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?

Question

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?

Answer 1

conservation of momentum

.201 (.3) + .105 (.1) = .201 (v) + .105 (.26)

Answer 2

To find the new velocity of the 0.201-kg ball after the collision, we can use the law of conservation of momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision.

The momentum of an object is calculated by multiplying its mass by its velocity:

Momentum = Mass x Velocity

So, we can calculate the initial momentum of the system before the collision:

Initial momentum = (Mass1 x Velocity1) + (Mass2 x Velocity2)

Here, Mass1 is the mass of the 0.201-kg ball, Velocity1 is its velocity before the collision, Mass2 is the mass of the 0.105-kg ball, and Velocity2 is its velocity before the collision.

Next, we need to calculate the final momentum of the system after the collision:

Final momentum = (Mass1 x Velocity1') + (Mass2 x Velocity2')

Here, Velocity1' is the new velocity of the 0.201-kg ball after the collision and Velocity2' is the new velocity of the 0.105-kg ball after the collision.

Since the collision is elastic and both balls continue moving in the same original direction, we can set up the equation as follows:

(Mass1 x Velocity1) + (Mass2 x Velocity2) = (Mass1 x Velocity1') + (Mass2 x Velocity2')

Now we can plug in the given values:

(0.201 kg x 0.30 m/s) + (0.105 kg x 0.10 m/s) = (0.201 kg x Velocity1') + (0.105 kg x 0.26 m/s)

Simplifying this equation, we have:

0.0603 kg m/s + 0.0105 kg m/s = 0.201 kg x Velocity1' + 0.0273 kg m/s

0.0708 kg m/s = 0.201 kg x Velocity1' + 0.0273 kg m/s

Rearranging the equation, we get:

0.0708 kg m/s - 0.0273 kg m/s = 0.201 kg x Velocity1'

0.0435 kg m/s = 0.201 kg x Velocity1'

Dividing both sides of the equation by 0.201 kg, we find:

Velocity1' = 0.0435 kg m/s / 0.201 kg

Velocity1' ≈ 0.216 m/s

Therefore, the new velocity of the 0.201-kg ball after the collision is approximately 0.216 m/s.