B Colliding balls: Conservation of momentum and changes in kinetic energy?

AI Thread Summary
The discussion explores the relationship between momentum and kinetic energy in the context of collisions, specifically using the example of cue balls. It highlights that while momentum can be conserved in a collision, kinetic energy may not be conserved due to energy being transformed into other forms, such as heat and sound. The initial confusion arises from the assumption that a lighter ball can have greater kinetic energy while maintaining the same momentum as a heavier ball. Clarification is provided that in a perfectly elastic collision, the final velocities of both balls differ, demonstrating that energy is not "created" but redistributed. Ultimately, the conversation emphasizes the importance of applying both conservation laws to understand the dynamics of collisions accurately.
cueballbullet
Messages
1
Reaction score
0
I got curious about firearm ballistics and googled something similar to "bullet momentum vs kinetic energy".

IIRC, momentum P = mv (checked); and kE = (mv^2)/2 (also checked).

So I essentially wondered if it's worse to get hit by a bullet with greater kE than by one with lesser kE, presuming that P remains the same (same momentum (also same shape and size); yet different masses and velocities).

Quickly I learned that the faster, lighter bullet causes more damage and has (/because it has) more kE, as the greater amount of kE gets transferred to the bodily tissues.

Cool. Yet this led me to wonder about something else:

Posit that a rolling cue ball, B, of mass M, moving at velocity V, hits another cue ball, b, of mass M/2. If momentum is conserved, then the latter, lighter cue ball, b, will start rolling at velocity 2V... So, same momentum, and different velocities. This means that b has greater kinetic energy than B.

Everything makes sense in my non-physicist mind up until that last sentence. For the life of me I can't guess at all where that extra energy comes from. Same momentum, but twice the speed, because of half the weight. Cool. But again, if the momentum is indeed the same, but the speeds are different, then the kE should also be different, right? How does this work? I may have misunderstood something along the way and perhaps the energy is not greater in b than in B, afterall.
 
Physics news on Phys.org
cueballbullet said:
Posit that a rolling cue ball, B, of mass M, moving at velocity V, hits another cue ball, b, of mass M/2. If momentum is conserved, then the latter, lighter cue ball, b, will start rolling at velocity 2V... So, same momentum, and different velocities. This means that b has greater kinetic energy than B.
You are assuming that the rolling ball transfers all its momentum to the second ball, then stops dead. That's not how it works. To figure out the speeds of both after the collision, one must apply both conservation of momentum (total momentum of both) and conservation of energy. (If anything, in a real collision, some of the energy will be "lost" to heat and sound.)
cueballbullet said:
Everything makes sense in my non-physicist mind up until that last sentence. For the life of me I can't guess at all where that extra energy comes from.
That's good instinct to sense something's not right. The answer: There is no extra energy!
 
Just for fun, here are the final speeds of each. (Assuming a perfectly elastic head-on collision, which is the simplest to analyze.)

Final speed of the first ball: V/3
Final speed of the second ball: 4V/3
 
The rope is tied into the person (the load of 200 pounds) and the rope goes up from the person to a fixed pulley and back down to his hands. He hauls the rope to suspend himself in the air. What is the mechanical advantage of the system? The person will indeed only have to lift half of his body weight (roughly 100 pounds) because he now lessened the load by that same amount. This APPEARS to be a 2:1 because he can hold himself with half the force, but my question is: is that mechanical...
Let there be a person in a not yet optimally designed sled at h meters in height. Let this sled free fall but user can steer by tilting their body weight in the sled or by optimal sled shape design point it in some horizontal direction where it is wanted to go - in any horizontal direction but once picked fixed. How to calculate horizontal distance d achievable as function of height h. Thus what is f(h) = d. Put another way, imagine a helicopter rises to a height h, but then shuts off all...
Some physics textbook writer told me that Newton's first law applies only on bodies that feel no interactions at all. He said that if a body is on rest or moves in constant velocity, there is no external force acting on it. But I have heard another form of the law that says the net force acting on a body must be zero. This means there is interactions involved after all. So which one is correct?
Back
Top