A small ball is set in horizontal motion by rolling it with a speed of 3.00 m/s across a room 12.0 m long, between two walls. Assume that the collisions made with each wall are perfectly elastic and that the motion is perpendicular to the two walls.
(a) Show that the motion is periodic, and determine its period
(b) Is this motion simple harmonic? explain
umm i need help on this problem i tried for a couple days now and it still is not working for me. So if someone can help me solve it it would be great. Thanks
2007-03-16 16:31:37 · 4 answers · asked by Becky 2 in Science & Mathematics ➔ Physics
OK, what you have here is just a ball bouncing back and forth between two walls. Its speed never varies (except in the instant when it's changing directions when it comes in contact with the wall, but that doesn't matter) so right off the bat you can say it's not simple harmonic, because simple harmonic motion by definition means that SPEED depends on POSITION. That means depending on where the ball is, the speed is different. And that's not true for this problem - the speed is ALWAYS 3 m/s. OK. So no simple harmonic motion.
How to determine the period? Well, in this case, the period is just the time taken for the ball to get from a certain place back to that place. That means if it starts at one end of the room, you need to find the time it takes to go to the opposite wall and come back. Not particularly hard - how long does it take a ball to roll 24.0 m (to the opposite wall and back) if it's rolling at 3.00 m/s? Use the fact that speed = distance/time: 3.00 m/s = 24.0 m/(time)... so (time) = 24.0 m/(3.00 m/s) = 8.00 s.
2007-03-16 16:37:35 · answer #1 · answered by dac2chari 3 · 1⤊ 0⤋
Since perfectly elastic collisions assume an instantaneous change in velocity ( in this case, a reversal), the ball travels 12m from one wall, reflects and travels 12 m back to its original position, where it reflects again. With no energy loss, this goes on interminably. The period is simply 24 m / 3 m/s = 8 seconds. If you graph the position of the ball versus time, you see a triangular waveform. Simple harmonic motion has a sinusoidal waveform.
2007-03-16 17:02:59 · answer #2 · answered by Helmut 7 · 0⤊ 0⤋
Clearly the motion is periodic and has a period of 8 seconds.
But even tho it's periodic, it isn't caused by any type of elastic restoring force, so it fails to be 'harmonic'.
HTH ☺
Doug
2007-03-16 16:47:13 · answer #3 · answered by doug_donaghue 7 · 0⤊ 0⤋
Its motion is simple-harmonic because there isn't friction dampening the ball or an external force being applied to it.
2007-03-16 16:53:09 · answer #4 · answered by Blahblah_bbbllaah 2 · 0⤊ 1⤋