# Elastic collision between two moving objects

• captainmustard
In summary, the question is about finding the velocities of two blocks, one with a mass of 0.2 kg and the other with a mass of 0.6 kg, after an elastic collision. The equations of conservation of momentum and conservation of energy are used, but there is not enough information to solve for the velocities as there are three unknowns. The problem would still be unsolvable even if it were a completely inelastic collision."
captainmustard

## Homework Statement

A 0.2 kg block, moving at 6 m/s, is catching up and colliding elastically with a 0.6 kg block that is moving along the same line and in the same direction. Find the velocities of the ball after this one-dimensional collision.

## Homework Equations

Conservation of momentum, conservation of energy

## The Attempt at a Solution

First, I figured the momentum and kinetic energy would be conserved so I setup a couple of equations:

m1v1i + m2v2i = m1v1f + m2v2f
and
m1v1i^2 + m2v2i^2 = m1v1f^2 + m2v2f^2

At this point, I realize I have 3 unknowns (v2i, v1f and v2f) and I simply don't know what I can even do with this information. Any ideas at all would be helpful.

Hi, captainmustard. Welcome to PF!

You are right. There is not enough information to answer the question. You have set up the correct equations.

Thank you for the response. I thought I was going crazy for a moment there. Would this be possible if it were a completely inelastic collision? I would imagine it would involve some tedious algebra if so.

No, you need the initial velocity of the 0.6 kg ball, too.

ehild

I would approach this problem by first defining the variables and their units. The mass of the first block, m1, is 0.2 kg and its initial velocity, v1i, is 6 m/s. The mass of the second block, m2, is 0.6 kg and its initial velocity, v2i, is also 6 m/s. The final velocities of both blocks after the collision are v1f and v2f.

Next, I would use the equations of conservation of momentum and conservation of energy to solve for the unknowns. In an elastic collision, both momentum and kinetic energy are conserved.

Using the conservation of momentum equation, we can write:

m1v1i + m2v2i = m1v1f + m2v2f

Substituting in the known values, we get:

0.2(6) + 0.6(6) = 0.2(v1f) + 0.6(v2f)

Simplifying, we get:

1.2 = 0.2(v1f) + 0.6(v2f)

Next, using the conservation of energy equation, we can write:

m1v1i^2 + m2v2i^2 = m1v1f^2 + m2v2f^2

Substituting in the known values, we get:

0.2(6)^2 + 0.6(6)^2 = 0.2(v1f)^2 + 0.6(v2f)^2

Simplifying, we get:

7.2 = 0.2(v1f)^2 + 0.6(v2f)^2

Now we have two equations and two unknowns (v1f and v2f). We can solve for these unknowns by using algebraic manipulation or by using a graphing calculator.

Solving for v1f in the first equation, we get:

v1f = (1.2 - 0.6(v2f))/0.2

Substituting this into the second equation, we get:

7.2 = 0.2[(1.2 - 0.6(v2f))/0.2]^2 + 0.6(v2f)^2

Simplifying, we get a quadratic equation:

(v

## 1. What is an elastic collision?

An elastic collision is a type of collision between two objects in which kinetic energy is conserved. This means that after the collision, the total amount of kinetic energy in the system remains the same as it was before the collision.

## 2. How is the speed of the objects affected in an elastic collision?

In an elastic collision, the speed of the objects may change, but the total kinetic energy of the system remains the same. This means that if one object's speed increases, the other object's speed will decrease in order to maintain the same total kinetic energy.

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

In an elastic collision, kinetic energy is conserved, while in an inelastic collision, some kinetic energy is lost. In an inelastic collision, the objects may also stick together or deform, while in an elastic collision, they bounce off each other.

## 4. How can I calculate the velocities of the objects after an elastic collision?

The velocities of the objects after an elastic collision can be calculated using the conservation of momentum and the conservation of kinetic energy equations. These equations take into account the masses, initial velocities, and final velocities of the objects.

## 5. Can an elastic collision occur between objects of different masses?

Yes, an elastic collision can occur between objects of different masses. The final velocities of the objects will depend on their initial velocities and masses, but the total kinetic energy of the system will remain constant.

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