Question

A model airplane with mass 0.754 kg is tethered to the ground by a wire so that it flies in a horizontal circle 31.0 m in radius. The airplane engine provides a net thrust of 0.796 N perpendicular to the tethering wire.

(a) Find the magnitude of the torque the net thrust produces about the center of the circle.
N · m

(b) Find the magnitude of the angular acceleration of the airplane.
rad/s²

(c) Find the magnitude of the translational acceleration of the airplane tangent to its flight path.
m/s²

Answer 1

Solution :

Given :

mass (m) = 0.754 kg

radius (r) = 31 m

Thrust (F) = 0.796 N

Part (a) Solution :

the magnitude of the torque the net thrust produces about the center of the circle = r F = (31 m)(0.796 N) = 24.676 Nm

Part (b) Solution :

Here, the magnitude of the translational acceleration of the airplane tangent to its flight path :

a_trans = F/m = (0.796 N) / (0.754 kg) = 1.0557 m/s²

the magnitude of the angular acceleration of the airplane = a_trans / r = (1.0557 m/s² ) / (31 m) = 0.034 rad/s²

Part (c) Solution :

Here, the magnitude of the translational acceleration of the airplane tangent to its flight path :

a_trans = F/m = (0.796 N) / (0.754 kg) = 1.0557 m/s²