91Ó°ÊÓ

Momentum is a fundamental concept in physics that describes the motion of an object. It is the product of an object's mass and velocity. The formula for momentum (\(p\)) is expressed as:

• \(p = m \cdot v\)

Here, \(m\) stands for mass and \(v\) is velocity. For example, in the case of the ball, its momentum before hitting the floor is its mass times its velocity: \(1.2 \, \text{kg} \times 25 \, \text{m/s}\).

Momentum is a vector quantity, which means it has both magnitude and direction. When an object changes direction, as the ball does when it rebounds, its momentum also changes. This ability to quantify both mass and velocity simultaneously helps quantify how hard it is to stop a moving object. High momentum objects, like a speeding car, need a lot more force to be stopped than low momentum objects, like a slowly rolling tennis ball.

Impulse is a concept closely linked with momentum. It's the change in momentum of an object when a force is applied over a certain time interval. The Impulse-Momentum Theorem provides the relation, stating that:

• Impulse (\(J\)) = Change in momentum (\(Δp\))
• \(J = m(v_f - v_i)\)

Where \(v_f\) is the final velocity and \(v_i\) is the initial velocity. For the ball in the exercise, the impulse is calculated by multiplying its mass by the difference in its final and initial velocities, which results in \(-42 \, \text{Ns}\).

The negative impulse indicates that the force direction is opposite to the initial motion (the downward direction of the ball). Impulse helps us understand how forces change the motion of objects; it is not merely about having a force, but how long that force is applied.

The average force is related to impulse and provides insight into the strength of the force applied during the motion change. It can be described mathematically by the formula:

• \(F = \frac{J}{Δt}\)

Where \(J\) is the impulse, and \(Δt\) is the time duration. In the exercise, the impulse is \(-42 \, \text{Ns}\), and the contact time is \(0.020 \, \text{s}\).

By substituting these into the equation, we find the average force to be \(-2100 \, \text{N}\). The negative sign shows the force acts in the opposite direction to the initial motion. This large force over a short time period reflects a quick and significant change in the motion of the ball. Understanding average force is crucial in scenarios like car crashes or sports, where we need to minimize or maximize force impacts effectively.