A .50kg ball is rolling on a frictionless surface at a speed of .75m/s. it collides with a second ball with a mass of 1kg which is also moving in the same direction as the first ball with a speed of .38m/s. After the collision the firt ball continues at a reduced speed of .35m/s. what is the new speed of the second ball after the collision?
The new speed of the second ball is whatever conserves linear momentum.
Call it V2f
M1*V1i + M2*V2f = M1*V1f + M2*V2f
0.50*0.75 + 1.00*0.38 = 0.50*0.35 + 1.00*V2f
V2f = 0.58 m/s
To solve this problem, we can use the principles of conservation of momentum and conservation of kinetic energy. Both principles state that the total momentum and total kinetic energy of a system remain constant before and after a collision.
1. Conservation of momentum:
- The momentum of an object is defined as the product of its mass and velocity (p = m * v).
- In this case, the momentum before the collision is the sum of the momenta of the two balls:
- Momentum before collision = (mass of ball 1) * (velocity of ball 1) + (mass of ball 2) * (velocity of ball 2)
- Momentum before collision = (0.50 kg) * (0.75 m/s) + (1 kg) * (0.38 m/s)
2. Conservation of kinetic energy:
- The kinetic energy of an object is defined as half of its mass times the square of its velocity (KE = 0.5 * m * v^2).
- Before the collision, the total kinetic energy is the sum of the kinetic energies of the two balls:
- Kinetic energy before collision = (0.5 * mass of ball 1 * (velocity of ball 1)^2) + (0.5 * mass of ball 2 * (velocity of ball 2)^2)
- Kinetic energy before collision = (0.5 * 0.50 kg * (0.75 m/s)^2) + (0.5 * 1 kg * (0.38 m/s)^2)
Considering that both momentum and kinetic energy are conserved during the collision, we can equate the values before and after the collision for both principles:
1. Conservation of momentum:
- Momentum before collision = Momentum after collision
- (0.50 kg) * (0.75 m/s) + (1 kg) * (0.38 m/s) = (0.50 kg) * (0.35 m/s) + (1 kg) * (new velocity of ball 2)
2. Conservation of kinetic energy:
- Kinetic energy before collision = Kinetic energy after collision
- (0.5 * 0.50 kg * (0.75 m/s)^2) + (0.5 * 1 kg * (0.38 m/s)^2) = (0.5 * 0.50 kg * (0.35 m/s)^2) + (0.5 * 1 kg * (new velocity of ball 2)^2)
Now, we can solve these two equations simultaneously to find the new velocity of the second ball after the collision.