Peter catches a 4.7-kg striped bass on a fishing line 0.60mm in diameter and beg

Question

Peter catches a 4.7-kg striped bass on a fishing line 0.60mm in diameter and begins to reel it in. He fishes from a pier well above the water, and his fish hangs vertically from the line out of the water.

The fishing line has a Young's modulus of 5.1 x 10^9.

a) What is the fractional increase in length of the fishing line if the fish is at rest?

b)What is the fractional increase in the fishing line's length when the fish is pulled upward with a constant speed of 1.5

m/s?

c) What is the fractional increase in the fishing line's length when the fish is pulled upward with a constant acceleration of 1.4

m/s2 ?

Explanation / Answer

weight of fish = 4.7*9.8 = 46.06 N

so.. stress due to weight = 46.06 * 4/ ( pi * 0.0006^2 ) = 162903926.19583776 Pa

so.. strain = stress / Y = 162903926.195837759 / (5.1 * 10^9 ) = 0.0319419463

so.. fractional increase in length = 0.031941946


b) if speed is constant. then no addidtional force will act...

so.. fractional increase in length = 0.031941946


c) for acceleration of 1.4 m/sec2 ...

downward force of fish = 4.7*(9.8 + 1.4) = 52.64 N

so.. stress due to weight = 52.64 * 4/ ( pi * 0.0006^2 ) = 186175915.65238601 Pa

so.. strain = stress / Y = 186175915.65238601/ (5.1 * 10^9 ) = 0.036505

so.. fractional increase in length = 0.036505

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