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

Answer:

Tension in the cable is T = 16653.32 N

Explanation:

Give data:

Cross section Area A = 1.3 m^2

Drag coefficient CD = 1.2

Velocity V = 4.3 m/s

Angle made by cable with horizontal  =30 degree

Density $\rho \ of\ water= 1000 kg/m3$

 Drag force FD is given as

$F_{D} = \fracP{1}{2} \rho v^{2} C_{D} A$

        $= 0.5\times 1000\times 4.32\times 1.2\times 1.3$

Drag force = 14422.2 N acting opposite to the motion

As cable made angle  of 30 degree with horizontal  thus horizontal component is take into action to calculate drag force

TCos30 = F_D

$T = \frac{F_D}{cos30}$

$T =\frac{ 14422.2}{cos 30}$

T = 16653.32 N