Free Response Problems(40% of exam, 20 poll 13. A helicopter flies over the aret

Question

Free Response Problems(40% of exam, 20 poll 13. A helicopter flies over the aretic ice pack at a constant altitude, towing an airborne 129- laser sensor that measures the thickness of the ice. (The sensor is hanging behind aned below the helicopter with the cable at an angle to the vertical) The helicopter and the sensor both move only in the horizontal direction and have a horizontal acceleration of magnitude 2.84 m/s'. Ignoring air resistance, find the tension in the cable towing the sensor. a = 2.84 m/s2 Tsinet/T m=129 kg Tcose mg

Explanation / Answer

Using Newton's law:

Force balance in horizontal direction

T*cos theta = m*a

Force balance in vertical direction

T*sin theta = m*g

Now square and add both equation

T^2*(sin theta)^2 + T^2*(cos theta)^2 = (m*a)^2 + (m*g)^2

Since, (sin theta)^2 + (cos theta)^2 = 1, So

T^2 = m^2*(a^2 + g^2)

T = m*sqrt (a^2 + g^2)

Using given values:

T = 129*sqrt (2.84^2 + 9.81^2)

T = 1317.45 N

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