Question

A helicopter flies over the arctic ice pack at a constant altitude, towing an airborne 193-kg laser sensor which measures the thickness of the ice (see the drawing). the helicopter and the sensor move only in the horizontal direction and have a horizontal acceleration of magnitude 2.31 m/s2. ignoring air resistance, find the tension in the cable towing the sensor.

Answer 1

Refer to the diagram shown below.

m = 193 kg, the mass of the sensor
W = mg = (193 kg)*(9.8 m/s²) = 1891.4 N, the weight of the sensot
T = the tension in the cable.
a = 2.31 m/s², the acceleration
θ = the vertical angle between the helicopter and the sensor.

For vertical equilibrium
T cosθ = W = 1891.4 N (1)

For horizontal motion,
T sin θ = (193 kg)*(2.31 m/s²) = 445.83 N (2)

Divide (2) by (1).
tan θ = 445.83/1891.4 = 0.2357
θ = tan⁻¹ 0.2357 = 13.26°

From (2), obtain
T = 445.83/sin(13.26°) = 1943.3 N

Answer: 1943.3 N