A cylindrical fishing reel has a mass of 0.634 kg and a radius of 3.9 cm. A friction clutch in the reel exerts a restraining torque of 1.52 N · m if a fish pulls on the line. The fish- erman gets a bite, and the reel begins to spin with an angular acceleration of 54 rad/s 2 . What force does the fish exert on the line?

Explanation:

Given:

Mass, m = 0.634 kg

Radius, r = 3.9 cm

= 0.039 m

Torque, Trest = 1.52 Nm

Angular acceleration, α = 54 rad/s^2

Torque, T = I × α

Where,

I = moment of inertia

Moment of inertia of a solid cylinder, I = 1/2 × m × r^2

Net torque = summation of all the total torque around the reel

Tfish = Trest + Treel

F × r = Trest + I × α

Inputting values,

0.039F = 1.52 + ((1/2 × 0.634 × (0.039)^2)) × 54)

= 1.52 + 0.026

= 1.546

Solving for Force, F,

F = 1.546/0.039

= 39.64 N

= 39.6 N.