To find the average force exerted by the bat on the ball, we can use the impulse-momentum theorem, which states that the impulse (force multiplied by the time the force acts) is equal to the change in momentum of the object.
First, we need to convert the speed of the baseball from kilometers per hour to meters per second:
- 180 km/h = (180 * 1000 m) / (3600 s) = 50 m/s
The initial momentum of the ball is zero because the ball is at rest before the batter hits it. After the batter hits it back toward the pitcher, we can determine the change in momentum.
The mass of the ball (m) is 0.150 kg, the initial velocity (u) is 0 m/s, and the final velocity (v) is -50 m/s (the negative indicates the direction is opposite). Thus, the change in momentum (Δp) is:
- Δp = m(v – u) = 0.150 kg (-50 m/s – 0 m/s) = -7.5 kg·m/s
The magnitude of the change in momentum is 7.5 kg·m/s. Now, we can find the average force (F) using the formula:
- F = Δp / Δt
Where Δt is the time of the collision, which is 5.0 ms or 0.005 seconds:
- F = 7.5 kg·m/s / 0.005 s = 1500 N
Thus, the magnitude of the average force exerted by the bat on the ball is 1500 N.