91Ó°ÊÓ

When a person stands on a scale in a stationary elevator, the force the scale reads is the result of the Earth's gravity on their body. This force is known as the "normal force." The term "normal" here implies perpendicular or vertical force. In this scenario, the force can be calculated using the equation:

• \( N = mg \)

where \( m \) is the mass of the person (72 kg) and \( g \) is the gravitational acceleration constant, approximately \( 9.8 \, m/s^2 \).
This gives us the normal force or weight when the elevator is at rest or traveling at constant speed, equaling \( 705.6 \, N \).
The normal force indicates how much the ground needs to "push back" to support the person standing still. This force keeps us from falling through floors or slipping, and in an elevator, it's what the scale measures.

Newton's Second Law of Motion explains how an object will accelerate if acted on by an unbalanced force. It can be expressed as \( F = ma \), linking net force \( F \), mass \( m \), and acceleration \( a \).
In the case of the accelerating elevator, the person's body experiences additional forces due to the motion.
When the elevator first starts moving upwards, it accelerates, causing the net force to increase.
The scale measures this increased force, and you feel your "weight" or the normal force increase as the elevator begins its ascent.
The extra force required to accelerate is calculated by:

• Net force due to acceleration \( = ma \) = \( 72 \, kg \times 1.5 \, m/s^2 \) = \( 108 \, N \).

Thus, the total force reading during this phase becomes the normal force due to gravity plus this additional force. So, you feel heavier temporarily as the scale reads \( 813.6 \, N \), adding the accelerating force with the gravitational force.

Acceleration refers to the rate of change of velocity. It's how quickly an object's speed increases or decreases.
For the elevator example, it initially accelerates upwards to reach its maximum speed.
We calculate this acceleration using the formula:

• \( a = \frac{v}{t} \)

where \( v \) is the final velocity of \( 1.2 \, m/s \) and \( t \) is the time of \( 0.80 \, s \).
In this situation, the elevator experiences an upward acceleration, calculated to be \( 1.5 \, m/s^2 \).
During acceleration, you feel heavier because of the additional upward force. The scale registers this as the sum of gravitational pull and the force from accelerating upwards.
Understanding acceleration helps explain why you feel these changes in weight when the elevator starts or stops moving.

Deceleration is the process of slowing down or reducing speed, essentially negative acceleration.
When the elevator slows down, the direction of the acceleration is downward relative to the elevator's upward movement.
Assuming the acceleration rate remains the same (\( 1.5 \, m/s^2 \)), we calculate the downward force similarly:

• Force due to deceleration \( = ma' \) = \( 72 \, kg \times 1.5 \, m/s^2 \) = \( 108 \, N \).

During this time, the normal force or what the scale reads is decreased.
The scale now records the original normal force minus the decreasing force (\( 705.6 \, N - 108 \, N = 597.6 \, N \)).
When the elevator decelerates, you feel lighter as the effective weight lessens.
It's akin to riding a rollercoaster where you feel lighter during parts of descent. Recognizing deceleration's impact on forces helps explain the sensations you encounter in elevators.