Weighing Scale Reading in a Decelerating Elevator

Concept Used

The weighing scale measures the normal reaction force, not the true weight. This normal reaction is called the apparent weight.

Since the elevator is moving upward but slowing down, its acceleration is downward.

First, calculate the acceleration of the elevator.

Step 1: Calculate the Acceleration

Using the first equation of motion,

v = u + at

Substituting the given values,

0 = 1 + a × 2

2a = −1

a = −0.5 m/s²

The negative sign indicates that the acceleration is downward.

Step 2: Determine the Apparent Weight

When the elevator accelerates downward, the normal reaction is given by

N = m(g − a)

where a is the magnitude of the downward acceleration.

Substituting the values,

N = 70(9.8 − 0.5)

N = 70 × 9.3

N = 651 N

Therefore, the weighing scale reads 651 N.

Alternative Method Using Newton’s Second Law

Two forces act on the man:

• The normal reaction N acting upward.
• The gravitational force mg acting downward.

Since the acceleration is downward,

mg − N = ma

Rearranging,

N = m(g − a)

Substituting the values again gives

N = 651 N.

Why Does the Reading Decrease?

Although the elevator is moving upward, it is slowing down. A body that slows down while moving upward must have a downward acceleration. Because of this downward acceleration, the floor of the elevator exerts a smaller normal reaction on the man than when the elevator is at rest. Since the weighing scale measures the normal reaction, the reading decreases below the true weight.

The true weight of the man is

W = mg = 70 × 9.8 = 686 N

During deceleration, the apparent weight becomes

651 N, which is less than the true weight.

Special Cases of Elevator Motion

Elevator at Rest or Moving with Constant Velocity

N = mg

The weighing scale shows the true weight.

Elevator Accelerating Upward

N = m(g + a)

The apparent weight is greater than the true weight.

Elevator Accelerating Downward

N = m(g − a)

The apparent weight is less than the true weight.

Free Fall

N = 0

The person experiences weightlessness.

Detailed Explanation of Common Mistakes

A common mistake is to think that because the elevator is moving upward, the apparent weight should increase. However, the weighing scale depends on acceleration, not on the direction of motion. In this problem, the elevator is moving upward but accelerating downward because it is slowing down. Therefore, the apparent weight decreases.

Important Formulae

True Weight

W = mg

Apparent Weight (Upward Acceleration)

N = m(g + a)

Apparent Weight (Downward Acceleration)

N = m(g − a)

Equation of Motion

v = u + at

Key Points to Remember

The weighing scale always measures the normal reaction force. The direction of acceleration determines whether the apparent weight increases or decreases. Upward acceleration increases the reading, while downward acceleration decreases it. The direction of motion alone has no effect on the scale reading.

Final Answer

The reading of the weighing scale just before the elevator comes to rest is

651 N