Approximate a fishing reel to be two solid disks, each of radius 6.1 cm and comb

Question

Approximate a fishing reel to be two solid disks, each of radius 6.1 cm and combined mass 0.85 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 applies a constant force of 1.7 N on the fishing line, pulling the reel counterclockwise. (a) What is the angular acceleration of the fishing reel? alpha = rad/s^2 (b) Immediately after taking the bait, how much fishing line does the fish pull from the reel in 0.31 s? (Assume this time interval is short enough that radius of the fishing line wrapped around the reel does not appreciably change during it.) line pulled off = cm (c) Suppose instead this fisherman had cast his bait much further out, so that the fishing line left on the reel was only halfway out to the edge (see Fig 1b). If all other givens are the same, re-answer parts a & b. alpha = rad/s^2 line pulled off = cm

Explanation / Answer

a) torque = F*r = 1.7N*0.061m = 0.1037Nm

torque = moment of inertia*angular acceleration

angular acceleration = 0.5*m*r^2/torque

= 0.5*0.85*(0.061)^2/0.1037 = 0.01525rad/s^2

b) a = 0.01525*0.061= 0.00093m/s

s = u*t+0.5*a*t^2 = 0*0.31+0.5*0.00093*(0.31)^2

s = 4.46*10^-3cm

c) Since, torque will become half

angular acceleration = 0.01525/2 = 0.0076rad/s^2

line pulled of = 4.46*e-3/4 = 1.115*10^-3cm

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