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Sagot :
- The force constant of the spring is 5308 N/m.
- The period of oscillation of the fish is 0.381 s.
- The maximum speed of the fish is 1.93 m/s.
To find the force constant of the spring, we can use Hooke's Law, which states that the force exerted by a spring is proportional to the displacement of the spring. Mathematically, this can be written as:
F = -kx
where F is the force exerted by the spring, k is the force constant of the spring, and x is the displacement of the spring.
In this case, the force is the weight of the fish, which is the force of gravity acting on the fish. The weight of the fish is equal to its mass times the acceleration due to gravity, or
W = mg = (65.0 kg)(9.8 m/s^2) = 637 N.
The displacement of the spring is 0.120 m, so we can substitute these values into the equation for Hooke's Law to find the force constant:
F = -kx
637 N = -k(0.120 m)
k = -637 N / 0.120 m
k = 5308 N/m
For part (b), the period of oscillation is the time it takes for the fish to complete one full oscillation. The period of a simple harmonic oscillator is given by the equation:
T = 2[tex]\pi[/tex][tex]\sqrt{\frac{m}{k} }[/tex]
where T is the period, m is the mass of the oscillating object, and k is the force constant of the spring. Substituting the values we found earlier, we get:
T = 2[tex]\pi[/tex][tex]\sqrt{\frac{65}{5308} }[/tex]
T = 0.381 s
For part (c), the maximum speed of the oscillating fish can be found using the equation for simple harmonic motion:
v = [tex]\sqrt{\frac{k}{m} }[/tex] * x
where v is the speed, k is the force constant of the spring, m is the mass of the oscillating object, and x is the displacement of the spring. Substituting the values we found earlier, we get:
v = [tex]\sqrt{\frac{5308}{65} }[/tex] * 0.120 m
v = 1.93 m/s
So the maximum speed of the fish is 1.93 m/s.
Learn more about Hooke's Law, here https://brainly.com/question/29126957
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