Collisions -- conceptual questions

In summary, to find the final velocities of particles 1 and 2 after an elastic collision, you can use the momentum equation (mv_1 + mv_2 = mv) and the kinetic energy equation (0.5m(v_1)^2 + 0.5m(v_2)^2 = 0.5mv^2) to solve for v_1 and v_2.
  • #1
HSchuster
2
0

Homework Statement


Let two particles of equal mass m collide. Particle 1 has initial velocity v, directed to the right, and particle 2 is initially stationary.

A: If the collision is elastic, what are the final velocities v_1 and v_2 of particles 1 and 2?

B: Now assume that the mass of particle 1 is 2m, while the mass of particle 2 remains m. If the collision is elastic, what are the final velocities v_1 and v_2 of particles 1 and 2?

Homework Equations


i:[/B] mv_1 + mv_2 = mv
ii: 0.5m(v_1)^2 + 0.5m(v_2)^2 = 0.5mv^2
iii: 2mv_1 + mv_2 = 2mv
iv: 0.5(2m)(v_1)^2 + 0.5m(v_2)^2 = 0.5(2m)v^2

The Attempt at a Solution


For A, after factoring out m and rearranging equation i to solve for v_2 I replaced v_2 in equation i with v_2 = (v - v_1) to yield:
v_1 + v_2 = v_1 + (v - v_1) = v_1 - v_1 + v = v, therefore
v = v.

I guessed (correctly) that v_1 = 0 and v_2 = v, but I'm not sure how I can find those answers using this equation.

It's the same thing with part B.

I tried rearranging the kinetic energy equations ii and iv for both parts A and B but still came out with such useless results as v^2 = v^2.

Why does particle 1 in part A transfer all of its momentum to particle 2?
 
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  • #2
HSchuster said:

Homework Statement


Let two particles of equal mass m collide. Particle 1 has initial velocity v, directed to the right, and particle 2 is initially stationary.

A: If the collision is elastic, what are the final velocities v_1 and v_2 of particles 1 and 2?

B: Now assume that the mass of particle 1 is 2m, while the mass of particle 2 remains m. If the collision is elastic, what are the final velocities v_1 and v_2 of particles 1 and 2?

Homework Equations


i:[/B] mv_1 + mv_2 = mv
ii: 0.5m(v_1)^2 + 0.5m(v_2)^2 = 0.5mv^2
iii: 2mv_1 + mv_2 = 2mv
iv: 0.5(2m)(v_1)^2 + 0.5m(v_2)^2 = 0.5(2m)v^2

The Attempt at a Solution


For A, after factoring out m and rearranging equation i to solve for v_2 I replaced v_2 in equation i with v_2 = (v - v_1) to yield:
v_1 + v_2 = v_1 + (v - v_1) = v_1 - v_1 + v = v, therefore
v = v.

I guessed (correctly) that v_1 = 0 and v_2 = v, but I'm not sure how I can find those answers using this equation.

Substitute v_2 = (v - v_1) into the energy equation.

HSchuster said:
It's the same thing with part B.
Again, use both equations, momentum and energy. Express v_2 with v_1 from the momentum equation and substitute into the energy equation.
HSchuster said:
I tried rearranging the kinetic energy equations ii and iv for both parts A and B but still came out with such useless results as v^2 = v^2.

Why does particle 1 in part A transfer all of its momentum to particle 2?
It is the solution of the system of equation i and ii.
 
  • #3
ehild said:
Substitute v_2 = (v - v_1) into the energy equation.Again, use both equations, momentum and energy. Express v_2 with v_1 from the momentum equation and substitute into the energy equation.

It is the solution of the system of equation i and ii.

That makes sense, thanks!
 

1. What is a collision?

A collision is an event in which two or more objects come into contact with each other and exchange energy or momentum.

2. What factors determine the outcome of a collision?

The outcome of a collision is determined by factors such as the mass, velocity, and direction of the objects involved, as well as the type of collision (elastic or inelastic).

3. What is the difference between an elastic and inelastic collision?

In an elastic collision, the total kinetic energy of the system is conserved, meaning there is no loss of energy during the collision. In an inelastic collision, some energy is lost in the form of heat or sound, resulting in a decrease in the total kinetic energy of the system.

4. Can collisions be perfectly elastic?

Yes, in a perfectly elastic collision, the total kinetic energy of the system is conserved and there is no loss of energy. This type of collision is only possible in an idealized scenario where there is no friction or deformation of the objects involved.

5. How do collisions affect the motion of objects?

Collisions can cause objects to change direction, speed up, slow down, or come to a complete stop. The specific effect on an object's motion depends on the type of collision and the properties of the objects involved.

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