# Acceleration of gravity conflicts with F=MA, why?

1. Feb 11, 2012

### LearninDaMath

I just started learning about forces. Here is what is confusing me.

First, they say that no matter the mass of an object, it will accelerate towards earth at exactly the same rate. So a car and a baseball would hit the ground at the same time even though their masses differ.

However, they also say that A = F/M which states that if there is some force (such as the force of gravity), and acceleration changes as a mass changes.

So a car and a baseball have two different masses. So one law states that their accelerations will be different from each other due to differing masses. And the other law states that their accelerations will be the same as each other regardless of their differeing masses.

What am i missing here?

2. Feb 11, 2012

### Staff: Mentor

You're missing the fact that the gravitational force on each object is proportional to its mass. If the same force acts on two different masses, then the more massive one would accelerate less. But with gravity the force increases with mass, leading to a constant acceleration for all falling bodies.

3. Feb 11, 2012

### Andrew Mason

You are overlooking the fact that the force of gravity between two bodies is proportional to the mass of each body.

AM

4. Feb 11, 2012

### Staff: Mentor

The force acting on the two objects is not the same, as you note. Larger mass → larger force due to gravity. HOWEVER, the inertial mass, that is the resistance to acceleration as per the formula F = MA, also scales at the same rate. This is known as the Equivalence Principle. So while the force due to gravity scales with the mass, so does the resistance to acceleration. The two effects exactly cancel.

5. Feb 11, 2012

### LearninDaMath

so gravity will pull harder on an object with more mass, so as to keep its acceleration at 9.8m/s^2 at all times. The earth can't be conciously thinking to itself, okay, i'm going to pull on that rock more than I am going to pull on that feather so as to keep the earthly acceleration constant.

If I had a 1 kilogram ball with some constant acceleration, say 9.8m/s^2 being applied to it, and I wanted to make a 1000 kilogram vehicle accelerate at the same rate as the ball. I would have to calculate F=MA: 1000kg*9.8m/s^2 = 10,000 Newtons of force to make the car accelerate at the same rate as the 1 kilogram baseball. The earth doesn't even have eyes to observe the motion of the ball or the car, much less a pen, paper, or consciousness to determine this appropriate amount of force to use, so how does the earth do this???

6. Feb 11, 2012

### Staff: Mentor

Write the equation for the force due to gravity on some mass m at radial distance R from the center of the Earth (mass M). Divide that force by m in order to yield acceleration (a = f/m). How does a depend upon m in the result?

7. Feb 11, 2012

### Staff: Mentor

No reason to think consciousness or a calculator is needed for any of the usual 'physical' laws to hold. (Why pick on gravity? How in the world does a mass know to abide by Newton's 2nd law!...or any other law.)

The best we can do is describe how things work, sometimes at a very deep level.

8. Feb 11, 2012

### Redbelly98

Staff Emeritus
LearningDaMath has just started learning about forces. The gravity equation will not be introduced until later on.

9. Feb 11, 2012

### Andrew Mason

Nobody knows. One of the great mysteries of the universe.

Newton figured out how gravity behaves. Einstein refined the theory. But no one understands why masses attract each other or, as Einstein might prefer to say, why masses curve space-time. No one understands why inertia exists, either. We just know that if it didn't exist we would not be able to ask the question.

AM