (one positive, the other negative) but the
magnitudes vary inversely with the masses. It's a chance to re-emphasize
the third law and the second law. And then when the velocities match, like
magic, the forces vanish, the velocity stays constant and is at the value
momentum conservation requires. Very tidy.

One argument for the "harder" solution method is that it extends to the next
question:

Nord, Paul wrote:

Try this variation: If you strike a queue ball straight on, how far does it
travel before it is rolling without >slipping?


This is the one that I called the bowling ball question. This solution parallels
the previous question: dynamics to find the accelerations, followed by
kinematics to determine when the linear velocity "matches" the angular
velocity -- V= omega r.

I have simulated this one as well. In my simulation, the radius of the ball = 1.
You can control the initial linear and rotational velocities, the friction
coefficients and then, for the adventurous, the angle of the ramp. And
again, the velocity graphs tell the story...

The simulations are posted here, in the last two rows of the chart.

http://www.holmdel.k12.nj.us/faculty/pkeller/interactivephysics.htm

As in the past, clicking on the picture gets you a brief clip of the simulation.
Clicking on the left column gets you the actual file but you need Interactive
Physics to run it. -- Phil

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