# Solving Elastic Collision Homework - Exam Prep Question

• bobred
In summary, the problem involves a collision between two particles, A and B, with masses 3m and m respectively. The collision is elastic, and after the collision, particle A is observed to be moving along the positive y-axis. The final speeds of the two particles can be found using the conservation of kinetic energy and linear momentum. To solve the problem, equations for both the x and y components of momentum can be written, with the final velocities of the particles represented as λj and αi + βj.
bobred

## Homework Statement

This is an exam prep question

Particle A has mass 3m and velocity i + 2j, it collides with particle B mass m velocity -i + j. Collision is elastic. After collision Particle A is observed to be moving along the +ve y-axis. Find the final speeds of the two particles.(two possible cases)

## Homework Equations

Being elastic the kinetic energy is the same before the collision and after.
We are given the answers ($$3/2,\sqrt{41}/2$$ or $$2,\sqrt{5}$$.

## The Attempt at a Solution

Could someone give me a little nudge in the right direction? I can't see where to begin, what is the state of B after the collision?

Thanks

Right, so you can form the conservation of kinetic energy equation.

You also need to use conservation of linear momentum. Momentum before = momentum after.

Since you do not know the magnitudes of the final velocities, here is how I put them as

vAj and vBi + βj

I got that far but can't see how to proceed.

As rock.freak suggested write up the equations for both the x and y components of the momentum.

ehild

I would approach this problem by first understanding the concept of elastic collisions. An elastic collision is one in which the total kinetic energy of the system is conserved. In this case, we can use the conservation of kinetic energy to solve for the final speeds of the two particles.

To begin, we can use the given information about the masses and velocities of the particles before the collision to calculate their initial kinetic energies. We know that kinetic energy is equal to 1/2 * mass * velocity^2. So for particle A, the initial kinetic energy would be (1/2)*(3m)*(i+2j)^2 and for particle B, the initial kinetic energy would be (1/2)*(m)*(-i+j)^2.

Next, we can use the fact that the total kinetic energy is conserved to set up an equation where the sum of the initial kinetic energies is equal to the sum of the final kinetic energies. This would look like (1/2)*(3m)*(i+2j)^2 + (1/2)*(m)*(-i+j)^2 = (1/2)*(3m)*(0+j)^2 + (1/2)*(m)*(0+0)^2. This equation can be simplified to (1/2)*(3m)*(i^2+4j^2+4ij) + (1/2)*(m)*(i^2+j^2-2ij) = (1/2)*(3m)*(j^2) + 0. From here, we can solve for the final speed of particle A, which would be equal to the square root of (3j^2)/4m.

To find the final speed of particle B, we can use the fact that momentum is also conserved in elastic collisions. Since we know the final velocity of particle A, we can use the equation m1v1 + m2v2 = m1v1' + m2v2' to solve for v2'. Plugging in the values, we get (3m)*(i+2j) + (m)*(-i+j) = (3m)*(0+j) + (m)*v2'. Simplifying this equation, we get v2' = (2i+3j)/4m. We can then use the Pythagorean theorem to find the magnitude of v2', which would be equal to the square root of (2

## 1. What is an elastic collision?

An elastic collision is a type of collision between two objects where there is no net loss of kinetic energy. This means that the total kinetic energy before and after the collision is the same.

## 2. How do you calculate the final velocities in an elastic collision?

The final velocities in 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 and initial velocities of the objects.

## 3. What are the conditions for an elastic collision to occur?

In order for a collision to be considered elastic, the objects involved must be able to return to their original shape after the collision and there can be no external forces acting on the objects during the collision.

## 4. Can an elastic collision occur in real life?

Yes, an elastic collision can occur in real life, although it is rare. Examples include collisions between subatomic particles and collisions between gas molecules.

## 5. How does an elastic collision differ from an inelastic collision?

An inelastic collision is a type of collision where there is a loss of kinetic energy, meaning that the total kinetic energy before and after the collision is not the same. In contrast, an elastic collision has no net loss of kinetic energy.

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