Question

NOTE THERE ARE 11 QUESTIONS AT 10 POINTS EACH, THES PROBLEM 1 30 points (see figures 1 and 2) Santa Claus uses a drone that weighs 1300 lbf, has a propeller of 30 inches of diameter and has an angular speed 0-20 rad/sec and an angular acceleration α-10 rad/sec2 A. Determine the velocity and acceleration vector of point A (see figure) if the drone is on the ground (no vertical motion) and is not moving Now assuming that the drone starts moving and goes up in the vertical direction (Z axis) starting at rest and reaches a height of 100 ft in 3 seconds, determine the velocity and acceleration vectors of the center of the drone Determine the complete velocity and acceleration vectors of point A when the drone is going up in the Z direction (as stated in Part B) and the propeller is moving at an angular speed ω 20 rad/sec and an angular acceleration α-12 rad/sec 8. C. ω, α DRO propeller figure 2 figure 1 at comester 2018-19, Ivan Baiges

Answer 1

Given, Weight of drone=1300lbf, Diameter of propeller, D = 30 inches=762mm

A. Velocity vector of point A when drone is on the ground

V₁​= $\omega r$

Given $\omega$ ​=20 rad/sec,    $\alpha$ =10 rad/sec²

V₁​=20 X 381 X 10^-3= 7.62m/sec

Angular acceleration, $\alpha$ = $\omega$ ​/t

t_​1=20/10=2 sec

Therefore, Acceleration vector a_​1​=V₁​/t_^​1​= 7.62/2

a₁=3.81 m/sec²

B. ​Velocity vector of center of drone when h=100 ft, t=3sec

h=30.48m

V_c​=h/t =30.48/3

V_c​=10.16m/sec

From Equation of motion,

v²​=u²+2as

Initial velocity of center of drone u=0

V_c^​2​=2 X a_c X h

a_c ​= V_c^​2​/ (2 X h) = 10.16 X 10.16 / (2 X 30.48)

a_c = 1.69 m/sec

C.​ Given $\omega$ ​=20 rad/sec, $\alpha$ ​​=​12 rad/sec^​2

t_​2= $\omega$ / $\alpha$ = 20/12 = 1.67sec

Velocity vector at point A, V_​2​=   $\omega$ r

V_​2= 20 X 381 X 10^-3 ​=7.62m/sec

a_​2 = V_​2/t_​2 ​ =7.62/1.67

a_^​​2 = 4.56m/sec^​2

^​​Complete velocity and acceleration at point A

V= V_​c+V_​2= 10.16+7.62 = 17.78m/sec

a=a_​c+a_​2= 1.69+4.56 = 6.25m/sec^​2