Question

a model airplane with mass 0.750 kg is flying at constant speed in a horizontal circle at one end of a 30 m cord and a height of 18 m. the other end of the cord is tethered to the ground. The airplane makes 5.5 red/min and the lift is perpendicular to the wings. a. What is the acceleration of the plane? b. What is the tension in the cord? c. What is the lift produced by the plane's wings?

Answer 1

you should always draw these first


for a), you are looking for the radial acceleration of the plane which is \(a = \omega^2 r\)

you'll get r from a bit of pythagoreas

\(\omega\) is measured in radians/ sec. it is not totally clear what the units are for the 5.5 you quote, are they revs or radians?

so for part (a) , sort those bits out and just plug and play

for part b, the tension in the cord, when resolved along the horizontal direction, should equal the centripetal force, ie the force that is making the plane move in a circle. so \(T \cos \theta = m \omega^2 r\). bit of trig needed, \(\theta\) is the angle between the rope and the ground in case it's not clear

for c), once you know T, in the vertical direction you know that Lift = \(mg + T \sin \theta\) where mg is the weight of the plane.

if not clear, do tag