Final answer:
To stop a 5 kg bowling ball moving at 7.7 m/s, the barrier must deliver an impulse of -38.5 kg·m/s, which is the product of the ball's mass and the negative change in its velocity.
Step-by-step explanation:
To calculate the impulse required to stop a 5 kg bowling ball moving at 7.7 m/s, you need to understand that impulse equals the change in momentum. The impulse can be found using the formula Impulse = Δp = m × Δv, where Δp is the change in momentum, m is the mass, and Δv is the change in velocity.
Since the initial velocity is 7.7 m/s and the final velocity is 0 m/s (as the ball comes to a stop), the change in velocity is 7.7 m/s. Therefore, the impulse required to stop the ball can be calculated as follows:
- Mass (m) of the ball = 5 kg
- Change in velocity (Δv) = Final velocity - Initial velocity = 0 m/s - 7.7 m/s = -7.7 m/s (the negative sign indicates a decrease in velocity)
Impulse (J) = m × Δv = 5 kg × (-7.7 m/s) = -38.5 kg·m/s
The negative sign in the impulse indicates that the direction of the impulse is opposite to the direction of the initial velocity, which makes sense since the barrier has to exert a force in the opposite direction to stop the ball.