Hi everyone,

The apparent weight of an object underwater is calculated by considering the buoyant force that the water exerts on the object. This buoyant force, which acts upwards against gravity, is the reason why objects weigh less in water than they do in air. To understand how apparent weight is calculated and how it relates to the actual weight of the object, let's look at the relevant principles and calculations.

Principles Involved

    Buoyant Force: According to Archimedes' principle, the buoyant force on a submerged object is equal to the weight of the fluid it displaces. This force acts upward and opposes the gravitational force acting downward on the object.

    Gravitational Force (Actual Weight): This is the weight of the object in air and is calculated as the product of its mass and the acceleration due to gravity (W = mg).

Calculation of Apparent Weight

Apparent Weight (W') is the weight of the object as it appears when submerged in a fluid. It can be calculated using the following steps:

    Calculate the Volume of the Object (V): Depending on the shape of the object, its volume can be calculated through various geometric formulas.

    Calculate the Buoyant Force (B): The buoyant force can be calculated using the formula:

    B=ρfluid×V×g

    where ρfluidρfluid​ is the density of the fluid, VV is the volume of the object, and gg is the acceleration due to gravity.

    Calculate the Apparent Weight (W'):

    W′=W−B

    where W  is the actual weight of the object.

The apparent weight is thus the actual weight minus the buoyant force. If the buoyant force is equal to the actual weight, the object will experience neutral buoyancy and float suspended in the fluid. If the buoyant force is greater than the actual weight, the object will rise to the surface and float; if less, the object will sink.

Relationship to Actual Weight

The relationship between the apparent weight and the actual weight is directly influenced by the buoyant force. The greater the volume of the object relative to its weight (i.e., the lower its density compared to the fluid), the greater the effect of the buoyant force on reducing its apparent weight. This is why objects that are less dense than water (like wood or ice) have an apparent weight that can be very small or even negative, leading them to float, while denser objects like metals have a higher apparent weight underwater but still weigh less than their weight in air.

Based on the questions you have asked us, we have attempted to discuss the topic of weight measurement and scales both socially and technically. Weight measurement has undoubtedly been one of the most important topics in known history. Throughout our lives, we are all involved in weight measurement in production, consumption, trade, art, sports, etc.

General Questions:

++ Weight standards

- What's the difference between mass and weight, and their measurement methods? 
- How does gravity's acceleration affect an object's weight on different planets? 
- What are the uses and accuracy factors of precision scales and balances in weight measurement? 
- How does weight measurement help determine an object's density? 
- How is an object's apparent weight underwater calculated and related to its actual weight? 

Industrial Automation and Production:

- How is weight measurement and control integrated into industrial production, and its impact on efficiency? 
- What role do automatic weight control systems play in quality control, and how do they improve product quality? 
- How are weight sensors selected and configured in industrial automation, and their accuracy evaluated? 
- What are the latest developments in weight measurement technologies for industrial automation? 
- What software and tools are used for weight data analysis in industrial automation, and their impact on workflow? 

For the General Public:

- How can I test the accuracy of home kitchen scales? 
- Which bathroom scale is best for tracking body weight, and what are the differences between models? 
- How can I accurately measure luggage weight for travel and comply with airline limits? 
- What type of kitchen scale should I use for measuring food portion sizes for healthy eating? 
- How can I determine if my children are at a healthy weight, and what methods should I use? 

Historical

- Archimedes and "Eureka!
- What instruments were used for weight measurement in ancient times?  
- What were the units of weight in ancient civilizations?  
- How important was weight measurement in trade in ancient societies?  
- How did the first scales for measuring weight work in ancient times?  
- How were standards for weight measurement established in ancient times?  
- What were some significant discoveries related to weight measurement in ancient history?  
- What methods were used to prevent fraud in weight measurement in ancient times?  
- What events can be considered turning points in the history of weight measurement?  
- How were weight measurement units compared between different cultures in ancient times?  
- What are some written sources about weight measurement in ancient history?  

++ Weight measuring devices homepage 

"These questions often include those that may come to mind for many people regarding 'Weight measurement.' Each user or student will have their own specific questions depending on a particular situation or application. The answers are not binding or entirely definitive. There is no objection to sharing our above article, citing it as a source. - Automation Mall Community, 02/2021"  

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