91Ó°ÊÓ

When a bat hits a baseball, it exerts a certain amount of force over a specific period. This action is referred to as an impulse. Impulse is an important concept in physics because it directly relates to the change in an object's momentum. The impulse exerted on an object can be calculated using the formula:

• Impule (\( I \)) = Force (\( F \)) \( \times \) Time (\( \Delta t \))

In our baseball scenario, the impulse applied by the bat is also equal to the change in momentum of the ball. Since the momentum has been roundly calculated as 14.5 \( \mathrm{kg \cdot m/s} \), the impulse is also 14.5 \( \mathrm{kg \cdot m/s} \). This tells us how much the velocity of the baseball has been altered by interacting with the bat. Understanding impulse can help us predict or calculate how objects will respond to forces over time. This is valuable in any situation involving impacts or sudden force changes.

The concept of average force helps us understand the total impact of a force applied over time. It's particularly useful when the force varies or is applied quickly, like when a bat connects with a baseball. To calculate average force, we use the impulse-momentum theorem. This theorem states that the change in momentum of an object is equal to the impulse applied to it. Knowing this, we can calculate the average force using:

• Average Force (\( F \)) = Impulse (\( I \)) / Time (\( \Delta t \))

In the exercise, the impulse was found to be 14.5 \( \mathrm{kg \cdot m/s} \) and the provided time of contact is 0.002 seconds. Plugging in these values gives us:

• \( F = \frac{14.5 \, \mathrm{kg \cdot m/s}}{0.002 \, \mathrm{s}} = 7250 \, \mathrm{N} \)

This means that during the brief moment of contact, the bat exerted an average force of 7250 Newtons on the ball. Understanding average force gives insight into how much power was needed to change the ball's momentum.

Momentum, a fundamental concept in physics, represents the quantity of motion an object has. It depends on both the mass and velocity of the object. When a moving object encounters a force, its momentum can change. This change is crucial for understanding how the object's motion is affected.In our baseball scenario, the change in momentum is calculated by finding the difference between the final and initial momentum of the baseball. The formula for change in momentum (\( \Delta p \)) is:

• \( \Delta p = m(v_f - v_i) \)

Where:

• \( m \) is the mass of the baseball (0.145 kg)
• \( v_f \) is the final velocity (-55.0 m/s, opposite direction)
• \( v_i \) is the initial velocity (45.0 m/s)

Substituting the given numbers:

• \( \Delta p = 0.145 \times (-55.0 - 45.0) = -14.5 \, \mathrm{kg \cdot m/s} \)

The negative sign indicates a direction change, but for magnitude, we ignore the sign and state the change as 14.5 \( \mathrm{kg \cdot m/s} \). Recognizing how momentum changes helps us decode the effects of forces in motion.