Why F = m * a? vs Why not F = m + a?

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In summary, the formula F = m * a is the result of experimental evidence and is explained by Newton's second law of motion, which states that the change in motion is directly proportional to the applied force and occurs in the direction of that force. This law is expressed mathematically by the formula F = m * a, where m is the mass and a is the acceleration. This formula makes sense when considering the units involved and cannot be replaced by a simpler formula such as F = m + a. However, it is theoretically possible to have a more complex formula involving constants with the correct units.
  • #1
optics.tech
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Why F = m * a?

Why not F = m + a?
 
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  • #2
Adding acceleration and mass is just like adding apples and oranges, it can't be done.

Look at the units involved and combine them in a manner which makes sense.
 
  • #3
Of course, it would be (mathematically) possible to have something like [itex]F= C_1mz+ C_2a[/itex] where [itex]C_1[/itex] and [itex]C_2[/itex] are constants with the correct units ([itex]C_1[/itex] would have to have units of "Newtons per kg" or "meters per second squared" and [itex]C_2[/itex] has units of "Newtons-seconds square per meter" or "kilograms".

But the only good Physics explanation as to why a specific formula is true is "that is what the experimental evidence shows".
 
  • #4
From: http://en.wikipedia.org/wiki/Newton's_laws_of_motion

"Newton's original Latin reads:
Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur.
This was translated quite closely in Motte's 1729 translation as:
Law II: The alteration of motion is ever proportional to the motive force impress'd; and is made in the direction of the right line in which that force is impress'd."
 

FAQ: Why F = m * a? vs Why not F = m + a?

Why is the equation F = m * a instead of F = m + a?

The equation F = m * a is known as Newton's second law of motion. It states that the force exerted on an object is directly proportional to its mass and acceleration. This means that as the mass of an object increases, the force required to accelerate it also increases. Similarly, as the acceleration of an object increases, the force required to produce that acceleration also increases. This relationship can only be represented by multiplication, not addition.

Can you explain the concept of mass and acceleration in the equation F = m * a?

Mass refers to the amount of matter in an object, while acceleration refers to the rate of change of an object's velocity. In simpler terms, mass is a measure of an object's inertia, or resistance to change in motion, and acceleration is a measure of how much an object's motion is changing over time. In the equation F = m * a, mass and acceleration are the two factors that determine the force required to move an object.

Why is it important to use F = m * a in scientific calculations?

Using the equation F = m * a is important because it accurately describes the relationship between force, mass, and acceleration. This equation allows scientists to make predictions and calculations about how objects will behave in various situations, such as in motion or under the influence of external forces. It is a fundamental principle in physics and is used in many scientific fields, including mechanics, engineering, and astronomy.

Are there any real-life examples that demonstrate F = m * a?

Yes, there are many real-life examples that demonstrate the relationship between force, mass, and acceleration. One example is when a car accelerates from rest. The force of the car's engine is directly proportional to its mass and the acceleration it produces. Another example is a person pushing a cart. The force they exert on the cart is directly proportional to their mass and the acceleration of the cart. These examples follow the same principle as the equation F = m * a.

Is there a situation where the equation F = m + a would be more accurate than F = m * a?

No, the equation F = m * a is always more accurate than F = m + a when describing the relationship between force, mass, and acceleration. This is because the equation F = m * a takes into account the fact that force, mass, and acceleration are all directly proportional to each other. This relationship cannot be accurately represented by addition, as it does not account for the varying degrees of change in each factor. Therefore, F = m * a is the most accurate and scientifically accepted equation for describing this relationship.

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