An airplane of mass 850kg is flown along a circular loop in a vertical plane. Th
ID: 1494661 • Letter: A
Question
An airplane of mass 850kg is flown along a circular loop in a vertical plane. The radius of the loop is 400m. The airplane’s speed is kept constant at 80m/s and the aerodynamic drag has a constant magnitude of 1200N. Find the lift force generated by the wings when the plane is (a) at the bottom of the loop, (b) climbing vertically and (c) at the top of the loop. Find (d) the work done by the engine and (e) the average power produced by the engine as the plane climbs from bottom to top. (1hp = 745.7W)
Explanation / Answer
a) at bottom of plane,
Applying Fnet = ma
FL - mg = m v^2/r
FL = mg + mv^2/r = 850 ( 9.8 + (80^2 / 400)) = 21930 N
b) climbing vertically,
FL - drag forcr - mg = 0
FL = 1200 + (850 x 9.8) = 9530 N
c) mg - FL = mv^2/r
FL= mg - mv^2/r = 5270 N
d) USing work energy theorem,
work done by gravity + work done by drag force + work done by engine = change in KE
- mg(2r) - Fdrag (pi r ) + We = mv^2/2 - mv^2/2 = 0
W = 2mgr + pi r Fdrag
W = (2 x 850 x 9.8 x 400) + (pi x 400 x 1200)
W = 8.172 x 10^6 J
e) time taken = pi r / v = (pi x 400 ) / (80 ) = 15.71 sec
Power = W/t = 5.202 x 10^5 Watt
in hp, Power = (5.202 x 10^5 ) / (745.7) = 697.66 hp