# Mass and Acceleration

1. Jan 1, 2004

### celect

How does mass affect the rate of acceleration in free fall:

a. In air?

b. In a vacuum?

If I understand Newtons' Second law all objects in free fall have the same acceleration.

I don't get the question for vaccum.

2. Jan 1, 2004

### Mathechyst

Try thinking about how various objects move when you drop them into water versus when you drop them in air.

Doug

3. Jan 2, 2004

### jcm15

acceleration

so how would air resistance affect the acceleration of free fall of an object compared in a vacum, if both situations have the same force of gravity acting on the object? considering that an object has an acceleration of 9.8ms-2 before it reaches its maximum veloctiy.

4. Jan 2, 2004

### celect

I understand that in a vaccum there is no air resistance, What I don't understand about the question is how mass effects acceleration.

In a vaccum objects will fall without resistance of air.

In the pressence of air resistance I understand you have resistance.

I guess I getting confused with mass and weight.

5. Jan 2, 2004

### Staff: Mentor

You need to understand two things. First is Newton's 2nd law, which tells us that a = F/m. So, if you knew the net force on an object, and the mass of the object, you can calculate its acceleration.

For an object falling in a vacuum, the only force acting is gravity. It just so happens that the weight (the force of gravity) of an object is proportional to its mass. (That's the second thing you need to understand.) So the ratio (F/m) is a constant. That's the acceleration due to gravity. So, in a vacuum, the mass of a falling object does not affect its acceleration: all objects accelerate at the same rate.

6. Jan 3, 2004

### jcm15

getting a bit confused

Doctor Al. I'm a bit confused with what you said about objects accelerating at the same rate regarding with whether they are moving in vacum or air. Isn't it true acceleration depends on v/t. If in our atmposphere, the velocity changes, So acceleration's got to have some effects in terms of it's rate of change. Eg. in space, the object would probably be accelerating 15ms-2, but in our atmosphere, it will probably be traveling 10ms-2, due to the force of air resistance. Right?

7. Jan 3, 2004

### Jimmy

Re: getting a bit confused

Gravitational acceleration depends on Ag=GM/r^2

The acceleration of gravity is the same for all objects in vacuum or in air. When an object falls through the air, however, a new force is introduced which works in the opposite direction of gravitational acceleration/force. Drag force.

$$F_d = \frac{\rho C_d A V^2}{2}$$

Fd is drag force
p is air density
Cd is the drag coefficient
A is the frontal surface area of the object
V is the velocity of the object

We will only worry about the velocity and area in this case, as the air density and drag coefficient will be the same for our falling objects.

The point at which drag force equals gravitational force is referred to as the terminal velocity. At the terminal velocity, there will be no 'net' force acting on the falling object so it will cease to accelerate but continue to fall at a constant velocity.

http://hyperphysics.phy-astr.gsu.edu/hbase/airfri2.html

Consider two spheres which are the same size but one sphere is more massive. The sphere with the higher mass naturally has a higher gravitational force acting on it. It will take an equally higher drag force to balance the gravitational force so it's terminal velocity will be higher. IOW, it will have to reach a higher velocity before the drag force will balance the gravitational force. Refer to the drag force equation above. All other factors being the same, A higher V will result in a higher drag force. The heavier sphere will fall faster than the lighter sphere.

The frontal area of an object is another critical component of drag force. The frontal area being the area which is pushing against the air.

Consider two spheres which have the same mass but one is larger. The terminal velocity of the larger sphere is lower so it will fall slower than the smaller sphere. This can be easily demonstrated by taking two sheets of paper and crumbling one sheet into a ball and leaving the other flat. Let them both fall. You can guess what the outcome will be.

Hope this helps a little.

Last edited: Jan 3, 2004
8. Jan 3, 2004

### Staff: Mentor

Re: getting a bit confused

Please reread my earlier post. Nowhere do I make any statement comparing what happens in vacuum to what happens in air. The first step is to understand what happens in a vacuum without the complications of air resistance.
I really have no idea what you are saying. Acceleration is the rate of change of velocity. That's what the word means.
No, not right. In a vacuum, the acceleration will simply be due to gravity. Near the earth's surface, that acceleration would be about 9.8 m/s2. In space, who knows? It depends where you are.

So, for ordinary falling bodies near the earth's surface, the acceleration is g = 9.8 m/s2. What happens when you add in air resistance? Air resistance is a force opposing the object's motion. So the net acceleration is less than normal. Jimmy provides some details, but the basic idea is that the same air resistance (which depends on cross-sectional area and speed) will have a greater effect on the object with least mass---a light object will fall with less acceleration that a heavy one with the same size and shape.

We are talking here about objects that are exactly the same except for mass. If, instead, you keep the mass the same but increase the area, that will greatly increase the air resistance. That's how a parachute works.