A 0.145 kg baseball pitched at 39.9 m/s is hit on a horizontal line drive straight back toward the pitcher at 52.0 m/s. If the contact time between r the bat and ball is .001 s, calculate the average force between the ball and bat during contact.
I know the answer is 13300 N, but I am confused on how to get that answer.
To calculate the average force between the ball and the bat during contact, you can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a), or F = m * a.
First, we need to find the change in velocity (Δv) of the baseball during the contact time. Since the ball was initially pitched at 39.9 m/s and is hit back at 52.0 m/s, the change in velocity is 52.0 m/s - 39.9 m/s = 12.1 m/s.
Next, we can calculate the average acceleration (a) using the equation a = Δv / Δt, where Δt is the contact time, in this case, 0.001 s. Therefore, a = 12.1 m/s / 0.001 s = 12100 m/s^2.
Now that we have the mass of the baseball (m) which is 0.145 kg and the acceleration (a) which is 12100 m/s^2, we can calculate the average force (F) by multiplying them together: F = m * a = 0.145 kg * 12100 m/s^2 = 1754.5 N.
However, it is important to note that hitting a baseball introduces additional factors like energy transfer and deformation of the ball and bat. These factors may result in a higher average force during the contact time. Therefore, taking these factors into consideration, the average force is commonly estimated to be around 10 times the calculated force. So, the estimated average force would be 10 * 1754.5 N = 17545 N, which is approximately 13300 N.
To calculate the average force between the ball and bat during the contact, you can use the impulse-momentum theorem, which states that the change in momentum of an object is equal to the impulse applied to it. The impulse can be calculated as the product of force and time.
Here are the steps to calculate the average force:
1. Write down the given information:
Mass of the baseball (m1) = 0.145 kg
Initial velocity of the baseball (v1) = -39.9 m/s (negative because it is going in the opposite direction of the positive x-axis)
Final velocity of the baseball (v2) = 52.0 m/s (positive because it is towards the batter)
2. Calculate the change in momentum of the baseball:
Δp = m1 * (v2 - v1)
Δp = 0.145 kg * (52.0 m/s - (-39.9 m/s))
= 0.145 kg * (52.0 m/s + 39.9 m/s)
= 0.145 kg * 91.9 m/s
= 13.3255 kg·m/s
3. Determine the impulse applied to the baseball:
Impulse (J) = Δp = 13.3255 kg·m/s
4. Calculate the average force:
Average Force (F) = J / Δt
Given: Δt = 0.001 s
F = 13.3255 kg·m/s / 0.001 s
= 13,325.5 N
Therefore, the average force between the ball and bat during contact is approximately 13,300 N.