A baseball with a mass of 150 g is thrown horizontally with a speed of 39.5 m/s (88 mi/h) at a bat. The ball is in contact with the bat for 1.15 ms and then travels straight back at a speed of 45.0 m/s (101 mi/h). Determine the average force exerted on the ball by the bat. Neglect the weight of the ball (it is much smaller than the force of the bat) and choose the direction of the incoming ball to be positive. (Indicate the direction with the sign of your answer.)
I got 11021 N as my answer but it is incorrect? What am I missing, the direction?
Is it supposed to be -11000 N ?
To determine the average force exerted on the ball by the bat, you need to consider the change in momentum of the ball.
The momentum of an object is given by the equation: momentum = mass × velocity.
In this case, we have the mass of the baseball (150 g = 0.15 kg), the initial velocity before hitting the bat (39.5 m/s), and the final velocity after hitting the bat (-45.0 m/s, since it is opposite to the incoming direction).
First, calculate the initial momentum of the ball:
initial momentum = mass × initial velocity = 0.15 kg × 39.5 m/s = 5.925 kg·m/s.
Next, calculate the final momentum of the ball:
final momentum = mass × final velocity = 0.15 kg × (-45.0 m/s) = -6.75 kg·m/s.
The change in momentum is given by the difference between the final and initial momentum:
change in momentum = final momentum - initial momentum = -6.75 kg·m/s - 5.925 kg·m/s = -12.675 kg·m/s.
Since the force is defined as the rate of change of momentum, you can calculate the average force by dividing the change in momentum by the contact time (in this case, 1.15 ms):
average force = change in momentum / contact time = (-12.675 kg·m/s) / (0.00115 s) ≈ -11021.74 N.
The negative sign indicates that the force exerted by the bat on the ball is in the opposite direction to the initial velocity of the ball.
Therefore, your answer of 11021 N is correct, but you missed the negative sign indicating the direction of the average force exerted by the bat on the ball.