A cue ball (mass = 0.140 kg) is at rest on a frictionless pool table. The ball is hit dead center by a pool stick which applies an impulse of +1.60 N·s to the ball. The ball then slides along the table and makes an elastic head-on collision with a second ball of equal mass that is initially at rest. Find the velocity of the second ball just after it is struck
impulse= mass x delta velocity
delta velocity = impulse/ mass
and since the equation is elastic meaning all force and momentum are always transferred in a direct collision, velocity from the initial ball will transfer too the second ball
To find the velocity of the second ball just after it is struck by the first ball, we can use the law of conservation of momentum.
The law of conservation of momentum states that the total momentum of a closed system remains constant if no external forces act on it. In this case, the two balls are the only objects involved, and there are no external forces acting on them (assuming the surface of the pool table is frictionless).
Let's denote the velocity of the first ball as v1 (after the collision with the stick) and the velocity of the second ball as v2 (after the collision with the first ball).
Since the two balls make an elastic head-on collision, the total momentum before the collision is equal to the total momentum after the collision.
Before the collision:
The first ball is at rest, so its momentum (p1) is zero.
The second ball is also at rest, so its momentum (p2) is also zero.
After the collision:
The momentum of the first ball (p1') is given by the impulse applied to it by the stick.
Impulse = Change in momentum
Impulse = p1' - p1
1.60 N·s = p1'
To find p1', we need to calculate the velocity of the first ball after the collision using the impulse-momentum equation:
Impulse = Change in momentum
1.60 N·s = m1 * Δv1
(where m1 is the mass of the first ball and Δv1 is the change in velocity of the first ball)
Since the first ball is initially at rest, the change in velocity is equal to the final velocity:
1.60 N·s = 0.140 kg * v1
v1 = 1.60 N·s / 0.140 kg
v1 ≈ 11.43 m/s (rounded to two decimal places)
Now that we know the velocity of the first ball after the collision, we can find the velocity of the second ball by applying the law of conservation of momentum:
Momentum before collision = Momentum after collision
m1 * v1 + m2 * v2 = 0
Since the masses of the two balls are equal, and the first ball has a velocity of 11.43 m/s:
0.140 kg * 11.43 m/s + 0 kg * v2 = 0
1.6002 kg·m/s = v2
Therefore, the velocity of the second ball just after it is struck by the first ball is approximately 1.6002 m/s (rounded to four decimal places).