Question

during a neighborhood baseball game in a vacant lot, a particularly wild hit sends a 0.148 kg baseball crashing through the pane of a second - floor window in a nearby building. the ball strikes the glass at 15.3 m/s, shatters the glass as it passes through, and leaves the window at 11.3 m/s with no change of direction.
calculate the magnitude ( j ) of this impulse.
the ball is in contact with the glass for 0.0102 s as it passes through. find the magnitude ( f_{av} ) of the average force of the glass on the ball.
what is the direction of the impulse that the glass imparts to the baseball?
○ neither of these
○ opposite the direction of the balls motion
○ in the direction of the balls motion
( j=) ( ncdot s )
( f_{av}=) ( n )

Explanation:

Step1: Calculate the impulse

Impulse \(J\) is given by the change in momentum. The formula for momentum is \(p = mv\).
The initial velocity \(v_{i}=15.3\ m/s\) and the final velocity \(v_{f} = 11.3\ m/s\), and mass \(m = 0.148\ kg\).
\(J=\Delta p=m(v_{f}-v_{i})\)
\(J = 0.148\times(11.3 - 15.3)\)
\(J=0.148\times(- 4)\)
\(J=- 0.592\ N\cdot s\)
The magnitude of the impulse \(|J| = 0.592\ N\cdot s\)

Step2: Calculate the average force

The formula for impulse is also \(J = F_{av}\Delta t\), where \(\Delta t=0.0102\ s\)
We can solve for \(F_{av}\): \(F_{av}=\frac{J}{\Delta t}\)
Since \(|J| = 0.592\ N\cdot s\) and \(\Delta t = 0.0102\ s\)
\(F_{av}=\frac{0.592}{0.0102}\approx58.04\ N\)

Step3: Determine the direction of the impulse

Since the ball slows down ( \(v_{f}

Answer:

• \(J = 0.592\ N\cdot s\)
• \(F_{av}\approx58.04\ N\)
• Direction of impulse: opposite the direction of the ball's motion