What is the Physical Meaning of Multiplication in Physics?

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Discussion Overview

The discussion revolves around the physical meaning of multiplication in physics, particularly how multiplying two quantities results in a single quantity with physical significance. Examples include mass multiplied by acceleration to yield force, and other instances such as distance and area calculations.

Discussion Character

  • Conceptual clarification
  • Exploratory
  • Technical explanation

Main Points Raised

  • One participant suggests that understanding multiplication in physics can be clarified through simple examples, such as calculating distance traveled by an object moving at a constant speed.
  • Another participant points out that multiplication results in a quantity that has dimensions equal to the product of the dimensions of the individual factors, citing examples like distance and area.
  • A different viewpoint emphasizes that the multiplication itself may not hold intrinsic meaning, but the resulting quantity is often conserved or measurable, using kinetic energy and momentum as examples.
  • It is noted that the significance of products in physics often arises from their conservation properties in physical interactions, rather than the act of multiplication itself.

Areas of Agreement / Disagreement

Participants express varying perspectives on the meaning and significance of multiplication in physics, indicating that multiple competing views remain without a consensus on a singular interpretation.

Contextual Notes

Some assumptions about the nature of physical quantities and their relationships may not be explicitly stated, and the discussion does not resolve the deeper implications of multiplication in different physical contexts.

Gurasees
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What is the physical meaning of multiplication when we multiply two quantities in physics to get a single quantity? Eg. Mass * acceleration = force.
 
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I think it's easier to understand if you focus on a simple example. Take an object going 5 m/s for 3 seconds. For each second, the object has traveled 5 meters. So over 3 seconds, the object must have traveled 15 meters (3*5=15). You can see why this would be obvious and you should be able to use that basic train of thought for more difficult problems. I hope that helps.
 
You mean like with distance = velocity * time ?
Or area = length * width ?

Physically you get something that has a dimension that is equal to the product of the dimensions of the individual factors.
 
The multiplication, in and of itself, is not meaningful. But the quantity which is composed of the product is usually something that is conserved or easily measured.

Consider kinetic energy: ##{1\over2}mv^2##. It is not the fact that you take half of the product of mass and the square of the velocity that is important. It is the fact that, when work is done on a free particle, it is this quantity that changes.

Mass times velocity may be (Newtonian) momentum, but it was not the idea of the product that came first, it was the fact that, if you have a collision between two objects (without friction), it is this quantity that is conserved. It just so happens to be the afore-mentioned product.

ZM
 

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