Question

A helicopter flies over the arctic ice pack at a constant altitude, towing an airborne 129-kg laser sensor that measures the thickness of the ice (see the drawing). The helicopter and the sensor both move only in the horizontal direction and have a horizontal acceleration of magnitude 2.84 m/s2 . Ignoring air resistance, find the tension in the cable towing the sensor.

Answer 1

Answer:

1317.52 Newton

Explanation:

Mass of sensor = m = 129 kg

Acceleration of the sensor = a = 2.84 m/s²

g = Acceleration due to gravity = 9.81 m/s²

$F_m$ = Force on the laser sensor due to motion = 129×2.84 = 366.36 N

$F_g$ = Force due to gravity on the laser = mg = 129×9.81 = 1265.49 N

Tension in the cable

$T=\sqrt{F_m^2+F_h^2}\\\Rightarrow T=\sqrt{366.36^2+1265.49^2}\\\Rightarrow T=1317.52\ N$

∴ The tension in the cable towing the sensor is 1317.52 Newton