A 0.01-kg baseball traveling in a horizontal direction with a speed of 12 m/s hits a bat and is popped straight up with a speed of 15 m/s.
(a) What is the change in momentum (magnitude and direction) of the baseball?
(b) If the bat was in contact with the ball for 26 ms, what was the average force of the bat on the ball?
To answer these questions, we need to understand the concepts of momentum, change in momentum, and impulse.
(a) The change in momentum of an object is given by the equation:
Change in momentum = Final momentum - Initial momentum
Momentum is a vector quantity, meaning it has both magnitude and direction. In this case, we are given the initial and final speeds of the baseball, but we also need to consider that the baseball changes direction as it is popped straight up.
To calculate the change in momentum, we can use the equation:
Change in momentum = (mass of the baseball) * (final velocity - initial velocity)
In this case, the mass of the baseball is given as 0.01 kg, the initial velocity is 12 m/s (horizontal), and the final velocity is 15 m/s (vertical).
Change in momentum = (0.01 kg) * (15 m/s - 12 m/s)
Simplifying the equation, we get:
Change in momentum = 0.01 kg * 3 m/s
Therefore, the change in momentum of the baseball is 0.03 kg*m/s, directed vertically upward.
(b) The average force exerted by an object can be calculated using the concept of impulse. Impulse is defined as the change in momentum of an object, and it is also equal to the product of force and the time over which the force is applied.
Impulse = Force * Time
In this case, we are given the time of contact between the bat and the ball as 26 ms, which we need to convert to seconds by dividing it by 1000.
Time = 26 ms / 1000 = 0.026 s
Using the equation for impulse, we can rearrange it to solve for force:
Force = Impulse / Time
Since the impulse is equal to the change in momentum, we can substitute the change in momentum we calculated in part (a) into the equation:
Force = (Change in momentum) / Time
Substituting the values:
Force = (0.03 kg*m/s) / 0.026 s
Simplifying the equation, we get:
Force = 1.154 kg*m/s^2
Therefore, the average force exerted by the bat on the ball is approximately 1.154 N.