Exploring the Meaning of Force: F=ma vs. F=mdx/dt

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aaaa202
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I thought to myself yesterday: Is there really any way of measuring a force independent of F=ma? I don't see there is so you can more or less take F=ma as the definition of force and then use that to derive the expressions for the fundamental forces of nature. But then it occurred to me: Why did we then choose F=ma. Why didnøt we just pick F=mdx/dt and adjusted the expressions for the fundamental forces from that?
 
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  • #2
aaaa202 said:
I thought to myself yesterday: Is there really any way of measuring a force independent of F=ma? I don't see there is so you can more or less take F=ma as the definition of force and then use that to derive the expressions for the fundamental forces of nature. But then it occurred to me: Why did we then choose F=ma. Why didnøt we just pick F=mdx/dt and adjusted the expressions for the fundamental forces from that?

http://en.wikipedia.org/wiki/Torsion_bar_experiment
 
  • #3
aaaa202 said:
I thought to myself yesterday: Is there really any way of measuring a force independent of F=ma? I don't see there is so you can more or less take F=ma as the definition of force and then use that to derive the expressions for the fundamental forces of nature. But then it occurred to me: Why did we then choose F=ma. Why didnøt we just pick F=mdx/dt and adjusted the expressions for the fundamental forces from that?
This has been discussed at length in several threads eg: https://www.physicsforums.com/showthread.php?t=631147.

The concept of force exists independently of the second law eg. a standard spring exerts a standard force if stretched a standard distance. Double the number of such stretched springs and you double the force.

AM
 

FAQ: Exploring the Meaning of Force: F=ma vs. F=mdx/dt

1. What is the difference between F=ma and F=mdx/dt?

The equation F=ma represents Newton's second law of motion, which states that the force acting on an object is directly proportional to its mass and acceleration. This equation is used to calculate the net force on an object when its mass and acceleration are known. On the other hand, F=mdx/dt represents the more general form of Newton's second law, where x represents the displacement of the object and t represents time. This equation takes into account the changing velocity of an object over a period of time, rather than just its acceleration.

2. Which equation is more accurate?

Both equations are equally accurate and valid in their respective applications. F=ma is typically used for objects with constant mass and acceleration, while F=mdx/dt is used for objects with varying mass and acceleration. In certain situations, the more general form of Newton's second law may be more appropriate.

3. How do these equations relate to the concept of force?

The equations F=ma and F=mdx/dt are mathematical representations of the relationship between force, mass, and acceleration. They demonstrate that force is directly proportional to both mass and acceleration, and that the rate of change of an object's velocity is also directly proportional to its mass and acceleration.

4. Can these equations be applied to all types of forces?

Yes, these equations can be applied to all types of forces, as long as the force, mass, and acceleration are known or can be measured. They are fundamental laws of physics and can be used to describe a wide range of physical phenomena.

5. What are some real-world examples of these equations in action?

Examples of F=ma include calculating the force required to accelerate a car from 0 to 60 mph in a certain amount of time, or determining the force exerted on an object when it falls due to gravity. F=mdx/dt can be seen in the trajectory of a rocket, where the mass of the rocket decreases as fuel is burned and the velocity changes over time. It can also be applied in analyzing the motion of a pendulum or a swinging object.

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