A 0.210 kg plastic ball moves with a velocity of 0.30 m/s. It collides with a second plastic ball of mass 0.109 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 0.109 kg ball is 0.26 m/s. What is the new velocity of the first ball?

Whatever conserves linear momentum

To find the new velocity of the first ball after the collision, we need to apply the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.

The momentum of an object can be calculated by multiplying its mass and velocity. Therefore, the total momentum before the collision can be expressed as 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)

Plugging in the given values:

Total momentum before = (0.210 kg) × (0.30 m/s) + (0.109 kg) × (0.10 m/s)

Now, to find the total momentum after the collision, we need the mass and velocity of both balls. From the question, we know that both balls continue moving in the same, original direction, and the post-collision velocity of the second ball (0.109 kg ball) is given as 0.26 m/s.

Total momentum after = (mass of first ball) × (new velocity of first ball) + (mass of second ball) × (new velocity of second ball)

Let's assume the new velocity of the first ball is V1. Plugging in the known values:

Total momentum after = (0.210 kg) × (V1) + (0.109 kg) × (0.26 m/s)

Since the total momentum before and after the collision should be equal, we can set up the following equation:

(0.210 kg) × (0.30 m/s) + (0.109 kg) × (0.10 m/s) = (0.210 kg) × (V1) + (0.109 kg) × (0.26 m/s)

Simplifying the equation:

0.063 kg·m/s + 0.0109 kg·m/s = (0.210 kg) × (V1) + 0.02834 kg·m/s

Rearranging and solving for V1:

(0.210 kg) × (V1) = 0.063 kg·m/s + 0.0109 kg·m/s - 0.02834 kg·m/s

(0.210 kg) × (V1) = 0.04556 kg·m/s

Dividing both sides of the equation by (0.210 kg):

V1 = 0.04556 kg·m/s / 0.210 kg

V1 ≈ 0.2175 m/s

Therefore, the new velocity of the first ball after the collision is approximately 0.2175 m/s.