Billiard Ball Collision

In summary, the balls have the same initial momentum, but the incoming ball has a higher final speed.
  • #1
Naeem
194
0
A ball of mass m = 2.1 kg moving with a speed of v0 = 15.2 m/s strikes an identical ball which was initially at rest. After the collision, the incoming ball (ball 1) goes off at q1 = 28° relative to its original direction and the struck ball (ball 2) moves off at q2 = 38° as shown in the diagram.

a) What is the magnitude of the initial momentum of the two ball system?

Ans, Used momentum m1v1 = m2v2 , Got the answer
b) What is the ratio of the balls' final speeds?
Since there is no vertical momentum before the collision, the net vertical momentum must be zero after the collision.
Since the vertical momentum must be zero after the collision, what does that tell us about the ratio of vertical momentum of the two balls?



c) What is the final speed of the incoming ball? v1

d)What is the final speed of the struck ball? v2

Need help with b , c , and d .
 

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  • #2
If i read your question correct then c and d are to be solved before b ...

Ok have u derived any equation whatsoever for the system ?? If so post it , because note that the system has two unknowns v1 and v2 and u should have two equations for this.

-- AI
 
  • #3
How do I do that ?

For the x direction would it be,

v1 cos theta1 and

for the y direction v2 sin (-theta2)

This is what I know, just a vauge idea, but I don't now if the eqns are correct .

Please guide.!
Appreciate ur help!111
 
  • #4
resolve the velocity vectors v1 and v2 along x and y directions
find the momentum equation along x - direction
find the momentum equation along y - direction

these form the two equation in two unknowns...
solve these to find v1 and v2 ...

-- AI
 
  • #5
There is only 1 vector pointing in the x and y directions

would it be

v1 cos theta1 + v1 sin theta2 = 0

and

v2 cos theta2 + v2sin theta2 = 0



How do i go about finding momentum... Please help
 
  • #6
Yes i think u have the equations on the right track

though ur second question is at err,
it should be v1sintheta1 = v2sintheta2
(can u see why??)
Now solve these two equations ...
obtain v1 and v2 ..

-- AI
 
  • #7
I have been trying this for a while now, but the ratio I am getting is incorrect.

Here is what I did:

Resolving components:

For the x- direction:

v1 cos theta1 + (-v1 cos(0)) = 0

Also,

-v2 cos (0) + v2 cos theta2 =0

For the y-direction:

v2 sin ( 90 - theta1) + (-v2 sin (90- theta2)) = 0

This is what I know so far,

Any insights would be appreciated!
 
  • #8
Naeem said:
A ball of mass m...strikes an identical ball ... at rest.
... (ball 1) goes off at q1 = 28° ...(ball 2) moves off at q2 = 38° as shown in the diagram.
.

[if] m1 = m 2 → θ1 + θ2 [should be] = 90°.
28°+38° = 66°
 
  • #9
Naeem said:
A ball of mass m = 2.1 ... After the collision, the incoming ball (ball 1) goes off at q1 = 28° relative to its original direction and the struck ball (ball 2) moves off at q2 = 38° as shown in the diagram.
.
if diagram is correct m2 should be ≈ 1
 

1. What is a billiard ball collision?

A billiard ball collision is when two billiard balls come into contact with each other, resulting in a change in their direction and speed.

2. What factors affect the outcome of a billiard ball collision?

The outcome of a billiard ball collision is affected by factors such as the mass, velocity, and angle of the balls, as well as the type of material the balls are made of.

3. How is the momentum of billiard balls affected during a collision?

During a billiard ball collision, the total momentum of the two balls remains the same, but it is transferred between the balls depending on their masses and velocities.

4. Are there any real-life applications of studying billiard ball collisions?

Yes, studying billiard ball collisions can help scientists understand and predict the movements of objects in other systems, such as particles in a gas or molecules in a chemical reaction.

5. How can the elasticity of billiard balls affect the outcome of a collision?

The elasticity of billiard balls, or how much they can deform and then return to their original shape, can impact the outcome of a collision. More elastic balls will transfer more energy between them, resulting in a more dramatic change in direction and speed.

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