In hitting a stationary pool ball with the mass of 170 g, a billiards player gives the ball impulse of 6.0 N-s. At what speed will the pool ball move toward the hole?
impulse (N-s) = (mass in kg)*(velocity in m/s)
so be sure to convert 170g to kg!
To find the speed of the pool ball after the impact, we need to use the principle of conservation of momentum.
Momentum is defined as the product of mass and velocity. In this case, the initial momentum (before the impact) is zero since the ball is stationary. The final momentum (after the impact) can be calculated using the impulse-momentum equation:
Impulse = Change in Momentum
Given that the impulse is 6.0 N-s and the mass of the pool ball is 170 g (convert to kg by dividing by 1000), we can find the change in momentum:
Change in Momentum = Impulse
Change in Momentum = 6.0 N-s
Now, we can set up the equation for the final momentum:
Final Momentum = Change in Momentum
Final Momentum = (mass of the ball) x (final velocity of the ball)
Plugging in the values:
Final Momentum = (0.170 kg) * (final velocity)
We can rearrange the equation to solve for the final velocity:
Final Velocity = Final Momentum / (mass of the ball)
Final Velocity = (6.0 N-s) / (0.170 kg)
Final Velocity ≈ 35.29 m/s
Therefore, the pool ball will move toward the hole with a speed of approximately 35.29 m/s.