A 0.145- kg baseball with an initial speed of 27 m/s rebounds with a speed of 32 m/s after being struck with a bat. If the duration of contact between ball and bat was 1.5 ms, what was the magnitude of the average force between ball and bat?
find change in momentum .145(27+32)
force = change in momentum/time
= change in momentum /(1.5*10^-3 )
To calculate the magnitude of the average force between the ball and bat, we can use Newton's second law of motion. The formula for force is:
force = mass * acceleration
In this case, the mass of the baseball is 0.145 kg. However, we don't have the acceleration directly given. But we can calculate the change in velocity (acceleration) using the formula:
acceleration = (final velocity - initial velocity) / time
Given:
- Initial velocity, u = 27 m/s
- Final velocity, v = 32 m/s
- Time of contact, t = 1.5 ms (which needs to be converted to seconds)
Converting time to seconds:
1 ms = 0.001 s
Therefore, 1.5 ms = 1.5 * 0.001 s = 0.0015 s
Now, we can calculate the acceleration:
acceleration = (32 m/s - 27 m/s) / 0.0015 s
Next, we calculate the force using Newton's second law:
force = mass * acceleration
force = 0.145 kg * acceleration
Finally, we substitute the value of acceleration in the equation to find the force.