Question

The fishing pole in the figure below makes an angle of 20.0° with the horizontal. What is the magnitude of the torque exerted by the fish about an axis perpendicular to the page and passing through the angler's hand if the fish pulls on the fishing line with a force = 122 N at an angle 37.0° below the horizontal? The force is applied at a point L = 1.94 m from the angler's hands

Answer 1

The line is at 37^o to the horizontal, making one angle of the triangle;

the pole is at 20^o, the line meets the pole at 180 - 37- 20 = 123^o.

To calculate the torque, the acting force must be decomposed in two components:

the perpendicular one, acting at 90^o to the pole, and the normal one, acting along the pole.

Only the former generates the torque.

The angle between the fishing line and the perpendicular line is

123 - 90 = 33^o

Therefore, the perpendicular component will be

F_p = F*cos 33 = 122 * 0.8386 = 102.32 N = 102 N

And the torque:

F_p*L = 102.32 * 1.94 = 198.5 Nm.

the magnitude of the torque exerted by the fish about an axis perpendicular to the page and passing through the angler's hand is 198.5 Nm