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

[Philip Keller <PKeller@holmdelschools.org>]

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