A marble with a mass of 0.5 kg is moving to the right at 1.25 m/s and a second marble with a mass of 0.35 kg is moving to the left at 2.15 m/s. If they collide head on and the collision is elastic find the final velocities of the two marbles
write the conservation of momentum. Find v2' in terms of m1, m2, and v1'
then write the conservation of energy. for v2' put in what you have from the first equation.
A bit of algebra is required.
I get V'2 = 1.09 m/s and V'1 = 1.99 m/s
Does anyone else concur?
To find the final velocities of the two marbles after the collision, we can use conservation of momentum and conservation of kinetic energy.
1. First, let's calculate the initial momentum of the system. The momentum of an object is given by the product of its mass and velocity.
For the first marble:
Initial momentum = mass * velocity = 0.5 kg * 1.25 m/s = 0.625 kg·m/s (to the right)
For the second marble:
Initial momentum = mass * velocity = 0.35 kg * (-2.15 m/s) = -0.7525 kg·m/s (to the left)
2. Next, since the collision is elastic, the total momentum of the system before the collision will be equal to the total momentum after the collision.
Therefore, the sum of the initial momenta of the two marbles will be equal to the sum of the final momenta:
Initial momentum of the system = Final momentum of the system
0.625 kg·m/s - 0.7525 kg·m/s = (mass1 * final velocity1) + (mass2 * final velocity2)
0.625 kg·m/s - 0.7525 kg·m/s = (0.5 kg * final velocity1) + (0.35 kg * final velocity2)
3. Now, let's use conservation of kinetic energy to form another equation. In an elastic collision, the total kinetic energy before the collision is equal to the total kinetic energy after the collision.
The kinetic energy of an object is given by the formula: KE = 0.5 * mass * (velocity^2)
Initial kinetic energy = Final kinetic energy
0.5 * 0.5 kg * (1.25 m/s)^2 + 0.5 * 0.35 kg * (-2.15 m/s)^2 = 0.5 * 0.5 kg * (final velocity1^2) + 0.5 * 0.35 kg * (final velocity2^2)
Please solve the above equations to find the final velocities of the two marbles.