# Calculating componants of a falling object.

doctorjanitor
Im doing a little investation.. nothing too detailed. Its into the way parachutes fall ect.
Im dropping parachutes out of a window with different weights on, up to a certain weight where the kenetic energy becomes too high. Then I am going to try to design a better shape to reduce the KE of the impact for that weight.

I know the surface area of my parachutes, the weight of the load hanging off the parachute, i also know the distance it is falling, and the time it took it to fall.

Im not too sure how to work it out at the moment i haven't put enough thought into it obviously.

I need to know Kenetic energy of the impact, the velocity it hits the ground with, and maybe its acceleration. Can i work it out from this? I was told something about stokes' law, the GPE and the amount of force disapated on its journy, the remaining would be the KE of the impact. But I am not sure what equations or how to use them.

I kinda need the advice asap!

If anyone could give me a bit of advice with what I am trying to do i'd be greatful.

Thanks alot!

maverick_starstrider
If you know the distance it is falling and the time it takes to fall that'll give you its final velocity and acceleration from which you can calculate the KE at impact. it's really just simple kinematics

Homework Helper
Welcome to PF!

Hi doctorjanitor! Welcome to PF!
If you know the distance it is falling and the time it takes to fall that'll give you its final velocity and acceleration from which you can calculate the KE at impact. it's really just simple kinematics

I don't think the acceleration is constant with a parachute.

In that case, knowing only the distance and time won't give you either the final velocity or the acceleration.

doctorjanitor, how accurately can you measure the time?

You may need to measure the time over different distances to get the final velocity at any particular distance.

(I can't think what you'd need the acceleration for, though.)

doctorjanitor
Further help.

Thanks tiny-tim.

I don't think i need acceleration, i just kind of threw that in for interest to see if it was possible for further investigation.

I can time to two decimal places, e.g to one hundredth of a second, its a stopwatch by eye so the accuracy is questionable, but reaction times tend to cancel out each end, and my times are all quite close. e.g
1.45
1.47
1.39
1.51
That kind of accuracy seems ok to me.. basically i can't really time to any more accuracy due to the equipment that's avaliable to me.

What I am doing is an investigation so I am trying to apply it to a real life use, even if it is nowhere near accurate to be realistic. I'm trying to measure parachutes for cargo use ect. I chose cargo instead of people as a lot of other variables come into place when you use a person and its shape.

I thought about using the SUVAT equations to find acceleration.. let me explain my investigation a bit first. I am using parachute, my first test is with no parachutes, to see how much the parachute slows flight (maybe in a % or fraction). I am going to increase the weight and keep doing so until i feel its enough that the parachute doesn't function properaly. The falling space is about 8.67 meters i counted bricks and morter and measured it so its quite accurate.

I want to work out the KE each test hits the floor with.. from this ill find a KE where i think the cargo wouldn't be able to stand the landing. Then with this ill try to design a new parachute (new shapes, adding holes ect) that will protect that weight and reduce its KE on landing.

I then want to try to scale it up, and maybe find a parachute size to weight ratio.. this might not be possible but it will be interesting to see if its linear ect.

I figured - from the advice of my tutor, that i know i can work out GPE

GPE = mass x gravity x height.

When something hits the ground all its GPE is converted to other energies.
If i wasnt doing parachutes i could ignore air resistance - but the whole point of a parachute is air resistance so it would be stupid to ignore it and use SUVAT in this situation. (as suvat is for constant motion i can't use it).

Because i know their is air resistance all GPE is not converted to movment energies, it is converted to heat on the way down too due to drag.

Also it would help to know the speed that it hits the ground with.. this is hard. BUT all good parachutes will have reached their terminal velocity before they hit the ground.. else is isn't really a parachute is it? So the speed it hits the ground with i will assume is the same as its terminal velocity.

I was told i could work out terminal velocity with "stokes' law", it states that where the drag force is equal to the gravity or something like that speed is constant.

Im not sure how but if i can work out what force there is against the object, i can times it by the height, and work out how much energy is disapated on the journy.

Know how much energy it started with GPE - (MINUS) the energy lost on the journy = (EQUALS) the amount of energy it hits the ground with!

I find this all very interesting and if it isn't possible i need to know soon because i don't want to get so far behind because i have to change my project. Anything anyone knows, tell me!

Thanks a lot everyone.

Homework Helper
Hi doctorjanitor!
Also it would help to know the speed that it hits the ground with.. this is hard. BUT all good parachutes will have reached their terminal velocity before they hit the ground.. else is isn't really a parachute is it? So the speed it hits the ground with i will assume is the same as its terminal velocity.

I was told i could work out terminal velocity with "stokes' law", it states that where the drag force is equal to the gravity or something like that speed is constant.

ah … that makes more sense …

… you need to measure the terminal velocity, and nothing else.

It seems to me that your main problem is not measuring the velocity, but making sure that it's terminal!

In other words: making sure that the acceleration has reached zero!

How will you do that?

(oh … and I don' know nuthin' 'bout no Stokes Law! )

doctorjanitor
Thanks!

Well yeah, your right all i need to know is the terminal velocity (i can't prove that the velocity it his the ground with is the terminal velocity, but i have to assume that). :)

I know KE = 1/2Mass x acceleration (so find acceleration might help?).. but i could do it too with velocity! I know its possible i just don't have the knowlege, but i do have to ability to understand it. Tonight i swear I've done nothing but browse the internet in search, i feel as though I am holding all the puzzle peices but i just can't get them going together.

If you think of any other ways or anything get back to me, you've been a great help. By telling you, you've kinda helped get me on the rails as to what I am looking for.

Thanks.

If anyone else can help further i'll be very greatful! :D

Homework Helper
Hi doctorjanitor!
I know KE = 1/2Mass x acceleration (so find acceleration might help?).. but i could do it too with velocity!

KE = 1/2Mass x acceleration is wrong.

It's always KE = 1/2Mass x velocity-squared.

But I really don't understand why you want the KE at all.

You said:
I want to work out the KE each test hits the floor with.. from this ill find a KE where i think the cargo wouldn't be able to stand the landing.

… but the ability of the cargo to stand the landing depends only on the forces it sustains on impact …

… and you can lessen them considerably by the way you pack the cargo.

It's not the KE that does the harm, it's the momentum (which depends only on speed), and the deceleration (which depends on the packing and on the ground surface).