Question

A uniform helicopter rotor blade is 8.97 m long, has a mass of 104 kg, and is attached to the rotor axle by a single bolt. (a) What is the magnitude of the force on the bolt from the axle when the rotor is turning at 329 rev/min? (Hint: For this calculation the blade can be considered to be a point mass at its center of mass. Why?) (b) Calculate the torque that must be applied to the rotor to bring it to full speed from rest in 7.68 s. Ignore air resistance. (The blade cannot be considered to be a point mass for this calculation. Why not? Assume the mass distribution of a uniform thin rod.) (c) How much work does the torque do on the blade for the blade to reach a speed of 329 rev/min?

Answer 1

sol:)

Given data

mass(m) = 104 kg

length (L ) = 8.97m

a.) Magnitude of the force:

convert revolution per minute in radians/ sec

above omega value substitute in magnitude force equation

Therefore, magnitude force exerted by the blade is 552.929*10³ N

b.) Torque:

we know that the torque formula is

given time (t) = 7.68 s

Hence, torque exerted by the rotor is 12.50*10³ N.m

c.) Workdone

we know that workdone formula is

given 329 rev/min

convert rpm to rad /s