Question

please help me with drag forces?

Part A and B is done. I just need help wit

part E F G and H

PHY241 su19 Assignment about Drag Forces Name Assignment for projectile with drag forces: Parts a and b of this question about an airplane and hanging sphere is from chapter 4 class notes / exploration (answer key is posted for parts a and b). Continue with part c A 100.0 kg sphere hangs from an airplane by a flexible cable at the angle shown. The plane is flying in the +x direction through the air at 120[m/s]. The plane, cable and sphere are all moving together at a constant velocity. There is a drag force, F, Assume the air is stationary on the sphere, opposite the direction of motion through the air. (Forces by gasses or liquids on objects are not in the force catalogue. We'll look at the details of those types of force later. For this example, there is enough information about it given in the question.) Horizontal. 60,0 Flexible Cable Hanging sphere a) Draw a free body diagram of the sphere showing the force acting on it. b) Find the magnitude of the resistance force, F, by the air on the sphere, find and the tension, T. in the cable T F= (Parts c and d are removed) For parts e & f, assume that the drag force is a viscous force. Show your work on a separate sheet for parts e & f. Explain in your own words how you found the height of the object at different times in part f. Don't share your words with others or copy from others. (You can share ideas but papers with same wording won't get credit for this part.) e) Find the value of b in the equation F =-bv, the time constant, and the terminal speed. Terminal Speed b= f) Suppose that when t-0, the cable breaks just above the sphere. Find the values of v, and v, and how far down the sphere is fallen (how much lower it is from the origitnal flying altitude) after 5.00[s], 10.0[s], and 30.0[s]. Assume that the airplane was high enough so that the sphere doesn't hit the ground before t-30.0[s]. how much lower than t [s] v [m/s] original height [m] v, [m's] 0.00 5.00 15.0 30.0 If the airplane kept flying forward at 120m/s, how far away from the airplane is the sphere when t-30.0[s]? You can ignore the cable length in the drawing of the plane. In other words, just consider the airplane and sphere to have been in approximately the same place when the cable broke. Distance from airplane - For parts g and h, assume that the drag force is aerodynamic, following the equation, Dv2 in direction opposite the direction of the sphere's velocity through the air Part g) Find the value ofD and the terminal speed Terminal Speed - D - Part h) Suppose that when t-0, the cable breaks just above the sphere. Find the values of v, and , and how far down the sphere is fallen (how much lower it is from the original flying altitude) after 5.00[s], 10.0(s], and 30.0[s]. Assume that the airplane was high enough so that the sphere doesn't hit the ground before t-30.0[s). Use the Excel calculator ""numerical calculator for aerodynamic drag" for this part. how much lower than original height [m] v. [m/s] v [m/s] t s 0.00 5.00 15.0 30.0 2 PHY241 su19 Assignment about Drag Forces Name Assignment for projectile with drag forces: Parts a and b of this question about an sphere is from chapter 4 class notes / exploration (answer key is posted for parts a and b). Continue with part c airplane and hanging A 100.0 kg sphere hangs from an the +x direction through the air at 120[m/s]. The plane, cable and sphere constant velocity. There is a Assume the air is stationary. airplane by a flexible cable at the angle shown. The plane is flying in are all moving together at a on the sphere, opposite the direction of motion through the air drag force, F, (Forces by gasses or types of force later. For this example, there is enough information about it given in the question.) on objects are not in the force catalogue. We'll look at the details of those liquids 1 y Horizontal 60.0 Flexible Cable wemg-90 Hanging sphere a) Draw a free body diagram of the sphere showing the force acting on it. b) Find the magnitude of the resistance force, F, by the air on the sphere, find and the tension, T, in the cable 1130 LN 5 66 T- F= (Parts c and d are removed) For parts e & f, assume that the drag force is a viscous force. Show your work on a separate sheet for parts e & f Explain in your own words how you found the height of the object at different times in part f. Don't share your words with others or copy from others. (You can share ideas but papers with same wording won't get credit for this part.) e) Find the value of b in the equation F=-bi, the time constant, and the terminal speed. Terminal Speed= 1H

Answer 1

e. Drag force F = 566N = -b   

= 120 m/s const.

b = -566/120 = -4.72 N-s/m

time const $\tau$ = m/b = 100/4.72 = 21.19

f. at t=0   _x = 120 m/s and v_y =0

velocity in x -direction changes as exp(-t/$\tau$) drag force is the only force opposing the motion in x- direction

t =5 _x = 120 *exp(-5/21.19) = 94.77 m/s

t = 15 = 120 exp(-15/21.19) = 59.12 m/s

t = 30 = 120 exp(-30/21.19) = 29.13 m/s

in vertical direction there is gain in vel due to gravity and loss due to drag force

v(t) = g$\tau$(1-exp(-t/$\tau$) )

t = 0 _y = 0

t =5 = 9.8*21.19 (1- exp(-5/21.19) ) = 43.65 m/s

t = 15 = 9.8*21.19 (1- exp(-15/21.19) ) = 105.35 m/s

t =30 =  9.8*21.19 (1- exp(-30/21.19) ) = 157.25 m/s

g)

F = D v² = 566 N

D = 566 /120² = 4.72  

at terminal speed the sphere false with const vel. no external force

mg = D ²   

Vter

= (100*9.8/4.72)^1/2 = 14.41 m/s

Vter