A billiard ball of mass m = 0.250 kg hits the cushion of a billiard table at an angle of θ1 = 63.4° at a speed of v1 = 24.8 m/s. It bounces off at an angle of θ2 = 71.0° and a speed of v2 = 10.0 m/s.
(a) What is the magnitude of the change in momentum of the billiard ball?
1
(b) In which direction does the change of momentum vector point? (Let up be the +y positive direction and to the right be the +x positive direction.)
2° (counter-clockwise from the +x-axis)
Subtract the final momentum vector from the initial momentum vector. That will be the change.
Don't expect us to do all the work for you.
To find the magnitude of the change in momentum of the billiard ball, we can use the formula:
Δp = m * |Δv|
Where Δp represents the change in momentum, m is the mass of the billiard ball, and Δv is the change in velocity.
In this case, the initial velocity of the billiard ball is given as v1 = 24.8 m/s, and the final velocity is v2 = 10.0 m/s. The change in velocity can be calculated as:
Δv = v2 - v1
Plugging in the values:
Δv = 10.0 m/s - 24.8 m/s
= -14.8 m/s
The change in velocity is negative because the direction of motion is reversed after the collision. The magnitude of Δv can be found by taking the absolute value:
|Δv| = |-14.8 m/s|
= 14.8 m/s
Now, we can calculate the change in momentum:
Δp = m * |Δv|
Given that the mass of the billiard ball is m = 0.250 kg:
Δp = 0.250 kg * 14.8 m/s
= 3.7 kg·m/s
So, the magnitude of the change in momentum of the billiard ball is 3.7 kg·m/s.
Now, let's determine the direction in which the change in momentum vector points. The angle of the initial velocity is given as θ1 = 63.4°, and the angle of the final velocity is θ2 = 71.0°.
To find the direction, we need to measure the angle of the change Δθ from the positive x-axis. This can be calculated by:
Δθ = θ2 - θ1
Plugging in the values:
Δθ = 71.0° - 63.4°
= 7.6°
Therefore, the change in momentum vector points in the direction 7.6° counter-clockwise from the positive x-axis.