HELP! If a cue ball hits an 8ball, then the cue ball stops, the 8ball speeds away, did the cue exert a force?

Question

You see i am confused in this case because I know that within any situation in which an object accelerates from a stop to a velocity, a force must have acted upon it.

At the same time though, The cue ball is in fact being decelerated by the friction of the felt table when it first collides with the 8ball. So how can the cue ball exert a forward force on the 8ball if the cue ball has no forward force itself?

I absolutely realize that what occurs is a transfer of momentum and that momentum is always conserved. But I still don't understand if a force is exerted by the cue ball. If no force is exerted, how can one rectify this position since the 8 ball accelerates from stationary to having the velocity that the cue approached it with. Does anyone else agree that this is a fair question?

attn: 1st answerer, you just completely disregarded my acknowledgment that this is a transfer of momentum! I am amazed at how bad of an answer you gave. I know that P=MV and F=MA. That still doesn't answer my question! You essentially restated that which i stated in the third paragraph of my explanatory information!!!!!!!

My question is: Did a force act on the 8 bal, which accelerated from a stop to having a velocity! does anyone understand my question?

So now that I am thinking about the answers I realized something:

A body that exerts a force (causes an acceleration) doesn't necessarily have to have any acceleration at all.

For instance if one drops a pack of printer paper on a table, the paper stops on a dime, but the table had an acceleration of zero.

It just seems odd to me that an object that is slowing down (losing accelerating in the direction of its velocity) can exert a force on an object in the direction of its velocity!

I guess a similar situation would be if I threw a golf ball hard at a ceiling tile. Even though the golf ball is decelerating as soon as it leaves my hand, it can still cause the ceiling tile to accelerate (exert a force on the ceiling tile).

SO I GUESS THE MORE CONCISE VERSION OF MY QUESTION WOULD BE AS FOLLOWS:

CAN AN OBJECT WHOSE VELOCITY IN ITS INITIAL TDIRECTION IS DECREASING STILL EXERT A FORCE IN THE DIRECTION OF ITS INITIAL TRAVEL?

Answer 1

I understand the confusion. True, the friction with the felt is irrelevant; you would have the same situation if the pool table were frictionless. Also, let's assume the table is perfectly level, so gravity does not affect the movement of the balls and can be ignored.

Your cue ball is moving across the table with a certain velocity and therefore momentum. When it contacts the 8 ball, it applies a force to the 8 ball, which applies an equal and opposite force to the cue ball. The force causes each ball to compress. By design and careful choice of materials, the balls act like ideal springs, with an F=-kx force which is proportional to displacement. Some or all of the kinetic energy is now stored in the springs as potential energy. As the balls expand, they release their potential energy as kinetic energy.

The only time force is being applied is when the balls are in contact and compressed, usually a very short time. The rest of the time, the balls are in uniform motion, with no forces in play.

Answer 2

The ball is not being deccelerated by the friction with the felt of the table, at least not until after it hits the 8 ball. In fact, all the friction with the felt does is create the rotation of a cue ball when it starts out with little to no rotation, which gets blotted out by friction AFTER the collision.

Modelling this problem is actually easy. Ignore for a moment the losses due to friction with the felt and rotation and look at the system immediately before the cue ball hits the 8 ball.

Instead of the cue ball moving toward the 8 ball at velocity V, shift your reference frame by V/2. (The inertial reference frame where total momentum = 0.) Now the cue ball and the 8 ball are moving towards each other at identical V/2 velocities. After impact, they move away from each other at identical (but reversed,) V/2 velocities. Now shift your reference frame back: The cue ball is now stationary and the 8 ball's moving away at V.

There's no problem with that collision. Energy is conserved, and momentum is conserved. The friction with the felt doesn't really factor in.

[EDIT]
Oh yeah: The cue ball does exert a force on the 8 ball. It's a very brief, (nearly instantaneous,) very strong force that occurs in collisions with hard, elastic bodies, called an IMPULSE. Mostly we ignore the magnitude of the force and the duration of the force and just look at the amount of momentum transferred, since the numbers don't really mean much. A 1m*kg/s impulse could consist of 10,000 N for 1/10,000 th of a second.
[/EDIT]

[EDIT2]
" I guess a similar situation would be if I threw a golf ball hard at a ceiling tile. Even though the golf ball is decelerating as soon as it leaves my hand, it can still cause the ceiling tile to accelerate (exert a force on the ceiling tile).

SO I GUESS THE MORE CONCISE VERSION OF MY QUESTION WOULD BE AS FOLLOWS:

CAN AN OBJECT WHOSE VELOCITY IN ITS INITIAL TDIRECTION IS DECREASING STILL EXERT A FORCE IN THE DIRECTION OF ITS INITIAL TRAVEL?"

Of course. When an object collides with another, they each exert force on each other. Doesn't matter what other forces are acting on them at the time, since all that factors in is their masses, their momentum vectors, and their energies. You're overly complicating the question, however: Look at it this way:

A Tonka truck is rolling along the ground at some velocity V (which would be decreasing due to air resistance, friction in the axles, etc...) It collides with a wall where someone has put a spring, so the truck compresses the spring and rebounds at (roughly) the same velocity in the opposite direction it had when it was coming in. The whole time the truck is slowing down due to friction, but that doesn't mean it simply STOPS. The compression of the spring stores up the kinetic energy of the truck and then imparts it back to the truck on it's way backwards.

Why am I suggesting this example? Because every collision is basically a simplification of a spring-damper-mass system. We just call them collisions because they're so short-lived, and occur over such short distances that they're nearly impossible to model directly, but what REALLY happens in a collision of two billiard balls is that when the atoms of the cue ball get sufficiently close to the atoms of the 8 ball, the electrons in the outer shells of those atoms start repelling each other because they're negatively charged. That potential energy, which was stored in a spring in the previous example, is stored as electrostatic potential, only over distances on the order of 10^-10 m or less. This is one of the reasons people study ideal spring systems, (which never exist in the real world: There's ALWAYS some damping effect.) It's because they're good models for a great many much more interesting physical systems.
[/EDIT2]

Answer 3

Yes, seems fair question to me.
And also yes, the cue ball exerts a force on the 8-ball. Force is not conserved, so you can have a situation where there is no force (or very little) at one moment, and quite a lot of force a few milliseconds later.

By the way, the 8-ball will not have all the velocity of the cue ball. Perhaps about 0.1% - 1% of the energy / momentum will be dissipated as heat. (momentum is conserved, it just goes into the momentum of the air & felt molecules).

Answer 4

Nope, your over-thinking it man. The cue ball causes the 8-ball to accelerate, therefore it exerts a force. The fact that the cue-ball is decelrating because of friction while it hits the 8-ball is altogether irrelevant. The force exerted by the cue-ball on the 8-ball is due to the velocity of the cue ball and has nothing to do with its own deceleration.

To say it another way, there is no such thing as the conservation of acceleration. :-)

Answer 5

The muscles in your arm accelerated (imparted its kinetic energy) the cue stick, (minus some lost to heat and friction), the cue stick in turn accelerated the cue ball (minus some lost to friction as the cue stick slid across your fingers), the cue ball then accelerated (again imparted its kinetic energy) the eight ball but in this case: the total remaining energy of the cue ball was lost to the friction of the felt table and the rest to accelerate the eight ball which left the cue ball with zero kinetic energy so it stops. A better way to visualize this is to look at breaking a full rack of balls with the cue ball. The balls along the edge of the rack move farther than the balls in the middle. The kinetic energy is being passed from ball to ball until it reaches the balls on the outside who have no one to give up their energy to so they keep on going until they lose all of their energy by the friction of the table , hitting other balls or their energy being absorbed by the rails. If you could add up all these forces at work and compute the total (including the friction, distance traveled and all of the other factors) they would exactly equal the initial force of your arm accelerating the cue stick. As the definition of force is: an influence on a body or system, producing or tending to produce a change in movement or in shape or other effects and as your arm, cue stick, cue ball and eight ball are all exhibiting a change in movement, I think it's safe to say that all the players are transferring force from one to the other.

Answer 6

Yes the cue did exert a force; It hit the 8 ball; and the cue ball was hit by the cue stick.

Answer 7

of course they cue exerted force .they force is the momentum that was transfered to the eight ball. since the momentum was transfered to the eight ball there is no force left to move the cue

Answer 8

The collision must occur during a short interval of time say, DELTA t. Thus the force exerted is given by (change of momentum)/DELTA t by Newton's 2nd law!

Answer 9

Its an impulse. Impulse is defined as

I = F*delta(t), where delta(t) is the change in time

F*delta(t) = mass*delta(v), where delta(v) is the change in velocity.

Answer 10

don't confuse force with velocity; remember, gravity is a force, though you can't "see it" or "touch it".