During a neighborhood baseball game in a vacant lot, a particularly wild hit sends a 148-g baseball crashing through the pane of a second-floor window in a nearby building. The ball strikes the glass at 10.1 m/s, shatters the glass as it passes through, and leaves the window at 8.95 m/s with no change of direction. Calculate the magnitude of this impulse.

Question

During a neighborhood baseball game in a vacant lot, a particularly wild hit sends a 148-g baseball crashing through the pane of a second-floor window in a nearby building. The ball strikes the glass at 10.1 m/s, shatters the glass as it passes through, and leaves the window at 8.95 m/s with no change of direction. Calculate the magnitude of this impulse.

___ N*s

And,

The ball is in contact with the glass for 10.1 ms as it passes through. Find the magnitude of the average force of the glass on the ball (a positive number).

___ N

Answer 1

To calculate the magnitude of the impulse, we can use the principle of conservation of momentum. The change in momentum of an object is equal to the impulse applied to it.

Impulse (J) = Change in momentum (Δp)

We can find the change in momentum by subtracting the initial momentum from the final momentum.

Initial momentum (p_initial) = mass (m) × initial velocity (v_initial)
Final momentum (p_final) = mass (m) × final velocity (v_final)

In this case, the initial momentum of the ball can be calculated as:
p_initial = 148 g × 10.1 m/s

Since the question asks for the magnitude of the impulse (a scalar value), we don't need to consider the direction. We can simply take the absolute value of the change in momentum.

Impulse (J) = |p_final - p_initial|

Now, let's calculate the impulse:

p_initial = 148 g × 10.1 m/s = (148/1000) kg × 10.1 m/s
p_final = 148 g × 8.95 m/s = (148/1000) kg × 8.95 m/s

Impulse (J) = |p_final - p_initial|

Finally, calculate the magnitude of the impulse and round it to the appropriate number of significant figures.

To find the magnitude of the average force of the glass on the ball, we can use the formula:

Average Force (F) = Impulse (J) / Time (t)

The time of contact between the ball and the glass is given as 10.1 ms, which we convert to seconds by dividing by 1000.

Now, let's calculate the magnitude of the average force:

Time (t) = 10.1 ms ÷ 1000

Average Force (F) = Impulse (J) / Time (t)

Finally, calculate the magnitude of the average force and round it to the appropriate number of significant figures.