91Ó°ÊÓ

Momentum is a fundamental concept in physics, describing the motion of an object. Momentum depends on two factors: the mass of the object and its velocity. It is calculated using the formula \[ p = m \times v \]where:

• \( p \) represents momentum,
• \( m \) is the mass of the object in kilograms,
• \( v \) is the velocity of the object in meters per second.

In our exercise, the billiard ball has a mass of 0.38 kg. To find the momentum before hitting the cushion, use the initial velocity of \( +2.1 \mathrm{m}/\mathrm{s} \). Calculate the initial momentum:\[ p_{\text{initial}} = 0.38 \text{ kg} \times (+2.1 \text{ m/s}) = 0.798 \text{ kg m/s} \]After rebounding, the velocity changes to \(-2.0 \mathrm{m}/\mathrm{s} \). Calculate the final momentum:\[ p_{\text{final}} = 0.38 \text{ kg} \times (-2.0 \text{ m/s}) = -0.76 \text{ kg m/s} \]
Understanding momentum helps in grasping how objects move and how forces affect their motion. Knowing the initial and final momenta is crucial for calculating any change in momentum.

The average net force is the constant force that would produce the same change in an object's momentum over a given time period as produced by the actual variable force. It is related to the impulse experienced by the object and thus to the change in momentum.On the billiard ball, to find the average net force exerted by the cushion, we use the change in momentum and the time during which the ball was in contact with the cushion. The impulse-momentum theorem links these concepts with the equation:\[ F_{\text{avg}} \times \Delta t = \Delta p \]
Here, \( F_{\text{avg}} \) is the average net force, \( \Delta t \) is the time interval, and \( \Delta p \) is the change in momentum.By rearranging, we solve for the average net force:\[ F_{\text{avg}} = \frac{\Delta p}{\Delta t} \]
In the exercise, \( \Delta t \) is \( 3.3 \times 10^{-3} \text{ s} \). By calculating the change in momentum using the initial and final momenta, we can determine the average net force applied on the ball by the cushion.

Change in momentum is a critical concept for understanding how collisions and interactions affect objects. It is calculated by subtracting the initial momentum from the final momentum, expressed as:\[ \Delta p = p_{\text{final}} - p_{\text{initial}} \]
This change is often a result of external forces acting on the object.In the context of our exercise, the billiard ball's momentum changes when it strikes and rebounds off the cushion. To find this change:

• Initial momentum was \( 0.798 \text{ kg m/s} \).
• Final momentum is \(-0.76 \text{ kg m/s} \).

Thus, the change in momentum is calculated as:\[ \Delta p = -0.76 \text{ kg m/s} - 0.798 \text{ kg m/s} = -1.558 \text{ kg m/s} \]
The negative sign indicates the direction change caused by the cushion. By understanding this change, we can calculate the force exerted and analyze how the billiard ball's motion is influenced by the collision with the cushion.