What is the tension in the cable towing the sensor?

A helicopter flies over the arctic ice pack at a constant altitude, towing an airborne 158-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 3.55 m/s2. Ignoring air resistance, find the tension in the cable towing the sensor.What is the tension in the cable towing the sensor?
Write equations from Newton鈥檚 2nd law for the forces acting horizontally and vertically on the 158kg mass. Horizontally, the only force is the horizontal component of tension, so:



鈭慒 = ma = Tcos胃-----------------%26gt;(1)



Vertically, you have the vertical component of tension and the weight (mg) of the mass:



鈭慒 = 0 = Tsin胃 - mg

mg = Tsin胃-----------------------%26gt;(2)



Dividing (2) by (1), you get:



mg/ma = Tsin胃/Tcos胃

g/a = tan胃

胃 = tan鈦宦?g/a)

= tan鈦宦?9.80m/s虏 / 3.55m/s虏)

= 70.1掳



Now from (1):



ma = Tcos胃

T = ma/cos胃

= (158kg)(3.55m/s虏) / cos70.1掳

= 1650N (rounded)



Hope this helps.

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