A 0.201-kg plastic ball moves with a velocity of 0.30 m/s. It collides with a second plastic ball of mass 0.105 kg, which is moving along the same line at a speed of 0.10 m/s. After the collision, both balls continue moving in the same, original direction. The speed of the 0.105-kg ball is 0.26 m/s. What is the new velocity of the 0.201-kg ball?
To solve this problem, we need to apply the principles of conservation of momentum and kinetic energy.
First, let's calculate the initial momentum of each ball. The momentum (p) is given by the product of mass (m) and velocity (v):
For the 0.201-kg ball:
Initial momentum = (mass of 0.201-kg ball) × (initial velocity of 0.201-kg ball)
= (0.201 kg) × (0.30 m/s)
For the 0.105-kg ball:
Initial momentum = (mass of 0.105-kg ball) × (initial velocity of 0.105-kg ball)
= (0.105 kg) × (0.10 m/s)
Next, we need to calculate the final momentum of each ball. Since both balls continue moving in the same direction, the final momentum is still the sum of the individual momenta:
For the 0.201-kg ball:
Final momentum = (mass of 0.201-kg ball) × (final velocity of 0.201-kg ball)
For the 0.105-kg ball:
Final momentum = (mass of 0.105-kg ball) × (final velocity of 0.105-kg ball)
According to the conservation of momentum principle, the initial momentum of the two balls must equal the final momentum after the collision. Mathematically, this can be expressed as:
Initial momentum of 0.201-kg ball + Initial momentum of 0.105-kg ball = Final momentum of 0.201-kg ball + Final momentum of 0.105-kg ball
Using the values we have, we can set up and solve this equation to find the final velocity of the 0.201-kg ball.
(0.201 kg) × (0.30 m/s) + (0.105 kg) × (0.10 m/s) = (0.201 kg) × (final velocity of 0.201-kg ball) + (0.105 kg) × (0.26 m/s)
Simplifying this equation will give us the final velocity of the 0.201-kg ball.