Final answer:
To calculate the average force exerted by the bat, we first convert the ball's velocity to SI units and apply the impulse-momentum theorem to find the impulse. Then, we divide the impulse by the time to obtain the average force of 536.448 N in the positive x-direction.
Step-by-step explanation:
Calculation of Average Force Exerted by the Bat on the Baseball
The question requires the application of the concept of impulse in physics. Impulse is the product of the average force exerted on an object and the time over which this force acts. Given that the baseball has a mass of 150 g (which is 0.15 kg in SI units), and it changes direction upon collision with the bat - going from 80 mi/h in the negative x-direction to 80 mi/h in the positive x-direction, we can calculate the change in momentum (impulse) and thereby determine the average force.
Firstly, we need to convert the speed of the baseball from miles per hour (mi/h) to meters per second (m/s). 1 mi/h is approximately equal to 0.44704 m/s, so:
Initial velocity (vi) = 80 mi/h = 80 × 0.44704 m/s = 35.7632 m/s (negative because it is in the -x-direction)
Final velocity (vf) = 80 mi/h = 80 × 0.44704 m/s = 35.7632 m/s (positive because it is in the +x-direction)
Using the impulse-momentum theorem, the impulse can be calculated as:
Impulse = Change in momentum = m(vf – vi)
Substitute the values we have:
Impulse = 0.15 kg × (35.7632 m/s - (-35.7632 m/s)) = 0.15 kg × (71.5264 m/s) = 10.72896 kg·m/s
Since the time of contact is given as 20 ms (or 0.02 seconds), we can find the average force (F) using the formula:
Impulse = Force × Time, thus Force = Impulse / Time
Average force (F) = 10.72896 kg·m/s / 0.02 s = 536.448 N
The direction of the average force is in the positive x-direction which is the direction of the final velocity after the collision, indicating that the bat has applied force in that direction.