A helicopter of mass m is taking off vertically. The only forces acting on it ar

Question

A helicopter of mass m is taking off vertically. The only forces acting on it are the earth's gravitational force and the force, Fair, of the air pushing up on the propeller blades. (a) If the helicopter lifts off at t=0, what is its vertical speed at time t? (b) Check that the units of your answer to part a make sense. (c) Discuss how your answer to part a depends on all three variables, and show that it makes sense. That is, for each variable, discuss what would happen to the result if you changed it while keeping the other two variables constant. Would a bigger value give a smaller result, or a bigger result? Once you've figured out this mathematical relationship, show that it makes sense physically. (d) Plug numbers into your equation from part a, using m=2300 kg, Fair=27000 N, and t=4.0 s.

Explanation / Answer

d) helicopter acceleration = (upward force,fair - downward force due to mass)/mass of helicopter

(F-Mg) / M = (F/M) - g  = (27000 - 2300*10)/2300 (kg-m/s2) / kg = 4000/2300 m/s2

velocity at t=4 sec V= a*t = 4000*4/2300 = 6.9565 m/sec

a,b,c)

velocity at time t = ((F/M) - g ) * t

units check: velocity=m/s

((F/M) - g ) * t = ((N/kg)-m/s2) * sec = m/sec as N= kg*m/s2

Effect of change in parameters on Velocity

1. as F increases, F/M increases so acceleration of helicopter also increases so V increases,

2. as M increases, F/M decreases so acceleration of helicopter also decreases so  V decreases.

3. as time increases , product of acceleration and time also increases so V will also increase.

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