What is the acceleration due to gravity?

[omar1]

Ok, I'm having some difficulty with a problem. It just doesn't add up.

1. Homework Statement
Consider a 2.4kg ball and a 12.4kg ball in free fall. A) Find the Force that is acting on each ball. B) Find the acceleration of each ball, given Earth's gravity of 9.80 m/s/s.

Homework Equations

$$\omega = mg$$

$$F=ma => a=\frac{F}{m}$$

The Attempt at a Solution

Forumla:

F₁=23.52N
F₂=121.52N$$\frac{23.52N}{2.4kg}= 9.80\frac{m}{s^2}$$
$$\frac{121.52N}{12.4kg}= 9.80\frac{m}{s^2}$$
I've solved the Force, part A, but the acceleration, part B, is making me crazier. I come out with g (9.8m/s2), this can't be correct!? So I think I must be missing a Kinematics formula, but I have neither velocity or time to work with.

The ball has a weight, so the acceleration of both balls must be faster than gravity? Correct?Any help in the right direction would be appreciated. Thanks!

 

[Doc Al]

I've solved the Force, part A, but the acceleration, part B, is making me crazier. I come out with g (9.8m/s2), this can't be correct!?

Why not?

So I think I must be missing a Kinematics formula, but I have neither velocity or time to work with.

Nope. You just realized that the acceleration of an object in free fall does not depend on its mass.

If you write this symbolically, you'll have an easier time seeing it:
$\Sigma F = ma$
$mg = ma$
$a = g$

The ball has a weight, so the acceleration of both balls must be faster than gravity? Correct?

No.

 

[omar1]

Ok, soo.. if I were to drop a feather and a Boeing 747 from 20k ft, they'd both have the same acceleration?

 

[leehufford]

If you ignore air resistance, yep. All objects on Earth have the same acceleration. The heavier weight is offset by its larger inertia. Feathers feel the force that air applies to them much more than a 747 would. But with no atmosphere to get in the way, the feather and 747 hit the ground simultaneously. It's beautiful when you think about it.

 

[Doc Al]

Ok, soo.. if I were to drop a feather and a Boeing 747 from 20k ft, they'd both have the same acceleration?

Yep, if they are in free fall. (Which means that the only force is gravity--no air resistance to worry about.)

 

[mfb]

Ok, soo.. if I were to drop a feather and a Boeing 747 from 20k ft, they'd both have the same acceleration?

In vacuum, yes. The crew of Apollo 15 demonstrated that on the moon. They didn't have a Boeing 747, they used a hammer.