Solving Elastic Collision: V1' = -2.5 m/s, 5.9 m/s

In summary: So, you should use the information about the direction of the initial velocity to identify which solution is the correct one.In summary, the problem involves an elastic head-on collision between two identical pool balls with initial velocities of 2.5 m/s and -5.9 m/s. By applying the equations of conservation of momentum and conservation of energy, we can solve for the velocities of the balls after the collision. After substituting the given values and solving for V1', we get two solutions: -2.5 m/s and 5.9 m/s. However, by considering the direction of the initial velocities, we can determine that the correct solution is V1' = -5.9 m/s and V2' = 2
  • #1
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Homework Statement


The problem is pretty simple, however I don't understand which value to use after using quad formula to solve. See below.

V1(initial) = 2.5 m/s
V2(Initial) = -5.9 m/s

A pool ball moving with a speed of 2.5 m/s makes an elastic head-on collision with an identical ball traveling in the opposite direction with a speed of 5.9 m/s. Find the velocities of the balls after the collision.

Homework Equations


ΣP(initial) = ΣP(final)
M1V1 + M2V2 = M1V1' + M2V2'
M1 = M2
2.5 + (-5.9) = V1' + V2'

V2' = -V1' - 3.4

Elastic collision: KE(initial) = KE(final)
(Mass cancels out)
V12+V22 = V1'2+V2'2

The Attempt at a Solution


From above, I got:
0 = 2V1'2 - 6.8V1' - 29.5
by substituting "V2' = -V1' - 3.4" for V2'

After applying quadratic equation I got:
V1' = -2.5 m/s, 5.9 m/s

My problem is I do not know which one is the correct answer. My answer key says V1' is equal to -2.5 m/s, but I have no idea why.
Any help is appreciated!
 
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  • #2
KoaDcT said:

Homework Statement


The problem is pretty simple, however I don't understand which value to use after using quad formula to solve. See below.

V1(initial) = 2.5 m/s
V2(Initial) = -5.9 m/s

A pool ball moving with a speed of 2.5 m/s makes an elastic head-on collision with an identical ball traveling in the opposite direction with a speed of 5.9 m/s. Find the velocities of the balls after the collision.

Homework Equations


ΣP(initial) = ΣP(final)
M1V1 + M2V2 = M1V1' + M2V2'
M1 = M2
2.5 + (-5.9) = V1' + V2'

V2' = -V1' - 3.4

Elastic collision: KE(initial) = KE(final)
(Mass cancels out)
V12+V22 = V1'2+V2'2

The Attempt at a Solution


From above, I got:
0 = 2V1'2 - 6.8V1' - 29.5
by substituting "V2' = -V1' - 3.4" for V2'

After applying quadratic equation I got:
V1' = -2.5 m/s, 5.9 m/s

My problem is I do not know which one is the correct answer. My answer key says V1' is equal to -2.5 m/s, but I have no idea why.
Any help is appreciated!
Check the signs of the solutions. The answer key can be wrong.
 
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  • #3
I don't really understand what you said in the brackets, do you mean if the initial velocity is positive, then the answer must be negative after collision?
I also have another problem with this question. In my solution I substituted "V2' = -V1' - 3.4", so if V1' is equal to -2.5 m/s then V2' should be -0.9 m/s. However the answer is V1' = -2.5 m/s, V2' = +5.9 m/s, which makes no sense.
 
  • #4
Ah, I found my mistake right after I posted. Now my final answer is V1' = -5.9 m/s, and V2' = 2.5 m/s. I think that is the right answer.
Thanks for the help :)
 
  • #5
KoaDcT said:
Ah, I found my mistake right after I posted. Now my final answer is V1' = -5.9 m/s, and V2' = 2.5 m/s. I think that is the right answer.
Thanks for the help :)
The balls just exchanged velocity due to the collision. The other solution v1'=2.5 m/s, v2'=-5.9 m/s means that nothing has changed, both balls keep moving with the original velocity. That means they did not collide. But the equations for conservation of momentum and conservation of energy are valid also in the case if the balls just pass each other and do not collide.
 

What is an elastic collision?

An elastic collision is a type of collision between two objects in which both kinetic energy and momentum are conserved. This means that the total energy and total momentum of the system before and after the collision are equal.

What are the equations used to solve elastic collisions?

The equations used to solve elastic collisions are the conservation of momentum equation (p1 + p2 = p'1 + p'2) and the conservation of kinetic energy equation (1/2m1v1^2 + 1/2m2v2^2 = 1/2m1v'1^2 + 1/2m2v'2^2).

What is the initial velocity (V1) in the given problem?

The initial velocity (V1) in the given problem is -2.5 m/s. It is important to note the negative sign, as it indicates that the object is moving in the opposite direction of the positive direction of the coordinate system.

What is the final velocity (V1') in the given problem?

The final velocity (V1') in the given problem is 5.9 m/s. This is the velocity of the first object after the collision has occurred.

How do I solve for the final velocity (V1') in this problem?

To solve for the final velocity (V1') in this problem, you can use the conservation of momentum and conservation of kinetic energy equations. Plug in the given values for momentum and kinetic energy before the collision, and solve for V1' using algebraic manipulation.

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