Question

A person of mass 100 kg starts the engine on a vintage aeroplane by pulling down hard on the tip of the propeller to initiate its rotation. The propeller blade is 54.0 cm long, and it makes a right-angle with the direction of his pull. He applies a force equal to his weight. Calculate the torque applied to the propeller.

A) 540 Nm
B) 490 Nm
C) 980 Nm
D) 1080 Nm

Answer 1

The torque applied to the aeroplane propeller by a person pulling with a force equal to their weight (981 N) on a 54.0 cm long blade at a right angle is 529.74 Nm, which does not match any of the provided options.

Step-by-step explanation:

The question involves the concept of torque in physics, specifically in the context of an aeroplane propeller. Torque is the measure of the force that can cause an object to rotate about an axis. The formula for torque (τ) is τ = r × F × sin(θ), where 'r' is the radius (distance from the axis of rotation), 'F' is the force applied, and 'θ' is the angle between the force vector and the lever arm. In this case, since the person applies a force equal to their weight and pulls at a right angle (90 degrees) to the propeller, the sin(θ) is 1. As the person's mass is 100 kg, the force of gravity on them is 100 kg × 9.81 m/s² = 981 N. With the propeller blade being 54.0 cm (or 0.54 m), the torque would be calculated as follows: τ = 0.54 m × 981 N × 1 = 529.74 Nm. This is not one of the provided options, suggesting a possible error in the question or options.