22. A fisherman hooks a big fish that swims away from the boat pulling the fishi

Question

22. A fisherman hooks a big fish that swims away from the boat pulling the fishing line from his fishing reel. The whole system is initially at rest and the fishing line unwinds from the reel at a radius of 4.50cm from its axis of rotation. The reel is given an angular acceleration of 110 rad/s2 for 2.00 seconds:

a. What is the final angular velocity of the reel?

b. At what speed is fishing line leaving the reel after 2.00 s elapses

c. How many revolutions does the reel make?

d. How many meters of fishing line come off the reel in this time?

e. Now the fisherman applies the brake to the spinning reel, achieving an angular acceleration of -300 rad/s2. How long does it take for the reel to come to a stop?

Explanation / Answer

Solution for (a)

Here and t are given and needs to be determined. The most straightforward equation to use is =0+t because the unknown is already on one side and all other terms are known. That equation states that

=0+t.

We are also given that 0=0 (it starts from rest), so that

=0+(110rad/s2)(2.00s)=220rad/s.

Solution for (b)

Now that is known, the speed v can most easily be found using the relationship

v=r,

where the radius r of the reel is given to be 4.50 cm; thus,

v=(0.0450 m)(220 rad/s)=9.90 m/s.

Note again that radians must always be used in any calculation relating linear and angular quantities. Also, because radians are dimensionless, we have m×rad=m.

Solution for (c)

Here, we are asked to find the number of revolutions. Because 1 rev=2 rad, we can find the number of revolutions by finding in radians. We are given and t, and we know 0 is zero, so that can be obtained using =0t+1/2t2.

==0t+1/2t2+(0.5)(110rad/s2)(2.00 s)2=220 rad.

Converting radians to revolutions gives

=(220 rad)1 rev2 rad=35.0 rev

Solution for (d)

The number of meters of fishing line is x, which can be obtained through its relationship with :

x=r=(0.0450 m)(220 rad)=9.90 m.

Calculations maybe wrong, but logic is correct.

Hope this helps :)

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