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$\bullet$ A proud deep-sea fisherman hangs a 65.0 $\mathrm{kg}$ fish from an ideal spring having negligible mass. The fish stretches the spring 0.120 $\mathrm{m} .$ (a) What is the force constant of the spring? (b) What is the period of oscillation of the fish if it is pulled down 3.50 $\mathrm{cm}$ and released?

$5.31 \times 10^{3} \mathrm{N} / \mathrm{m}$0.695 $\mathrm{s}$0.452 $\mathrm{m} / \mathrm{s}$

Physics 101 Mechanics

Chapter 11

Elasticity and Periodic Motion

Equilibrium and Elasticity

Periodic Motion

Cornell University

University of Michigan - Ann Arbor

Hope College

University of Sheffield

Lectures

04:12

In physics, potential energy is the energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors. The unit for energy in the International System of Units is the joule (J). One joule can be defined as the work required to produce one newton of force, or one newton times one metre. Potential energy is the energy of an object. It is the energy by virtue of an object's position relative to other objects. Potential energy is associated with restoring forces such as a spring or the force of gravity. The action of stretching the spring or lifting the mass is performed by a force which works against the force field of the potential. The potential energy of an object is the energy it possesses due to its position relative to other objects. It is said to be stored in the field. For example, a book lying on a table has a large amount of potential energy (it is said to be at a high potential energy) relative to the ground, which has a much lower potential energy. The book will gain potential energy if it is lifted off the table and held above the ground. The same book has less potential energy when on the ground than it did while on the table. If the book is dropped from a height, it gains kinetic energy, but loses a larger amount of potential energy, as it is now at a lower potential energy than before it was dropped.

02:18

In physics, an oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. The oscillation may be periodic or aperiodic.

03:38

A proud deep-sea fisherman…

03:52

01:00

03:03

Illustration:Given:

02:23

A fisherman's scale s…

03:43

If a fish is attached to a…

02:43

Fish are hung on a spring …

08:13

06:54

A 3.00-kg fish is attached…

when the fish is hanging in equilibrium has a fairly simple force diagram. We have mg, its weight pulling it down and we have the force of the spring pulling it up in these forces perfectly balanced one another to produce an emotion in the white direction. And so noone second long then tells us that offspring must be equal to G and so bloody and energy. We see that this is 65 kilograms times 9.8. And I'm not going to place into the calculator yet because we're not quite done with the part of the problem. But what we're going to do with this force of the spring is that we're going to relate it to the spring constant using hooks law. So force come spring is equal to K X. I'm ignoring the minus sign now because we already know the direction of this. It's upwards. This implies that Kay is equal to s spring over X. And then we've calculated that here it's 65 times nine point e and then the existence is 0.120 meters. This is given to the problem. It's okay is 5.31 times 10 to the third. And since we used all its light units here, the answer will be in sa units noons per meter. And that's final for part, at least for Part B. We can use this formula for the period of a simple harmonic oscillator. Tea is equal to pi times a squared of mass over Kay. Now we know the mass. We just figured out what K is. So a straightforward logic tells us that the period it's equal to 0.695 seconds. It's actually interesting to know that this formula for the period does not depend on the distance that the fish is pulled down. So it's entirely independent that distance that distance is extra information that the problems giving you to try to throw you off. But really, all you need to use is this formula here.

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