Parachute Problem, Figuring out largest load it can hold

[mathguy2]

Homework Statement

A cargo packed for aerial dropping can withstand an impact speed of 20 mph. A 100 foot diameter circular parachute is used for a particular load. What is the largest load (including the chute itself) that can be accommodated by this chute. [/B]

Homework Equations

V_t = SQUARE ROOT OF EVERYTHING OVER HERE [(2 x W x 32.2(Gravitational Constant) / .1(Coefficient of drag) x Area x .0805 ft cubed]

32.2; .1; and .0805 are unchanging constants. [/B]

The Attempt at a Solution

First I converted 20mph to 29.4 ft per sec, this is the plugin for Terminal velocity, V_t
Then I calculated the area of the circular chute. Since r = 50 and using piR²... I got 7853.91

Then I started solving the equation with all the plugins

And I got 848.24 lbs for W...

Is this correct? Does this look accurate to everyone? I figured I'd ask because its a new chapter and I'm uncomfortable with the problems.

 

[PhanthomJay]

Homework Statement

A cargo packed for aerial dropping can withstand an impact speed of 20 mph. A 100 foot diameter circular parachute is used for a particular load. What is the largest load (including the chute itself) that can be accommodated by this chute. [/B]

Homework Equations

V_t = SQUARE ROOT OF EVERYTHING OVER HERE [(2 x W x 32.2(Gravitational Constant) / .1(Coefficient of drag) x Area x .0805 ft cubed]

32.2; .1; and .0805 are unchanging constants. [/B]

The Attempt at a Solution

First I converted 20mph to 29.4 ft per sec, this is the plugin for Terminal velocity, V_t
Then I calculated the area of the circular chute. Since r = 50 and using piR²... I got 7853.91

Then I started solving the equation with all the plugins

And I got 848.24 lbs for W...

Is this correct? Does this look accurate to everyone? I figured I'd ask because its a new chapter and I'm uncomfortable with the problems.

Homework Statement

A cargo packed for aerial dropping can withstand an impact speed of 20 mph. A 100 foot diameter circular parachute is used for a particular load. What is the largest load (including the chute itself) that can be accommodated by this chute. [/B]

Homework Equations

V_t = SQUARE ROOT OF EVERYTHING OVER HERE [(2 x W x 32.2(Gravitational Constant) / .1(Coefficient of drag) x Area x .0805 ft cubed]

32.2; .1; and .0805 are unchanging constants. [/B]

The Attempt at a Solution

First I converted 20mph to 29.4 ft per sec, this is the plugin for Terminal velocity, V_t
Then I calculated the area of the circular chute. Since r = 50 and using piR²... I got 7853.91

Then I started solving the equation with all the plugins

And I got 848.24 lbs for W...

Is this correct? Does this look accurate to everyone? I figured I'd ask because its a new chapter and I'm uncomfortable with the problems.

I don't know where your numbers are coming from. Firstly, if you want to calculate the largest load in pounds (weight), don't multiply W by g, W is already in force units. And then, please show how you arrived at the drag factor and that 0.0805 value, and write out the equation you are using for terminal velocity using letter symbols.

 

[haruspex]

if you want to calculate the largest load in pounds (weight), don't multiply W by g

Yes, the answer, as a mass, has effectively been computed in slugs.

I got 848.24 pounds for the mass

I got 845 slugs.

 

[PhanthomJay]

W

Yes, the answer, as a mass, has effectively been computed in slugs.

I got 845 slugs.

with a drag coef of 0.1 for a parachute? Where does that come from , seems off by an order of magnitude

 

[haruspex]

W

with a drag coef of 0.1 for a parachute? Where does that come from , seems off by an order of magnitude

I should have clarified that I was trusting the given numbers.

 

[PhanthomJay]

I

I should have clarified that I was trusting the given numbers.

Using a drag factor of 0.1 , I get around 845 pounds for the weight. Using a more realistic drag factor of around 1, it's more like 8450 pounds