What Are the Velocities and Forces in This Elastic Collision?

AI Thread Summary
In an elastic collision involving a 0.24kg object moving at 3.5m/s and a 0.40kg object moving at 2.1m/s, the velocities after the collision were calculated using conservation of momentum and energy principles. The initial momentum was determined to be 1.68 kg*m/s, leading to final velocities of -1.75m/s for the first object and 3.15m/s for the second. There was confusion regarding the derivation of the equation "-v2i + v1i = -v1f + v2f" and the signs of the final velocities. Participants sought clarification on how to calculate the average force exerted during the 0.010s contact time. The discussion emphasized the importance of correctly applying momentum and energy conservation in solving such problems.
chrisfnet
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Homework Statement



A 0.24kg object traveling rightward at 3.5m/s collides head-on and elastically with a 0.40kg object traveling leftward at 2.1m/s.

What are their velocities after the collision?

If the objects are in contact for 0.010s during the collision, what is the magnitude of the average force that they exert on each other?

Homework Equations



-v2i + v1i = -v1f + v2f

The Attempt at a Solution



Initial Momentum = 0.24kg(3.50m/s) + 0.40kg(2.1m/s)
Initial Momentum = 1.68 kg*m/s

1.68kg*m/s = 0.24kg * v1f + 0.40kg*v2f

* Now I find a substitution. *

-v2i + v1i = -v1f + v2f

-v2i + v1i = -2.1m/s + 3.5m/s = 1.40m/s
1.40m/s = -v1f + v2f
v2f = v1f + 1.40m/s

* Now I substitute it back into the above equation. *

1.68kg*m/s = 0.24kg*v1f + 0.40kg*(v1f + 1.40m/s)
1.68kg*m/s = 0.24kg*v1f + 0.40kg*v1f + 0.56kg*m/s
1.12kg*m/s = 0.64kg*v1f
-1.75m/s = v1f (Negative to indicate direction.)

* Now I substitute v1f into the original equation. *

1.68kg*m/s = 0.24kg * v1f + 0.40kg*v2f
1.68kg*m/s = 0.24kg * 1.75m/s + 0.40kg*v2f
v2f = 3.15m/s

I have no idea how to figure out the force exerted on each other. Could someone help here, and also verify that the above answers are correct? Thanks!
 
Physics news on Phys.org
To find the velocities of the objects after collision, you have to use the conservation of momentum and energy.
 
rl.bhat said:
To find the velocities of the objects after collision, you have to use the conservation of momentum and energy.

How would I integrate the conservation of energy?
 
I am trying to solve a similar problem and I have a question.

How did you get this one: "-v2i + v1i = -v1f + v2f" ?

how is this derived? How did ou determine "-v1f + v2f" where v1f is negative if mass is not part of the equation?
 
I am trying to solve a similar problem and I have a question.

How did you get this one: "-v2i + v1i = -v1f + v2f" ?

how is this derived? How did ou determine "-v1f + v2f" where v1f is negative if mass is not part of the equation?

Besides, if v1f is negative, then shouldn't v1f in this equation be negative as well?
"1.68kg*m/s = 0.24kg * v1f + 0.40kg*v2f"

If so, your answer will come out different.
 

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