91Ó°ÊÓ

In an elevator scenario, where velocity changes over time, acceleration is a key factor. It tells us how quickly the speed of the elevator is changing. To find acceleration, we use the velocity function, which in this case is given as \(v(t) = (3.0 \, \text{m/s}^2) t + (0.20 \, \text{m/s}^3) t^2\). By differentiating this velocity function with respect to time, we get acceleration.
Doing this gives us \(a(t) = 3.0 \, \text{m/s}^2 + 2(0.20 \, \text{m/s}^3)t\). At a specific time, such as \( t = 4.0 \, \text{s}\), we substitute \(t\) into this equation to find \(a(4.0) = 4.6 \, \text{m/s}^2\).

• Acceleration is the rate of change of velocity.
• It helps determine how forces will affect apparent weight in the elevator.

The net force acting on you in an elevator, or in any physics problem, comprises different components of force. Here, it includes forces due to gravity and the acceleration of the elevator. Calculating these forces requires using Newton's Second Law, \( F = ma\), where \(F\) is the force, \(m\) is mass, and \(a\) is acceleration.
The gravitational force, \(F_g\), is straightforward, calculated using \(g\), the acceleration due to gravity (\(9.8 \, \text{m/s}^2\)). Thus, \(F_g = 72 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 705.6 \, \text{N}\).The additional force due to elevator's acceleration, \(F_a\), employs the total acceleration value: \(F_a = 72 \, \text{kg} \times 4.6 \, \text{m/s}^2 = 331.2 \, \text{N}\).

• Forces in dynamics are the product of mass and acceleration.
• Net force combines all relevant forces to determine apparent weight.

Apparent weight is what you "feel" as your weight when in a different accelerating context—like an elevator. This differs from your true weight because of the acceleration affecting the system.
In this problem, your apparent weight is determined by the scale reading, which accounts for both gravitational force and the extra force due to acceleration. Hence, the scale shows \(F_g + F_a\), totaling \(1036.8 \, \text{N}\).

• Apparent weight changes with acceleration.
• In an upward accelerating elevator, you feel heavier.

Elevator physics involves understanding how acceleration affects the forces we experience. It exemplifies Newton's laws in a real-world setting.
As the elevator moves, its acceleration alters the tension in the cable and the pressure on the scale. This is a prime example of physics concepts in action, illustrating how net force and resultant acceleration affect motion and perceived weight.

• Elevators demonstrate Newton's Second Law: \(F = ma\).
• Real-world applications help visualize theoretical physics concepts.