# Mechanics equation?

1. Oct 2, 2006

### smileandbehappy

hi I am currently doing my a-level A2 coursework on prachutes. I am using different size parchutes and also different masses attatched to them. However I want to work out the grad coeeficient, and have sort of combined a couple of equations to get:

mass*gravity = 0.5 * density of liquid * area * drag coefficient.

Is this right??? If it is I can calulate the grag coefficient by rearanging the equation and finding out the variables experimentaly. However I think that I may be mixing kinematics with dynamics in a way which is not allowed.

Thanks very much.

2. Oct 2, 2006

### Mindscrape

I'm not really sure without the context behind this question. You are talking about the drag of a parachute, yet I see the density of liquid. Grad coefficient, what is this?

One way to solve for drag could consist of making a differential equation where $$\Sigma F = m a = m\frac{dv}{dt}$$.

3. Oct 3, 2006

### andrevdh

The drag created by a parachute can be appoximated with

$$F_D = 0.5 \ C_d\ \rho v^2$$

the drag is therefore a function of the speed at which the parachute is moving through the air. The drag force is acting upwards, causing the object hanging from the chute to slow down. When the object reaches its terminal speed (the lowest speed) the weight of the object will be equal to the drag force. If you do not overload the chute it should reach teminal velocity quite quickly. A graph of the weight of the object hanging from the chute against the square of the terminal velocity will produce a linear graph with a gradient of

$$0.5 \ C_d \ \rho$$

You therefore need to determine the terminal velocity for several different weights suspended from the same parachute (each chute wil have its own drag coefficient) and draw a graph as explained above.

If you have some means of determining air speed the experiment can be performed by measuring the force exerted on a spring scale by the chute while holding it in front of a fan or blower on several different settings.

Last edited: Oct 3, 2006