Introduction

Understanding the concept of apparent weight is essential in various fields, such as physics, engineering, and even everyday life. Apparent weight is the weight perceived by an object due to its actual weight and other forces acting on it, such as buoyancy or an accelerating force. In this article, we will explore the concept of apparent weight and learn how to calculate it.

1. Understanding the Concept of Apparent Weight

Before delving into the calculations, it’s crucial to understand what apparent weight is and why it matters. Unlike true weight—which is the force exerted by gravity on an object—apparent weight takes into account any additional forces acting on the object. For example, when you stand on a weighing scale inside an elevator that’s accelerating upwards, you feel heavier because both gravity and the upward force of acceleration push down on you.

2. Calculating Apparent Weight

To calculate apparent weight, you’ll need several variables:

– The true weight (TW) of an object

– The buoyancy force (BF) acting on the object

– Any additional forces (AF) acting on the object – excluding buoyancy forces

The general formula for calculating apparent weight (AW) is as follows:

AW = TW + BF + AF

Let’s break down each component in more detail:

a. True Weight (TW)

The true weight of an object can be calculated using its mass (m) multiplied by the acceleration due to gravity (g).

TW = m × g

where:

m = mass of the object (kg)

g = acceleration due to gravity (~9.8 m/s²)

b. Buoyancy Force (BF)

If an object is submerged in a fluid or floating on its surface, a buoyant force acts on it that alters its perceived weight. To calculate buoyancy force, use Archimedes’ principle:

BF = V × ρ × g

where:

V = volume of the displaced fluid (m³)

ρ = density of the fluid (kg/m³)

g = acceleration due to gravity (~9.8 m/s²)

c. Additional Forces (AF)

Additional forces may include the centrifugal force experienced in a rotating frame, contact forces (such as tension or normal force), or any other external force acting on an object that’s not due to buoyancy.

3. Examples

a) Calculate apparent weight while standing in an accelerating elevator:

– Mass of person: 60 kg

– Acceleration due to gravity: 9.8 m/s²

– Upward acceleration of the elevator: 2 m/s²

TW = 60 × 9.8 = 588 N

AF = mass × acceleration = 60 × 2 = 120 N (upward direction)

AW = TW – AF (subtract because it’s an upward force) = 588 – 120 = 468 N

b) Calculate apparent weight of a submerged object:

– Mass of object: 10 kg

– Acceleration due to gravity: 9.8 m/s²

– Volume of object: 0.005 m³

– Density of water: 1000 kg/m³

TW = 10 × 9.8 = 98 N

BF = 0.005 × 1000 × 9.8 = 49 N

AW = TW – BF (subtract because it acts opposite to gravity) = 98 – 49 = 49 N

Conclusion

Understanding and calculating apparent weight is essential for various applications and scenarios, including physics problems and real-life situations such as using an elevator or diving underwater. By knowing how to account for additional forces.