Clan x86
General Forums => Academic / School => Topic started by: Sidoh on October 30, 2006, 11:24:44 pm
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I think that this is a bit more difficult than the last one I posted! I hope so, at least. In any case, here it is...
Center of Percussion
A baseball bat rests on a frictionless, horizontal surface. The bat has a length of 0.900 m, a mass of 0.800 kg, and its center of mass is 0.600 m from the handle end of the bat. The moment of inertia of the bat about its center of mass is (http://latex.sidoh.org/?render=0.0530+%5C%2C%7B%5Crm+kg%7D+%5Ccdot+%7B%5Crm+m%7D%5E%7B2%7D+). The bat is struck by a baseball traveling perpendicular to the bat. The impact applies an impulse (http://latex.sidoh.org/?render64=Sj1caW50Xnt0XzJ9X3t0XzF9e0YgZHR9) at a point a distance x from the handle end of the bat. The point on the bat you have located is called the center of percussion. Hitting a pitched ball at the center of percussion of the bat minimizes the "sting" the batter experiences on the hands.
Edit -- I got so caught up with making sure the format was correct that I forgot the rest of the question! Sorry.
What must x be be so that the handle end of the bat remains at rest as the bat begins to move? (Hint: Consider the motion of the center of mass and the rotation about the center of mass. Find so that these two motions combine to give (http://latex.sidoh.org/?render=v=0) for the end of the bat just after the collision. Also, note that the integration of equation (http://latex.sidoh.org/?render64=XGRpc3BsYXlzdHlsZSBcc3VtIFx2ZWN7XHRhdX09XGZyYWN7ZFx2ZWN7TH19e2R0fSA=) gives (http://latex.sidoh.org/?render64=XGRpc3BsYXlzdHlsZSBcRGVsdGEgTD1caW50Xnt0XzF9X3t0XzJ9e1xsZWZ0KFxzdW17XHRhdX1ccmlnaHQpZHQ=))
(http://sidoh.dark-wire.net/upload/files/0QKPF0OVFE-8bca9520f9ddb57c.jpg)
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I solved this one. If anyone is interested in the solution, I can post it.
Here's another difficult one...
The moment of inertia of the front wheel of a bicycle about its axle is 8.40*10^-2 kg*m^2 , its radius is 0.390 m, and the forward speed of the bicycle is 5.90 m/s.
With what angular velocity must the front wheel be turned about a vertical axis to counteract the capsizing torque due to a mass 54.0 kg located a distance 4.00×10^-2 m horizontally to the right or left of the line of contact of wheels and ground?
Here's some of the equations for angular motion:
(http://latex.sidoh.org/?render=\displaystyle \tau =I\alpha \Rightarrow \frac{\tau}{I}=\Delta\omega)
(http://latex.sidoh.org/?render=\displaystyle \omega =\frac{v}{r})
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Sidoh, why come Explicit no can read equations? :P
But yeah, I can't see it for some reason.
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Sidoh, why come Explicit no can read equations? :P
But yeah, I can't see it for some reason.
It's hosted on my home connection, so it could simply be the slow transfer speed. It took a while for it to load for me as well. I may try attempting to install the same rendering engine on my account here at school, but I sort of doubt they have ImageMagik installed on them, which is required for the script to work.
Can you access www.sidoh.org with any luck?
Edit: Hmm, it doesn't seem to be the connection. I can move around fine in SSH. Normally, when the bandwidth is being strangled (usually my sister downloading something), it becomes extremely painful to use SSH. I guess the thing is just behaving poorly. If it doesn't shape up, I'll reboot it. I need to rebuild the thing sometime soon... maybe over Christmas break.
In any case, here's the first problem in PDF form (http://sidoh.dark-wire.net/upload/files/8RGRINQ9QD-f80ab663183c1b06.pdf).
Here's the second in a PDF (http://sidoh.dark-wire.net/upload/files/7MHZJ7KA7W-405c06944efe77e2.pdf) as well.