What Are the Velocities and Forces in This Elastic Collision?

Click For Summary

Homework Help Overview

The discussion revolves around an elastic collision problem involving two objects of different masses and initial velocities. The original poster seeks to determine their velocities after the collision and the average force exerted during the contact time.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of conservation of momentum and energy principles to find the post-collision velocities. There are questions about the derivation of the equations used, particularly regarding the signs of the velocities and the assumptions made in the calculations.

Discussion Status

Some participants have provided guidance on using conservation laws, while others are questioning the derivation of specific equations and the implications of negative velocities. Multiple interpretations of the equations are being explored, and there is an ongoing inquiry into the correctness of the original poster's calculations.

Contextual Notes

There is a focus on the assumptions regarding the direction of velocities and the implications of negative values in the context of the problem. Participants are also considering the integration of energy conservation in their analyses.

chrisfnet
Messages
38
Reaction score
0

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.
 

Similar threads

How to Calculate Speed of Head of Driver After Collision?
  • · Replies 10 ·
Replies
10
Views
3K
Elastic head-on collision problem
  • · Replies 8 ·
Replies
8
Views
2K
Two dimensional Elastic Collision
  • · Replies 2 ·
Replies
2
Views
2K
Solve Elastic Collision: 2D Homework
  • · Replies 4 ·
Replies
4
Views
2K
Glancing elastic collision, and center of mass
  • · Replies 17 ·
Replies
17
Views
5K
Conservation of momentum - with understanding
  • · Replies 2 ·
Replies
2
Views
2K
What Happens to Sphere Velocities After an Elastic Collision?
  • · Replies 1 ·
Replies
1
Views
4K
Zero momentum reference frame and an inelastic collision
  • · Replies 4 ·
Replies
4
Views
3K
Elastic glancing collision problem
  • · Replies 4 ·
Replies
4
Views
3K
Elastic Collision Formula: Solving for Final Velocity and Mass Ratios
  • · Replies 2 ·
Replies
2
Views
2K