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25 July, 16:35

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.

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  1. 25 July, 16:47
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    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
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