Approximate a fishing reel to be two solid disks, each of radius 5.9 cm and comb

Question

Approximate a fishing reel to be two solid disks, each of radius 5.9 cm and combined mass 0.64 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 2.9 N on the fishing line, pulling the reel counterclockwise. Take the +z axis to be along the axis of rotation of the disk, pointing most nearly out of the page.

Explanation / Answer

initially the string is pulled from the rell at a distance of r= 5.9cm from the centre.

so initial torque = F*r = 2.9*5.9*10^-2 Nm

a)

initial angular acceleration(a):

Ia = torquea = torque/moment of inertia

I = mr^2/2 = (0.64*(5.9*10^-2)*2)/2

a = 153.6 rad/s^2

b)

angle turned in t seconds = 0.5*a*t^2

in 0.33 seconds = 0.5*153.6*(0.33)^2 = 8.36 rads

8.36 rads is aprroximately 1.33 rotations of the reel.

perimeter of the reel = 2*pi*r = 37.07cm

1.33 rotations = 1.33*37.07 = 49.3 cm

so 49.3 cm of string is pulled.

c)

in this case torques isapplied at a distance of r/2 from the centre.

so torque is half as that in previous case.

which in turn makes both angular acceleration and distance pulled in time t half.

answers:

angular acceleration = 76.8 rad/s^2

angle turned in 0.33 seconds = 4.18 rads

no of rotations = 0.65

string pulled = 0.6582*pi*r/2 = 0.25* 49.3

string pulled = 12.3 cm

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