hey physics geniuses

On October 23 2008 08:18 Crisis_ wrote:
Both objects will accelerate at the same rate if they are dropped at the exact same time. Gravity is the only acceleration acting upon both objects in this free-fall simulation, so right before one object reaches terminal velocity, their accelerations will be exactly the same, regardless of mass.

On October 23 2008 08:20 TheYango wrote:
No.

Drag force is given by -0.5ACdv^2

Where A is the surface area, C is the drag coefficient, d is the density of the fluid, and v is the velocity. Since they both feel the same drag force initially, they experience different accelerations, because the drag force is not proportional to the mass of the object.

Another way to look at it is that since terminal velocity is proportional to the square root of mass, they must have different terminal velocities, and therefore must reach 0 acceleration at different rates.

On October 23 2008 08:27 travis wrote:
ok wait what?
if in a vacuum they would accelerate at the same rate
why would their rates of acceleration change when both subjected to an equal drag force ?

terminal velocity determines acceleration?

On October 23 2008 08:32 micronesia wrote:
What prompted this question? BTW if you didn't see my edits I put them in the earlier post.

On October 23 2008 08:27 travis wrote:


ok wait what?
if in a vacuum they would accelerate at the same rate
why would their rates of acceleration change when both subjected to an equal drag force ?




terminal velocity determines acceleration?

On October 23 2008 08:34 travis wrote:


yes I saw them but I didn't understand them.



can you give me an equasion, with all variables explained?

pretty please?


this question was prompted by a prop bet I made with someone, me getting 10 to 1. though I will admit I really didn't know, so I expected to lose this bet

On October 23 2008 08:06 travis wrote:
here is my question.


2 objects, same shape, surface, and size. different masses.


both are dropped from an airplane.

before either object reaches terminal velocity, will they accelerate at the same rate?

On October 23 2008 08:41 Elvin_vn wrote:


same shape + surface + size ==> same resistance ==> they will accelerate at the same rate

On October 23 2008 08:41 Elvin_vn wrote:


same shape + surface + size ==> same resistance ==> they will accelerate at the same rate

On October 23 2008 08:33 TheYango wrote:


Gah, I'll try to be clearer.

Suppose at some time t, the two objects have the same velocity, and therefore, the same drag force. Since the drag FORCE is the same, we'll call it f. The equations for Newton's 2nd law would be
m1a1 = m1g - f
a1 = g - f/m1

m2a2 = m2g - f
a2 = g - f/m2

Where a1 and a2 are the accelerations for objects 1 and 2, g is acceleration due to gravity, and m1 and m2 are their masses.Unless m1 and m2 are equal, those accelerations CANNOT be equal, which means the acceleration functions must be different. An equal change in force does not mean an equal change in acceleration. It only is so for cases in which the force is proportional to the mass (as with the force of gravity).

terminal velocity determines acceleration?

On October 23 2008 08:50 3 Lions wrote:

Force = Mass x Acceleration
Force is equal, but mass is different, so they will not accelerate at the same rate. 9th grade physical science owns.

When you apply a force to an object, it accelerates. The more mass it has, the more it resists accelerating (inertia). The formula is Fnet = m*a

On October 23 2008 08:56 travis wrote:
micronesia, i do not understand
you say



I thought gravity was a constant for all objects. i don't know what role this equasion has

please bear with me I am probably a difficult student, understand I have no real background in mathematics I am better at just dealing with concepts and "the ways things work"

On October 23 2008 08:52 micronesia wrote:

I think this suffices as the short answer, believe it or not.

On October 23 2008 08:59 travis wrote:


but... force is not equal, I thought.
are not the forces of the 2 objects different?

the heavier one would surely hurt more if it fell on you

On October 23 2008 08:57 micronesia wrote:




What I wrote there is a universal truth... and gravity has not even been mentioned yet. Gravity is just one type of force. Any force applied to an object can make it accelerate (speed up). But you know full well if you push a truck it won't accelerate as much as if you push a small car (because it has more mass)

Feel free to ask for clarification on any other aspects of it since it's a somewhat advanced topic to discuss at length.

Oh good just like my students :p

On October 23 2008 09:00 Mooga wrote:


micronesia, under what assumptions are you stating that the accelerations will be different?

In a vacuum, the accelerations are equal, regardless of mass.

F=mg
ma=mg
a=g

The force exerted on the different mass objects are different, because the force is dependent on mass.

On October 23 2008 09:02 micronesia wrote:

Acceleration will be equal if the force changes according to the mass (specifically if the force is proportional to the mass)

edit: I don't believe I said anything to the contrary.

On October 23 2008 09:00 micronesia wrote:

You are engaging a common misconception that objects carry force. A force is an interaction between two or more objects. No one object can have a force.

A heavier object will hurt more because it has more energy and hits you with more momentum.

On October 23 2008 09:12 travis wrote:



ok so, the force of the objects is defined by gravity, which is a constant - so that is why their force is equal?

and their masses are different
so their acceleration must be different

well, now I am just confused by the equation F=M x A

why is acceleration part of an equasion for force? shouldn't it be velocity, not acceleration?

On October 23 2008 09:17 micronesia wrote:
The first force is determined by gravity. It is the weight of the object. The more weight there is, the more the Earth pulls the object down. The weights are actually not equal. What is equal is the force of friction (air resistance). This is because air resistance depends on the shape/size of an object as well as the speed it is moving at, and the objects have the same shape and surface area.

Keep in mind when there are two forces, you can't determine the acceleration of an object until you add both of those forces together. That why it's called the net force in the formula.


F=ma just talks about how objects respond to forces in general. The more force an object experiences, the more it will accelerate (as per f=ma). The only other factor to consider is mass. The more mass it has, the less it will accelerate.

The way we determine the value of actual forces is different. The weight of an object (for example) is equal to its mass (say, in kilograms) times the acceleration due to gravity on Earth (much higher than say, gravity on the moon).

edit: also, the only force in this discussion where velocity should be in the formula is the force due to air resistance (friction).

On October 23 2008 09:22 travis wrote:
micronesia, what is the role of "drag force" in all of this?

On October 23 2008 09:25 micronesia wrote:

The drag force is the force of friction, which is due to air resistance. If there was no air (vacuum) then the objects would fall exactly the same. But since there is air, there is an upward force acting on each of the objects. This opposes the force of gravity, and when this drag force gets big enough, the object achieves terminal velocity.

On October 23 2008 09:25 micronesia wrote:

The drag force is the force of friction, which is due to air resistance. If there was no air (vacuum) then the objects would fall exactly the same. But since there is air, there is an upward force acting on each of the objects. This opposes the force of gravity, and when this drag force gets big enough, the object achieves terminal velocity.

On October 23 2008 09:29 travis wrote:


so it comes down to:

drag force VS force of gravity

and the force of gravity is based upon mass of the objects?

On October 23 2008 09:30 micronesia wrote:

Correct.

edit: but I wouldn't consider that alone a sufficient explanation

On October 23 2008 09:34 travis wrote:


why not?


oh, because of terminal velocity?

On October 23 2008 09:37 micronesia wrote:

Well I suppose if you just wanted to know which one would have a bigger acceleration, everything else besides mass being equal, then that would be acceptable. If you want to discuss how the objects' motion would change over time, then you'd need to also recognize that the force of friction depends on the speed (in this case)

On October 23 2008 09:40 Mooga wrote:


micronesia,

drag force already accounts for velocity.

On October 23 2008 10:12 micronesia wrote:

You were going on the assumption that by saying 'drag force' you realize how the drag force works, besides the fact that it is simply a force that opposes motion in a fluid (such as air). I don't believe that was true, however it doesn't need to be given the nature of Travis' request.

BTW Travis who won?

On October 23 2008 10:34 Mooga wrote:


The drag force is a force F (you can double-check this by reducing the units of [check picture]) and this applies at any given time.



where p=density=F(L^-4)(T^2)
u=velocity=L(T^-1)
Cd= dimensionless
A= L^2

Thus, the drag force can be expressed as single force (at any given time).

Edit: Fixed the link to the pic

On October 23 2008 08:06 travis wrote:
here is my question.


2 objects, same shape, surface, and size. different masses.


both are dropped from an airplane.

before either object reaches terminal velocity, will they accelerate at the same rate?