Physics Homework

December 10, 2003 1:13 PM

Ok, its homework help time! You'll probably groan at me to do the work myself, but believe me, I am. I'm just a little short of time, and textbooks and Google are not helping me. I'm analysing the data collected from my Physics coursework, and realised I need to know: Is the coefficient of restitution of two particles a measure of the percentage of kinetic energy retained after a collision? Or is it the energy lost? Or something else entirely?
posted by Orange Goblin to Science & Nature (8 answers total)

From what I can see, yes. Check out here. Appears that the CoR is simply a ratio between 1 and 0 that tells you the elacisity of 2 objects colliding. If a colision is perfectly elastic, then the collision is perfectly elastic meaning that energy is conserved (something thats pretty much impossibly to achieve in an experiment). If a collision is perfectly inelastic, I forget if energy is conserved or not (we never used restitution in my physics class- we mainly used the KE=1/2(mv^2) formula that you can expand however necessary.
Hope that helps some...
posted by jmd82 at 1:28 PM on December 10, 2003

See here.
posted by monju_bosatsu at 1:28 PM on December 10, 2003

the coefficient of restitution (CR) is a measure of how much kinetic energy is retained during the collision.

If the coefficient is 1, then no kinetic energy (KE) has been lost. If it is 0, then all the kinetic energy has been transformed into some other energy (usually heat). If you need a percentage (of KE retained) then just multipy the CR by 100.
posted by vacapinta at 1:28 PM on December 10, 2003

Response by poster: Argh. My experimental data would have been perfect if the CoR was a measurement of energy lost, not energy conserved.

One thing that has me stumped is when the particles stick together, but continue to move. The CoR is 0, but the KE retained obviously isn't...
posted by Orange Goblin at 1:42 PM on December 10, 2003

Yeah, I wasnt really right. CR is just a measure of elasticity. Perfect elasticity means that KE and momentum were conserved, so both particles will go off with the same velocity they came in.

When CR=0 it just means that the elasticity was 0 - and both particles stuck together. Think of it as a measure of the "bounce". If both particles stick together, the system may still have some KE but there is definitely no bounce.

CR is most useful when one "particle" is a wall for example. Then the only particle you care about is the other one, and quantities like momentum (v), CR (v) and KE (v^2) line up nicely, even if KE is not proportional to the other two.

Above all, dont use CR in energy calculations since it is not a form of energy but simply a measurable quantity.
posted by vacapinta at 2:25 PM on December 10, 2003

Response by poster: So CR is NOT the percentage of energy retained? :/ I'm confused. Lets say both particles are mass 2kg, to keep things simple. One particle hits the other (which is at rest) with a speed of 10m/s. The KE of the system is thus 100J. The first particle stops, and the second continues at 9m/s. The KE of the system is thus 81J, and the percentage of KE retained is 81%. The CR would be 9/10 = 0.9, or 90%, which is obviously not the same.

Now, I just pulled those figures out of my arse, so it could be wrong, but basically: CR is a measurement useful for comparing the "bounce" of 2 particles, but not much else. Yes?
posted by Orange Goblin at 2:38 PM on December 10, 2003

So CR is NOT the percentage of energy retained?

Correct. KE is a sum of two velocity-squareds. CR is the difference between two velocities. Also energy depends on mass. So, two particles could transfer energy, still keep the total KE the same but the CR would be less than 1. Why? because momentum was not transferred correctly (which is mv) and thus the elasticity was not perfect.

CR is a measurement useful for comparing the "bounce" of 2 particles, but not much else. Yes?

Basically, yeah. Its a good macro tool for assessing the elasticity of a collision without having to deal with energies and momentums and masses. So, saying that a certain rubber ball has a CR of .8 when bounced off a wooden floor tells you a lot about the collision that will happen without getting bogged down in particulars.
posted by vacapinta at 2:49 PM on December 10, 2003

Response by poster: Right, cheers. As is often the case with these things, talking it out makes you realise what an idiot you are.
posted by Orange Goblin at 3:11 PM on December 10, 2003