During a neighborhood baseball game in a vacant lot, a particularly wild hit sends a 0.144-kg baseball crashing through the pane of a second-floor window in a nearby building. The ball strikes the glass at 14.9 m / s, shatters the glass as it passes through, and leaves the window at 11.3 m / s with no change of direction. What is the magnitude of this impulse
and the ball is in contact with the glass for 0.0107 s as it passes through. Find the magnitude of the average force of the glass on the ball (a positive number).
To find the magnitude of the impulse, we can use the equation:
Impulse = Change in momentum
The initial momentum of the ball is given by:
Initial momentum = mass x initial velocity
Initial momentum = (0.144 kg) x (14.9 m/s)
Next, we need to calculate the final momentum of the ball. Since the ball does not change direction after passing through the window, its final momentum would be equal to its initial momentum.
Final momentum = mass x final velocity
Final momentum = (0.144 kg) x (11.3 m/s)
Now, we can find the change in momentum:
Change in momentum = Final momentum - Initial momentum
Impulse = (0.144 kg) x (11.3 m/s) - (0.144 kg) x (14.9 m/s)
Impulse = (0.144 kg) x (11.3 m/s - 14.9 m/s)
Impulse = (0.144 kg) x (-3.6 m/s)
Impulse = -0.5184 kg m/s
The magnitude of the impulse is the absolute value of this result:
Magnitude of impulse = |-0.5184 kg m/s| = 0.5184 kg m/s
Now, let's move on to finding the magnitude of the average force exerted on the ball by the glass.
The average force can be found using the equation:
Average force = Impulse / Time
We know the impulse is 0.5184 kg m/s, and the time of contact is given as 0.0107 seconds.
Average force = (0.5184 kg m/s) / (0.0107 s)
Average force = 48.3 N
Therefore, the magnitude of the average force exerted by the glass on the ball is 48.3 Newtons.