A billiard cue ball having velocity of 5.0 cm/s and a mass 0.17 kg approaches a stationary red billiard ball of

mass 0.16 kg. If the cue ball is stationary after their collision, what is the new velocity for the red ball?

Hey, Google "conservation of momentum"

0.05 m/s * 0.17 kg = v * 0.16

Given:

M1 = 0.17kg, V1 = 0.05 m/s.
M2 = 0.16kg, V2 = 0.
V3 = 0. = Velocity of M1 after the collision.
V4 = ? = Velocity of M2(red ball) after the collision.

Momentum before = Momentum after.
M1*V1 + M2*V2 = M1*V3 + M2*V4.
0.17*0.05 + 0.16*0 = 0.17*0 + 0.16*V4,
0.16*V4 = 0.0085,
V4 = ?

4m/s

Well, this situation sounds like it requires a little bit of pool party physics! Let's see what we can figure out.

First things first, we can use the concept of conservation of momentum here. The total momentum before the collision should be equal to the total momentum after the collision.

The momentum of an object is given by its mass multiplied by its velocity. So we can calculate the total momentum before the collision by adding up the momentum of the cue ball and the red ball.

Now, since the cue ball is stationary after the collision, its velocity becomes zero. Therefore, the total momentum after the collision is simply the momentum of the red ball.

Since momentum is conserved, we can set up an equation:

(mass of cue ball * velocity of cue ball) + (mass of red ball * initial velocity of red ball) = (mass of red ball * final velocity of red ball)

Plugging in the values we know:

(0.17 kg * 0 cm/s) + (0.16 kg * initial velocity of red ball) = (0.16 kg * final velocity of red ball)

Simplifying this, we get:

0 + (0.16 kg * initial velocity of red ball) = 0.16 kg * final velocity of red ball

Since the left side is zero, we can rearrange the equation to solve for final velocity:

0.16 kg * final velocity of red ball = 0

This means that the final velocity of the red ball must be zero. So, after the collision, the red ball comes to a stop.

I hope that puts a smile on your face!

To solve this problem, we can use the concept of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.

The momentum (p) of an object is given by the formula p = mass * velocity.

For the cue ball:
Mass of cue ball (m1) = 0.17 kg
Initial velocity of cue ball (u1) = 5.0 cm/s = 0.05 m/s
Final velocity of cue ball (v1) = 0 m/s (since it becomes stationary)

For the red ball:
Mass of red ball (m2) = 0.16 kg
Initial velocity of red ball (u2) = 0 m/s (since it is stationary)
Final velocity of red ball (v2) = ?

Using the conservation of momentum equation:
(m1 * u1) + (m2 * u2) = (m1 * v1) + (m2 * v2)

Substituting the given values:
(0.17 kg * 0.05 m/s) + (0.16 kg * 0 m/s) = (0.17 kg * 0 m/s) + (0.16 kg * v2)

Simplifying the equation:
0.0085 kg*m/s = 0.0256 kg*v2

Dividing both sides of the equation by 0.0256 kg:
v2 = 0.0085 kg*m/s / 0.0256 kg
v2 = 0.33 m/s (rounded to two decimal places)

Therefore, the new velocity for the red ball after the collision is approximately 0.33 m/s.