Terminal Velocity + Drag Force

In summary, a sky diver with a mass of 79.5 kg jumps from a slow-moving aircraft and reaches a terminal speed of 53.0 m/s. The acceleration of the sky diver when her speed is 30.0 m/s is 6.792 m/s^2 and the drag force on the diver when her speed is 53.0 m/s is 779.1 N. To find the drag force at 30.0 m/s, the equation D*v^2 is used, resulting in a drag force of 239.096 N. However, WebAssign may not properly account for significant figures.
  • #1
africanmasks
12
0

Homework Statement



A sky diver of mass 79.5 kg jumps from a slow-moving aircraft and reaches a terminal speed of 53.0 m/s.

(a) What is the acceleration of the sky diver when her speed is 30.0 m/s?

What is the drag force on the diver when her speed is the following?
(b) 53.0 m/s (answer in N)
(c) 30.0 m/s (answer in N)

Homework Equations


The Attempt at a Solution



I found parts a and b (correct on Webassign), but I can't get part c.):

a.) a= 6.792 m/s2
b.) 779.1 N

Would part c.) just be: mg-ma?

(779.1)-(79.5)(6.792)
= 239.096 (WebAssign says it's incorrect)
 
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  • #2
Drag force in air ia approximately proportional to v^2. So f = D*v^2.
Using the result from b, find D.
Use this value to solve c.
 
  • #3
Thanks. I got it.
 
  • #4
Your answer looks good. Does WebAssign concern itself with doing significant figures properly?
 

1. What is terminal velocity?

Terminal velocity is the maximum speed that an object can reach when falling through a fluid, such as air or water. It occurs when the force of gravity pulling the object down is balanced by the drag force from the fluid pushing against it.

2. How is terminal velocity calculated?

The formula for calculating terminal velocity is Vt = √(2mg/ρAC), where Vt is terminal velocity, m is the mass of the object, g is the acceleration due to gravity, ρ is the density of the fluid, A is the cross-sectional area of the object, and C is the drag coefficient.

3. What factors affect terminal velocity?

The factors that affect terminal velocity include the mass and shape of the object, the density and viscosity of the fluid, and the acceleration due to gravity. Objects with larger surface areas or greater drag coefficients will have a lower terminal velocity, while objects with smaller surface areas or lower drag coefficients will have a higher terminal velocity.

4. How does drag force affect terminal velocity?

Drag force is the force that opposes the motion of an object through a fluid. As an object falls, it experiences an increase in drag force due to its increasing speed. Eventually, the drag force will equal the force of gravity, causing the object to reach terminal velocity and continue falling at a constant speed.

5. Can an object exceed terminal velocity?

No, an object cannot exceed terminal velocity in a fluid. However, if the object falls through a less dense fluid, such as air to water, it may experience a decrease in drag force and therefore increase in speed, potentially reaching a higher terminal velocity in the new fluid.

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