A skydiver of mass 81.5 kg (including outfit and equipment) floats downward suspended from her parachute, having reached terminal speed. The drag coefficient is 0.533, and the
area of her parachute is 20.96 m^2
. The density of air is 1.14 kg/m^3
. What is the air's drag
force on her? (Consider the skydiver and the parachute as one system. Take the upward
direction to be positive.)
Sorry, I wish I could help, but I cant. If you go to Khan Academy and search " physics "
it might help :)
They give you the answer right off so I think you asked the wrong question.
At terminal speed the drag force = the weight = m g = 81.5*9.81 = 800 N
Too easy. They intended to ask for the terminal velocity
Force = (1/2)Cd rho v^2 A = weight = m g
800 =(1/2)(.533)(1.14)(21)v^2
solve for v
I did not answer this because I assumed you had done so. Not much of a help :(
I get about 11.2 m/s
thank you so much for helping I really appreciate it because I don't know how to do any of my study guide questions. I don't want just the answer but how you do it to study for a test. My teacher doesn't explain any thing. I wish I could just post all the questions at one but it is too much so I just post one as a time and get different method from various tutors and learn more that way.
To calculate the air's drag force on the skydiver, we need to use the following formula:
Drag Force = 0.5 * Coefficient of Drag * Density of Air * Velocity^2 * Area
Where:
- Coefficient of Drag is given as 0.533
- Density of Air is given as 1.14 kg/m^3
- Velocity is the speed of the skydiver, which is the terminal speed (when the force of gravity equals the drag force), and we need to find it
First, let's solve for the velocity.
Since the skydiver is in terminal speed, the force due to gravity is equal to the drag force:
Force due to gravity = Mass * gravitational acceleration
Drag Force = Mass * gravitational acceleration
Rearranging the formula and solving for velocity:
Drag Force = 0.5 * Coefficient of Drag * Density of Air * Velocity^2 * Area
Mass * gravitational acceleration = 0.5 * Coefficient of Drag * Density of Air * Velocity^2 * Area
Now we can solve for velocity:
Velocity^2 = (2 * Mass * gravitational acceleration) / (Coefficient of Drag * Density of Air * Area)
Velocity = √[(2 * Mass * gravitational acceleration) / (Coefficient of Drag * Density of Air * Area)]
Substituting the given values:
Velocity = √[(2 * 81.5 kg * 9.8 m/s^2) / (0.533 * 1.14 kg/m^3 * 20.96 m^2)]
Calculating:
Velocity = √(1595.3 m^2/s^2 / 13.0704 kg/m^2)
Velocity = √(122 m^2/s^2)
Velocity = 11.05 m/s
Now we can calculate the drag force:
Drag Force = 0.5 * Coefficient of Drag * Density of Air * Velocity^2 * Area
Drag Force = 0.5 * 0.533 * 1.14 kg/m^3 * (11.05 m/s)^2 * 20.96 m^2
Calculating:
Drag Force = 62.488 N
Therefore, the air's drag force on the skydiver is 62.488 N.