# Speed of a falling object

1. Nov 27, 2010

### dalebennett

Hey Smart Guys,

At age 61, I am building a mechanical launching device (Trebuchet) and I need to know how fast my counterweight will be traveling.

How fast will it be traveling after 1 inch
How fast will it be traveling after 60 inch
How fast will it be traveling after 120 inch

Also, please provide the travel time to reach each point (1, 60 & 120 in.)

The counterweight surface is flat, weighs 2000 lbs with a square surface area of 1296 Sq Inches. (3'x3')

I don't do formulas very well, so plain English would be much appreciated!

Dale

Last edited: Nov 27, 2010
2. Nov 27, 2010

### brno17

Fg=Ek

Force of gravity will convert to Kenetic energy

mgh=1/2mv^2

solve for v
(Devide both sides by m, multiply by 2 and sq rt both sides)

v=sqrt/ 2gh

EDIT: g=gravity at 9.8m/s and h is height in meters and v is also in meters/second

When you find speed you already have distance

v=d/t

t=vd

Multiply the speed in m/s and distance in meters to get the time

3. Nov 27, 2010

### Integral

Staff Emeritus
There will be some energy lost to friction so the above analysis gives a high estimate. If you need better you will need to figure out a way to measure the velocity.

4. Nov 27, 2010

### dalebennett

I'm sorry, but I don't understand these equations. Would you be kind enough to do the actual calculation. I flunked out of algebra.

5. Nov 28, 2010

### Tide

The answer depends on what kind of trebuchet you want to build. In addition, you need to specify things like the length, weight and shape of the beam and where the axle is in relation to both the counterweight and payload.

6. Nov 28, 2010

### dalebennett

Actually, I just want to use this information as a reference point. For now, all I need are the raw answers. Please, just disregard the Trebuchet design for now. If you are interested in this project, I would be extremely interested in providing you more detail a little later.

This is a new concept for a Trebuchet and there are many physics questions that will need to be answered. For now, just the basic math, please.

I'm planning a 1 mile launch that has never been done before.

7. Nov 28, 2010

### DaleSwanson

8. Nov 28, 2010

### dalebennett

I copy/pasted that equation exactly as show into Excel and it did NOTHING.

Is '1 inch' suppose to be embedded into the equation?

What value do I change. I'm am truly sorry for my ignorance.

Can you give it EXACTLY as it should be put into an excel cell - for 1 in and 2 inches - then I will know how to modify the equation for any distance?

the following was the last thing I tried.

=sum(sqrt(2*(9.8(m/(s^2)))*1))

Obviously, I don't know what I'm doinh

Dale

9. Nov 28, 2010

### JolileChat

This might be useful for you, in particular the model described in figure 5(c).

Last edited by a moderator: May 5, 2017
10. Nov 28, 2010

### Tide

In the absence of any design specifications the best you can do is set limits for speed and time based on a free falling counterweight.

For what it's worth, here's what you get for the numbers:

1 inch: Max speed = 2.3 feet per second, Min time = 0.072 seconds
60 inch: Max speed = 18 feet per second, Min time = 0.56 seconds
120 inch: Max speed = 25 feet per second, Min time = 0.79 seconds

11. Nov 28, 2010

### DaleSwanson

That wasn't intended to be used in excel. Google has a built in calculator that understands units and constants. If you click the link you should see 1 inch gives an answer of 1.578 mph. If you want to change the distance you do so in the Google search box. You should notice that if you, for example, change 1 inch to 3 feet the answer pops up in a box directly below the search box. You don't even have to click search.

If you want to use excel the formulas should be:
Code (Text):

=SQRT(2 * 32.174 * 1) <- one [B]foot[/B], answer is 8.02 [B]feet[/B] per second
=SQRT(2 * 32.174 * 2) <- two [B]feet[/B], answer is 11.34 [B]feet[/B] per second
=SQRT(2 * 386.09 * 1) <- one [B]inch[/B], answer is 27.79 [B]inches[/B] per second
=SQRT(2 * 386.09 * 2) <- two [B]inches[/B], answer is 39.3 [B]inches[/B] per second

Pay careful attention to the difference between inches and feet in the above forumulas. Like I said, Google understands units and does the conversions for you. Excel does not, and you have to manually do the conversions.

12. Nov 29, 2010

### MagnetDave

There's a trebuchet simulator that is probably more useful for you:

http://www.trebuchet.com/sim/ [Broken]

Last edited by a moderator: May 5, 2017