A 0.203 kg plastic ball moves with a velocity of 0.30 m/s. It collides with a second plastic ball of mass 0.106 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, and the speed of the 0.106 kg ball is 0.26 m/s. What is the new velocity of the first ball?
To find the new velocity of the first ball after the collision, we can use the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it.
The momentum of an object is given by the formula: momentum = mass × velocity.
Before the collision, the total momentum of the system is the sum of the momenta of the two balls:
Total momentum before = (mass of first ball × velocity of first ball) + (mass of second ball × velocity of second ball)
Total momentum before = (0.203 kg × 0.30 m/s) + (0.106 kg × 0.10 m/s)
To find the new velocity of the first ball after the collision, we need to determine the total momentum after the collision. We can use the given information that both balls continue moving in the same original direction and the velocity of the second ball after the collision is 0.26 m/s.
Total momentum after = (mass of first ball × velocity of first ball after) + (mass of second ball × velocity of second ball after)
Total momentum after = (0.203 kg × velocity of first ball after) + (0.106 kg × 0.26 m/s)
Since the principle of conservation of momentum states that the initial momentum is equal to the final momentum:
Total momentum before = Total momentum after
(0.203 kg × 0.30 m/s) + (0.106 kg × 0.10 m/s) = (0.203 kg × velocity of first ball after) + (0.106 kg × 0.26 m/s)
Now we can solve for the velocity of the first ball after the collision:
(0.203 kg × velocity of first ball after) = (0.203 kg × 0.30 m/s) + (0.106 kg × 0.10 m/s) - (0.106 kg × 0.26 m/s)
Dividing both sides of the equation by 0.203 kg:
velocity of first ball after = [(0.203 kg × 0.30 m/s) + (0.106 kg × 0.10 m/s) - (0.106 kg × 0.26 m/s)] / 0.203 kg
Now you can plug in the values and calculate the new velocity of the first ball after the collision.