Question

A line drive was heading towards nathaniel at 36.1 m/s. he quickly raised his glove and caught the 0.145 kg ball with stiffly held arms, bringing it to rest after .0477 seconds of contract. what average force did nathaniel apply to the hall.

Answer 1

Nathaniel applied an average force of approximately -109.787 newtons (N) to the ball to bring it to rest, using the impulse-momentum theorem to calculate the impulse as the product of average force and time interval.

Step-by-step explanation:

To calculate the average force Nathaniel applied to the ball, we can use the impulse-momentum theorem, which expresses that the impulse applied to an object is equal to the change in its momentum. The impulse can be found by multiplying the average force (F) by the time interval (Δt) during which the force is applied. The change in momentum is the mass (m) of the ball multiplied by the change in its velocity (Δv).

The equation for the impulse-momentum theorem is:

F Δt = m Δv

In this problem, the ball's initial velocity is 36.1 m/s (towards Nathaniel), and the final velocity is 0 m/s (when it comes to rest). The mass of the ball is 0.145 kg, and the time interval of contact is 0.0477 seconds.

The change in velocity: Δv = 0 m/s - 36.1 m/s = -36.1 m/s (The negative sign indicates that the direction of the final velocity is opposite to the initial velocity).

Now, putting the values into the impulse-momentum theorem:

F • 0.0477 s = 0.145 kg • -36.1 m/s

Calculate the impulse:

Impulse = 0.145 kg • -36.1 m/s = -5.2345 kg•m/s

Now, we find the average force:

F = Impulse / Δt

F = -5.2345 kg•m/s / 0.0477 s

F = -109.787 kg•m/s²

F = -109.787 N

The negative sign indicates that Nathaniel applied the force in the direction opposite to the ball's initial motion, which is to be expected as he was stopping it.