What is the final velocity of a falling body?

[Randomer Guy]

Homework Statement

It is possible to calculate the velocity of falling bodies (ignoring air resistance of course) using a gravitational acceleration constant.

Assume:

You don't know what the resistance is.
The object started at rest.
You DO know there is downwards motion.
You don't know what the mass is.

I am trying to get at an ending velocity for about 3-10 meters of acceleration if that helps. Using that ending velocity, I can then easily calculate kinetic energy.

If there is some other resistance, other than air, is it reasonable to simply reduce the acceleration by some amount to account for that resistance, if one is trying to get at a reasonable range for kinetic energy (in terms of the objects mass)?

Homework Equations

body at rest acceleration and ending velocity:
v^2=2ad
ke=1/2mv^2

The Attempt at a Solution

This really simply requires a "reality" check to see if I am conceptually on track.

I may have some follow questions depending on how things work out, if y'all don't mind. I am trying to make sure that my concepts of physics are straight, so I can explain some of these concepts to a couple of people who know much less than I do.

 

[mathPimpDaddy]

yeah, mass don't matter... Potential energy? What is the formula?

 

[Randomer Guy]

yeah, mass don't matter... Potential energy? What is the formula?

PE = mgy
where m is the mass of an object, g is the acceleration due to gravity, and y is the distance the object is above some reference level.

I am really trying to find energy in terms of the mass involved, because I can't even reasonably get to the mass, but the mass relative to the force required to stop the motion is important.

Again, I am not even that far along in my work/explanation.

They seem to be hung up on the fact that I simply reduced the acceleration over the distance to account for resistance.

Given that a few of the variables are unknown and can't be known with certainty, is that bit reasonable, or am I missing a piece of the puzzle here?

 

[mathPimpDaddy]

PE = mgy
where m is the mass of an object, g is the acceleration due to gravity, and y is the distance the object is above some reference level.

I am really trying to find energy in terms of the mass involved, because I can't even reasonably get to the mass, but the mass relative to the force required to stop the motion is important.

Again, I am not even that far along in my work/explanation.

They seem to be hung up on the fact that I simply reduced the acceleration over the distance to account for resistance.

Given that a few of the variables are unknown and can't be known with certainty, is that bit reasonable, or am I missing a piece of the puzzle here?

What is y and what does Potential energy equal to when the object is at a certain distance in motion? You know that you are going to end up with a one dimensional distance-acceleration forumula right? Rotate the picture from it being vertical to horizontal motion and think there was an initial force that caused an acceleration.

 

[Randomer Guy]

What is y and what does Potential energy equal to when the object is at a certain distance in motion?

that goes back to the kinetic energy equation.

Would the ultimate height be irrelevant, if all one is doing is calculating the energy after 10 meters?

I am thinking of an object at great height, but only considering the first 3 to 11 meters of its fall.

I want to eventually get at a reasonable estimation of the force required to arrest the falling object (i.e. bring it to a complete stop) by catching it after it has been moving for a known distance but unknown acceleration.

 

[Randomer Guy]

What is y and what does Potential energy equal to when the object is at a certain distance in motion?

PE = mgy
where m is the mass of an object, g is the acceleration due to gravity, and y is the distance the object is above some reference level

But, I assume you are asking for a reason (thanks for helping, by the way), so let's go with this.

PE=m(9.8 meters/sec/sec)(3 meters)

or

PE=m(29.4 (meters)(meters)/sec/sec))

assuming that the distance was 11 meters

PE=m(107.8 (meters)(meters)/sec/sec))

 

[mathPimpDaddy]

Don't look at it as height, look at it as length, like when the object travels like in horizontal motion with force applied

 

[mathPimpDaddy]

and at that same distance there is kinetic energy right? I wonder what happens to the mass

 

[Randomer Guy]

PE = mgy
where m is the mass of an object, g is the acceleration due to gravity, and y is the distance the object is above some reference level

But, I assume you are asking for a reason (thanks for helping, by the way), so let's go with this.

PE=m(9.8 meters/sec/sec)(3 meters)

or

PE=m(29.4 (meters)(meters)/sec/sec))

assuming that the distance was 11 meters

PE=m(107.8 (meters)(meters)/sec/sec))

This is exactly the same as the calculations for an object in free fall by the way.

I have done the calculations, but the people I am talking to don't really believe they apply in the case in discussion.

They seem to think I am missing something and that the calculations are meaningless.

 

[mathPimpDaddy]

who are you talking to? I think you have the right Idea, I also believe that its a free falling motion, hence the "g"

 

[Randomer Guy]

who are you talking to? I think you have the right Idea, I also believe that its a free falling motion, hence the "g"

I would rather not get into exactly what is being discussed and to whom. It is the kind of thing that can get touchy with people.

Let's just say that I am talking to people with very little knowledge of physics and critical thinking.