Terminal Velocity?

Question

How long does it take objects to reach temanial Velocity?

Say, if you were to drop a 5 lb rock and a 1 lb rock out of a plane in the upper stratosphere, what is the maximum speed that they would reach, and what is the formula to caluculate this?

Answer 1

Terminal velocity is reached when the object is at a constant speed, i.e. when it is no longer accelerating). This means that the force of gravity (i.e the weight of the object) and the drag force caused by wind resistance are equal in magnitude. So let m=mass, g=9.81m/s^2, and D=drag force. Imagine that D is an upward force (positive D) trying to keep the object from falling and that mg (weight) is the downward force (we put a negative in front of mg) making the object fall. As you probably know, force equal mass times acceleration, i.e. mg (weight). We have

D-mg=0

This means that the net force acting on the object is zero, at which point there is no acceleration.

Now we can rearrange the equation to get D=mg

D is a function of of the speed, D=f(speed). So

f(speed)=mg

The function f(speed) might have to be determined by experimental data since it would depend on the shape of the object. Once you have that expression, you can solve for the speed.

Let's say for the sake of illustration that f(speed) is determined to be f(speed)=speed^2. Then speed^2=mg. Then if we solve for the speed, the terminal velocity will be speed=squareroot(mg)


Not all objects have the same terminal velocities since it all depends on their shape and weight. A feather and a bowling ball have different terminal velocities.

Answer 2

It depends on the shape of the rock. When air resistance equals the speed of gravity pulling an object to earth, the object will stay at this speed instead of gaining speed. A flat rock, for instance, would have less of a terminal velocity that a spherical rock of the same weight.

Answer 3

You need to reword the question. There is no real terminal velocity since the changing air density would keep the velocity constantly changing. Highest velocity would have a solution.
You need to know the density of the rocks and the altitude (since the rocks will go faster up high and slow down as they hit denser air). I guess we can assume that they're spherical since any other shape gets kinda complicated. Since you're dropping them through a constantly changing air density it's a bear. You'd need an equation that incorporated the rate the air changed density along with the resulting friction to find the solution of the highest velocity where friction was equal to weight.

Answer 4

ok, a 5lb and a 1lb weight have the same TV (term. velocity)
i think ALL objects (except those with wind resistance ie. feathers) fall aproximately at a rate of 9.8 meters per second... the thing is, i am not sure how many seconds of freefall it takes to reach terminal velocity

Answer 5

i think mass has no effect on an object that is falling, only air does. my phisics teach say a maximun velocity of an object falling is when it reaches the center of the Earth. (imagine there is a hole leading to the center of the Earth)

Answer 6

It's more complicated than that. You need a conversation, not a one-sentence answer. Messenger me on yahoo messenger. I'm a physics teacher. My ID is
fortitudinousskeptic