make your answers clear if you want a positive rating. Approximate a fishing ree

Question

make your answers clear if you want a positive rating.

Approximate a fishing reel to be two solid disks, each of radius 5.5 cm and combined mass 0.84 kg which can rotate without friction. String (of negligible mass) is wrapped around the reel (between the disks) all the way to its edge (see Fig 1a). The fishing line is strung with bait and left at rest in the water. A fish then suddenly takes the bait and starts to applies a constant force of 1.6 N on the fishing line, pulling the reel counterclockwise.

Explanation / Answer

a) torque = I x alpha

torque = r x F   and moment of inertia = m r^2 /2

r x 1.6 = 0.84 x r^2 x (alpha) /2

alpha = 3.2 / (0.84 x 0.055) = 69.26 rad/s^2

b) a = alpha *r   = 69.26 x 5.5 x 10^-2 =3.81 m/s^2

d = ut + at^2 /2

d = 0 + 3.81x0.29^2 /2 = 0.16 m

d = 16 cm

c) now force is acting at radial distance of r/2.

so,   (r/2) x 1.6 = m x r^2 x alpha /2

1.6 = 0.84 x 5.5 x 10^-2 x alpha

alpha = 34.63 rad/s

a = alpha * (r/2) = 0..95 m/s^2

d = 0.95 x 0.29^2 /2 =0.04 m

d = 4 cm

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