# Acceleration change in freefall

1. Jul 3, 2006

### uwmphysics

does anyone know the answer to this?

If the mass of an object in free fall is doubled, its acceleration
a. doubles
b. increases by a factor of four
c. stays the same
d. is cut in half

2. Jul 4, 2006

### JohnSimpson

Go take a bowling ball and a rubber ball, drop them from the same height, and find your answer.

3. Jul 4, 2006

### Mindscrape

I thought everyone knew the anecdote of Galileo on top of the leaning tower of Piza.

Here's another question that you should look at to get a better grasp on acceleration... If I drop a pen on the moon, it will:
a) Float around
b) Fall to the ground
c) Go to the earth
d) Abducted by moon martian

4. Jul 4, 2006

### MeJennifer

So let me get this right, say an object in free fall towards the earth suddenly increases its mass.
Now the movement of the object is determined by the curvature in space-time caused by the mass of the earth am I right? But the object also has mass and curves the space-time, be it extremely small compared to the curvature of the earth right? Are we saying that the space-time curvature between the two objects remain the same during the sudden mass increase?

5. Jul 4, 2006

### Mindscrape

Well, it would be one of those things where the difference is going to be something like 30 decimal places. The difference in forces, i.e. Newton's Second and Third Laws, are going to have a much greater impact on an object with a dynamic mass than relativistic effects (unless it is going super fast, then we could introduce general relativity).

6. Jul 4, 2006

### Kurdt

Staff Emeritus
I suggest looking up the weak equivalence principle or working it out for yourself. How do you find the acceleration of a free fall object?

Hint: Equate Newton's 2nd law with his gravitational law.

7. Jul 4, 2006

### arunbg

I'm sure the OP realised that this is a subforum for introductory physics and not advanced physics when he posted .

8. Jul 4, 2006

### CaptainJames

Actually, along with this, isn't the gravitational force of a more massive object slightly larger, although because of the earth's mass it's unnoticable?

9. Jul 4, 2006

### arunbg

Yes, you are correct .

10. Jul 4, 2006

### HallsofIvy

Staff Emeritus
Not just "slightly larger" and certainly not "unnoticable". If object A has twice the mass of object B, then the gravitational force on A is twice that on B. But the question was about acceleration- and F= ma. If both mass and force double, what happens to a?

11. Jul 5, 2006

### CaptainJames

Ahhh you're right, I misused terminology, I meant isn't the acceleration slightly larger.

12. Jul 5, 2006

### arunbg

I understood your ,misused terminology :)
Yes, it is larger .

13. Jul 5, 2006

### Hootenanny

Staff Emeritus
Wait a minute, an objects acceleration (due to gravity) is independent of its mass.

14. Jul 5, 2006

### garyljc

Free fall , doesnt take into account of mass . Acceleration is totally independent of mass .
Eg : If you drop a leaf and a tennis ball , you will notice that the tennis ball will reach the ground faster. This happens not because of the mass of the tennis ball , but the surface area of the tennis ball. Therefore , less air resistance or drag force acts upon the tennis ball , whereas the leaf has a much bigger surface.
When air resistance is equal to acceleration , terminal velocity is reached =)
I hope this helps though =) Cheers :P

15. Jul 5, 2006

### tyco05

Whoa whoa whoa.......... what about a small leaf...... with a surface area less than that of the cross sectional surface area of a tennis ball.....
It will still take longer.

And you mean when air resistance is equal to gravitational force.

Equilibration of forces.

16. Jul 5, 2006

### garyljc

I'm sorry that I did not state my assumptions before I quote on that statement .
Thanks though , and I meant ar resistance is equal to gravitational acceleration which is , g =)

17. Jul 5, 2006

### Mindscrape

Isn't drag force inversely proportional to the square root of the cross-sectional area or something?

Yes, I am pretty sure the original poster's question was from some kind of introductory physics class where the answer would obviously be the acceleration of an object is independent of mass, hence the Galileo and the leaning tower of Pisa anecdote. Doesn't every body know this? Galileo wanted to know if a heavier object fell faster than a lighter object, and so he took a boulder and a rock to the top of the leaning tower of Pisa and then dropped them both at the same time to see which would hit the ground first (thus accelerating the quickest). To his surpise, as the story goes (which is probably made up), both hit the ground at the same time.

18. Jul 5, 2006

### Hawknc

The actual equation for drag is $D = \frac{1}{2} \rho c_D u^2 A$, so drag is proportional to area. (Logical, if you think about it - a larger surface area doesn't create less drag!) It refers to, in this case, the cross-sectional area normal to the direction of travel. So at terminal velocity, Drag = Weight resulting in a net zero force and hence constant velocity. That's the really short and simple version of drag, at any rate.

19. Jul 6, 2006

### Mindscrape

Yeah, mechanical physics sucked too much for me to remember anything from it.