A winch is a mechanical device that is used to adjust the tension in a rope or line. A weekend sailor works the manual winch to trim the sail during an outing on the water. The radius of the winch drum is 4.0 cm and the man turns the winch at the rate of 2.9 complete revolutions every 1 second.

. A weekend sailor works the manual winch to trim the sail during an outing on the water. The radius of the winch drum is 4.0 cm and the man turns the winch at the rate of 2.9 complete revolutions every 1 second.

(a) What is the tangential speed of the line as he brings it in? m/s

Update 2:

(b) How would the value of the tangential speed change if the radius of the wheel were tripled?

The tangential speed would increase by a factor of 3.

The tangential speed would decrease by a factor of 3.

The tangential speed would increase by a factor of 9.

The tangential speed would decrease by a factor of 9.

The answer to the questions are as follows

a. The tangential speed = 0.729 m/s

b. The tangential speed would increase by a factor of 3.

Explanation:

a. The appropriate relations to help us find the tangential speed are

w = 2•pi•N and

w = v/r,

Where r = radius = 4.0 cm

v = velocity

N = rotational speed

From the question, N = 2.9 rotations/s or 2.9 Hz

Therefore w = 2•pi•2.9 = 18.22 r/s

Therefore,

v = w × r = (18.22 r/s) × (4.0 cm) = (18.22 r/s) × (0.040 m) = 0.729 m/s

The tangential speed = 0.729 m/s

b. Tripling the radius of the wheel we have, new radius = 4 × 3 = 12 cm

v = w × r = 18.22×0.12 = 2.1865 m/s

Finding the ratio of the two velocities, we have

(2.1865 m/s)/(0.729 m/s) = 3

Hence the tangential speed would increase by a factor of 3

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