Trouble finding correct acceleration of a ball

In summary, the conversation involves finding the acceleration of a pool ball after being hit by a cue. The final velocity of the cue is 2.9m/s with an acceleration of 41.42m/s*2. The final velocity of the ball is assumed to be the same as the initial velocity of the cue, but this assumption may not be accurate due to factors such as elasticity and the mass difference between the cue and ball. Further calculations and considerations are needed to accurately determine the ball's acceleration and final velocity.
  • #1
Drake M
19
0

Homework Statement


Well I need to find the acceleration of a pool ball after it has been hit by the cue. I measured the final velocity of the cue which was 2.9m/s and its acceleration was 41.42m/s*2. I know that the vf of the cue is the vi of the ball and because the ball has friction after it has had the force applied, the acceleration should be a negative value but it keeps coming positive and pretty large too.
OF CUE:
Vi=0m/s
t=.07s
d=.1016m

Used d=1/2(Vi+Vf)t to find Vf rearranged to vf=2d/t-Vi

OF BALL:
Vi=2.9m/s
t=.118s
d=.5588m

Used the ball values for equation below

Homework Equations


d=Vit+(1/2)at*2

The Attempt at a Solution


rearranging for a I get 2(d-(Vi t )) all divided by t*2=a

Substituting values in I get 2(.5588m-(2.9m/s x .118s) divided by .118s*2

That turns into 2(.5588-.3422)/.0139s

and once finished I got 31.16m/s*2 as my acceleration. But if that is the case then my Vf of the ball will be greater than the Vi and that wouldn't make sense considering its on a horizontal surface and friction is being applied. Did I make a mistake in the calculations or values. ANY help would be appreciated, thanks in advance.
 
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  • #2
Check your multiplication of the ball's initial speed by travel time.
 
  • #3
2.9 x .118 = .3422
 
  • #4
Drake M said:
2.9 x .118 = .3422
Hmm.. my mistake.
Maybe you are wrong to assume the ball's initial speed is no more than the cue's final speed. The cue will be more massive than the ball (3 times seems typical), there is some elasticity in the tip, and quite a bit in the shaft of the cue. (See http://dbkcues.ru/articles-2/investigation-in-some-wave-properties-of-a-billiards-cue/?lang=en.)
If you were to go to the extreme and assume a fully elastic collision then I expect you would find the ball's initial speed could be substantially greater than the cue's maximum speed.
 
  • #5
If I were to factor in elasticity, how would I figure out how it affects it. All I would have would be Vi(or Vf of the cue). Thanks for all the help by the way.
 
  • #6
Drake M said:
If I were to factor in elasticity, how would I figure out how it affects it. All I would have would be Vi(or Vf of the cue). Thanks for all the help by the way.
You'd need to know the relative masses. With an estimate of the elasticity you could then use momentum and energy considerations to derive the two velocities after the stroke.
 
  • #7
Ok, thanks
 

FAQ: Trouble finding correct acceleration of a ball

1. What is acceleration and how is it measured?

Acceleration is the rate at which the velocity of an object changes over time. It is measured in meters per second squared (m/s^2).

2. How is the acceleration of a ball affected by air resistance?

Air resistance, also known as drag, can slow down the acceleration of a ball. This is because the force of air resistance acts opposite to the direction of motion, reducing the overall net force and therefore decreasing the acceleration.

3. Can the mass of the ball affect its acceleration?

Yes, the mass of the ball can affect its acceleration. According to Newton's Second Law of Motion, the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. Therefore, a heavier ball will have a slower acceleration than a lighter ball, assuming the same amount of force is applied.

4. How does the surface a ball rolls on affect its acceleration?

The surface a ball rolls on can affect its acceleration by changing the amount of friction between the ball and the surface. A rough surface will have more friction, slowing down the ball's acceleration, while a smooth surface will have less friction, allowing for a faster acceleration.

5. Can the angle of a ramp affect the acceleration of a ball?

Yes, the angle of a ramp can affect the acceleration of a ball. The steeper the angle of the ramp, the greater the acceleration of the ball will be. This is because the force of gravity acting on the ball will have a larger component along the ramp, contributing to a greater overall net force and therefore a faster acceleration.

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