Question

Oceanographers use submerged sonar systems, towed by a cable from a ship, to map the ocean floor. In addition to their downward weight, there are buoyant forces and forces from the flowing water that allow them to travel in a horizontal path. One such submersible has a cross section area of 1.3m² , a drag coeffecient of 1.2, and when towed at 4.3 m/s, the tow cable makes an angle of 30 degrees with the horizontal. What is the tension in the cable? Take the water density to be 1000 kg / m³

Answer 1

Given cross section Area A = 1.3m²

drag coefficient C_D = 1.2

Velocity V =4.3 m/s

Angle made by tension with horizontal =30deg

density = 1000 kg/m³

now lets find drag force F_D

= 0.5*1000 *4.3² * 1.2 * 1.3

=14422.2 N (acting in opposite direction of movement)

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Since cable is at angle 30 deg

only the horizontal component of tension is used to balance drag Force F_D

TCos30 = F_D

T = F_D/cos30

T = 16653.32 N

ANSWER : Tension in cable = 16.6 KN