A drag force can be thought of as a type of air resistance that an object experi

Question

A drag force can be thought of as a type of air resistance that an object experiences. The drag force is analogous to friction in that it opposes an objects motion. The quantity known as terminal velocity is the velocity an object has as it's acceleration goes to zero, meaning that the drag force exactly balances the downward acceleration due to gravity. Consider a skydiver of mass m who jumps from a hot air balloon and falls a distance d before reaching a terminal velocity of magnitude v. Assume that the magnitude of the acceleration due to gravity is g. (a) Find the change in the skydiver's gravitational potential energy, after falling a distance d. Express your answer in terms of the given quantities. (b) Find the change in the skydiver's kinetic energy, after falling a distance d. Express your answer in terms of the given quantities. (c) What is the work W done on the skydiver, over the distance d, by the drag force of the air? Express your answer in terms of d, v, m, and g. (d) Find the magnitude F_4 of the drag force after the skydiver has reached terminal velocity. Express your answer in terms of the skydiver's mass m and other given quantities. (e) Find the power P_4 supplied by the drag force after the skydiver has reached terminal velocity v.

Explanation / Answer

a) change in potential energy = mgd , after falling a distance d

b) after falling a distance d, the terminal velicty = v

KE = 0.5mv2

c) by conservation of energy, work done by drage force

Wd = mgd -mv2/2

d) let Fd is the drage force, then work done by the force over a distance d

Wd = Fd *d = mgd -mv2/2

drag force Fd   = m(g-v2/2d)

e) Power = work doen per unit time

     after reaching terminal velocity v, the diver will move a distance of v in 1 s

   work done per 1s by drage force = Fd*v = mv(g-v2/2d)

                                                       = Pd , power delivered by the drag force.    

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.