Physics Oscillation question Problem 1 A fisherman\'s scale is a 60 cm long vert

Question

Physics Oscillation question

Problem 1 A fisherman's scale is a 60 cm long vertical spring, which is secured to a sturdy frame at one end, while the other end is fitted with a hook which can hold a fish to be weighed. A 10.8 kg fish is attached to the hook at the free end of the spring, and it is held at rest with the spring unstretched. However, the fisherman loses his hold on the fish, still wet and slippery, which then falls stretching the spring by 23.0 cm as it comes momentarily to rest at the lowest point of its vertical oscillation. (a) What is the value of the spring constant? (b) What is the maximum speed attained by the fish during its fall? (c) How far from the point of release is that maximum speed attained?

Explanation / Answer

a] Use conservation of energy

mgx = (1/2)kx2

k = (2mg/x) = (2x10.8 x 9.8/0.23) = 920.348 N/m

this is the spring constant.

b]

again, using conservation of energy

when the fish falls, the potential energy gets converted to kinetic energy

maximum energy = (1/2)kA2

(1/2)kA2 = (1/2)(460.174)(0.23)2 = 12.1716 J

at some distance x, this energy will be purely in the form of kinetic energy

so, 12.1716 = (1/2)mv2

=> v = 1.501 m/s

this is the maximum speed.

c]

when the speed is maximum

(1/2)mv2 - mgx = (1/2)kx2

=> 460.174x2 +105.84x - 12.1716 = 0

solving this quadratic gives the positive value of x to be:

x = 0.0842 m = 8.42 cm

so, the maximum speed is 8.42 cm from the point of release.

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