Simple elastic particle problem

[seanistic]

Homework Statement

A 61.9kg object moving to the right at 43.3 cm/s overtakes and collides elastically with a second 44.9kg object moving in the same direction at 26.9cm/s

Find the velocity of the second object after the collision.

Homework Equations

My homework says its in the chapter and section with "velocity of the center of mass" and "momentum in terms of velocity of CM" But I think its wrong and I should be looking at the elastic collision chapter.

The Attempt at a Solution

I tried doing conservation of momentum but I don't know the velocity of object 1 after collision.
I tried using the elastic collision equations but those use one mass having a velocity of 0.

I pretty much confused where to start.

 

[rock.freak667]

I tried doing conservation of momentum but I don't know the velocity of object 1 after collision.
I tried using the elastic collision equations but those use one mass having a velocity of 0.

I pretty much confused where to start.

Use the conservation of linear momentum with the two unknown final velocities.
and then remember that in an elastic collision, kinetic energy is conserved and you can now find the two values for the final velocities.

 

[Moetasim]

As a scientist, it is important to approach problems systematically and consider all relevant equations and concepts. In this case, you are correct to consider both the concepts of conservation of momentum and elastic collisions. The key to solving this problem is to remember that in an elastic collision, both momentum and kinetic energy are conserved.

To begin, you can use the equation for conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision. In this case, the total momentum before the collision is the sum of the individual momentums of the two objects. Let's call the initial velocity of object 1 as u1 and the initial velocity of object 2 as u2. Therefore, the total momentum before the collision is:

P1 + P2 = (61.9kg * 43.3 cm/s) + (44.9kg * 26.9 cm/s)
P1 + P2 = 2678.27 kg * cm/s + 1208.81 kg * cm/s
P1 + P2 = 3887.08 kg * cm/s

After the collision, the two objects will have new velocities, v1 and v2 respectively. Therefore, the total momentum after the collision can be written as:

P1 + P2 = (61.9kg * v1) + (44.9kg * v2)

Since we know that momentum is conserved, we can set these two expressions equal to each other and solve for the unknown velocities:

2678.27 kg * cm/s + 1208.81 kg * cm/s = (61.9kg * v1) + (44.9kg * v2)

Next, we can use the concept of conservation of kinetic energy to find another equation. In an elastic collision, the total kinetic energy before the collision is equal to the total kinetic energy after the collision. Therefore, we can write:

KE1 + KE2 = KE1' + KE2'

Where KE1 and KE2 are the initial kinetic energies of the two objects and KE1' and KE2' are the final kinetic energies after the collision. Since we know the mass and initial velocity of each object, we can calculate their initial kinetic energies using the equation KE = 1/2 * m * v^2. Therefore, we have:

KE1 = 1/2 * 61.9kg * (43.3