91Ó°ÊÓ

When discussing the average force, think of it as the constant force that, if applied over a certain time period, equals the force calculated during that time. It helps us understand how an impact spreads its effects over time.
In the context of the skater pushing against the wall, the average force (\( F_{\text{avg}} \)) is what she applies to the wall during her push. It combines her mass and velocity change with the time she maintains contact with the wall.
To find the average force, we use the formula:
\[F_{\text{avg}} = \frac{m \cdot \Delta v}{\Delta t}\]
where:

• \( m \) is the mass of the skater,
• \( \Delta v \) is the change in velocity, and
• \( \Delta t \) is the time of contact.

Using this formula, the average force gives insights into how her mass and change in velocity affect the force exerted over the duration of her push.

Momentum is a measure of motion that combines both an object's mass and velocity. It gives us an idea of how hard it is to stop a moving object.
The formula for momentum (\( p \)) is expressed as:\[p = m \cdot v\]In our example, the skater initially has zero momentum because she starts standing still. However, when she pushes against the wall, her velocity changes, which in turn changes her momentum.
The impulse-momentum theorem states that the change in momentum is equal to the impulse applied to the object. Impulse, like force applied over time, alters an object’s momentum. With the skater’s velocity changing from 0 to \(-1.2 \, \text{m/s}\), you can see the change in momentum as:\[\Delta p = m \cdot \Delta v = 46 \, \text{kg} \cdot (-1.2 \, \text{m/s})\]This numerical change in momentum is useful for understanding how pushing against a wall, or any force over time, changes an object’s motion.

Understanding velocity change is crucial in scenarios involving motion, especially when an object starts from rest and gains speed in another direction.
In this exercise, the skater goes from being still to moving backward at \(-1.2 \, \text{m/s}\). This change in velocity (\( \Delta v \)) is vital because it reflects how the skater's push against the wall altered her state of motion.
To calculate the velocity change, we use:\[\Delta v = v_f - v_i\]where:

• \( v_f \) is the final velocity, and
• \( v_i \) is the initial velocity.

For the skater, we go from \( 0 \, \text{m/s}\) to \(-1.2 \, \text{m/s}\), yielding a \( \Delta v \) of \(-1.2 \, \text{m/s}\). This negative sign denotes a backward motion, opposite to any initial forward direction. Understanding these changes helps tie together concepts of force, impulse, and the resulting movement.