How does mg = ma follow from F=ma?

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In summary, F=ma is Newton's 2nd law which states that the net force on an object must equal its mass times its acceleration. In the special case of an object in free fall, where the only force is gravity, this can be written as mg=ma, which further simplifies to g=a. However, in the real world, there are many other forces that can act on objects, so F=ma actually means the sum of all forces is equal to ma.
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memsces
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Can somebody explain in simpler terms F=ma and why that can be writtent as mg=ma. Which finally can be written as g=a.
 
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memsces said:
Can somebody explain in simpler terms F=ma and why that can be writtent as mg=ma. Which finally can be written as g=a.
Newton's 2nd law states that the net force on an object must equal ma. In the special case where the only force on an object is gravity, which equals mg, then the net force is just mg. Thus mg = ma, which implies that g = a. (The acceleration of an object in free fall is g downwards.)
 
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Doc_al is correct in saying that g = a when the object is in free fall (the only force acting on the object is gravity). However the world is not that simple, there are a lot more forces that can act on objects such as support force, air resistance, friction just to name a few. So therefore F=ma means the sum of all forces = ma, usually seen with the symbol sigma (meaning the sum of forces) before F. I hope that clarified things for you memsces.
 

FAQ: How does mg = ma follow from F=ma?

1. How does the equation mg = ma follow from F=ma?

The equation mg = ma is derived from Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. This can be written as F = ma. In the case of an object on Earth's surface, the acceleration due to gravity (g) is always constant. Therefore, the force of gravity (mg) acting on the object can be substituted for the net force (F) in the equation, resulting in mg = ma.

2. What is the significance of mg = ma in physics?

Mg = ma is significant because it shows the relationship between an object's mass, acceleration, and the forces acting on it. It is a fundamental equation in classical mechanics and is used to understand and predict the motion of objects, such as the motion of a falling object due to gravity.

3. Can mg = ma be applied to all objects?

Yes, the equation mg = ma can be applied to all objects, regardless of their mass or acceleration. The equation is a fundamental principle in classical mechanics and is used to describe the motion of objects in the presence of a force.

4. How does mg = ma relate to weight?

The equation mg = ma relates to weight because the force of gravity (mg) is also known as an object's weight. This means that the weight of an object is equal to its mass multiplied by the acceleration due to gravity.

5. Can mg = ma be used to calculate the acceleration of an object?

Yes, mg = ma can be used to calculate the acceleration of an object. By rearranging the equation to a = F/m, we can calculate the acceleration of an object by dividing the net force acting on it by its mass. This is useful in situations where the mass and force are known, and the acceleration needs to be determined.

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