# Solving Elastic Collisions Involving 3 Blocks

• lu22
Finally, use the conservation of momentum equation to find the final velocity of block A. In summary, the final velocities of blocks A, B, and C can be determined by using conservation of momentum and conservation of energy for elastic collisions, and the answers should be in terms of 'm' and the initial velocity 'v.'
lu22

## Homework Statement

There are 3 blocks, A B and C, arranged left to right. blocks A and C have masses of m and block B has mass of 2m. block A heads toward the other two with velocity v. determine the final velocity of each block after all subsequent collisions. assume all collisions are elastic.

## Homework Equations

conservation of momentum for elastic collisions -- m1vi + m2vi = m1v1f + m2v2f

conservation of energy for elastic collisions -- 1/2m1v1i2 + 1/2m2v2i2 = 1/2m1v1f2 +
1/2m2v1f2

## The Attempt at a Solution

I tried this a couple different ways but its confusing without numbers
I also don't know if I should use just momentum or just energy or a combination of both

thanks for the help!

You're going to have to use both conservation laws. In the end your answers should be in terms of only 'm' and the initial velocity 'v.' Start by looking at the first collision, and find the final velocities in terms of m and v. Once you have that, do the same thing for the second collision (between blocks B and C).

## 1. How do you calculate the final velocities of three blocks after an elastic collision?

To calculate the final velocities of three blocks after an elastic collision, you will need to use the conservation of momentum and the conservation of kinetic energy equations. First, calculate the total momentum and total kinetic energy before the collision. Then, use these values to solve for the final velocities of each block using the equations.

## 2. What is an elastic collision?

An elastic collision is a type of collision where the total kinetic energy of the system is conserved. This means that the objects involved in the collision do not lose any energy during the collision, and the total momentum of the system is also conserved.

## 3. Can the final velocities of three blocks in an elastic collision be negative?

Yes, the final velocities of the blocks can be negative in an elastic collision. This means that the blocks are moving in the opposite direction after the collision compared to before the collision. Negative velocities indicate the direction of motion, not the magnitude.

## 4. How do you determine if a collision is elastic?

To determine if a collision is elastic, you can calculate the total kinetic energy before and after the collision. If the total kinetic energy is the same, then the collision is considered to be elastic. Additionally, in an elastic collision, the objects involved should also bounce off each other without any deformation or loss of energy.

## 5. What is the difference between elastic and inelastic collisions?

The main difference between elastic and inelastic collisions is the conservation of kinetic energy. In an elastic collision, the total kinetic energy is conserved, while in an inelastic collision, some kinetic energy is lost due to deformation or conversion into other forms of energy. Additionally, objects involved in an elastic collision will bounce off each other, while objects in an inelastic collision will stick together or remain in contact after the collision.

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