When a spring is stretched to x centimeters from its equilibrium point at x = 0, a potential energy of U = ¿kx² is stored in the spring, where U has units of Joules and k is a positive constant. dU (a) What should the units of be? dx (b) When the string is stretched so that x > 0, does further stretching increase or dU decrease the potential energy? Use something about in your answer! d.x (c) Contrast the cases between 2 centimeters stretched and 3 centimeters stretched: where will stretching the spring by a further little bit cause the greater increase in potential energy stored in the spring?

When a spring is stretched to x centimeters from its equilibrium point at x = 0, a potential energy of U = ¿kx² is stored in the spring, where U has units of Joules and k is a positive constant. dU (a) What should the units of be? dx (b) When the string is stretched so that x > 0, does further stretching increase or dU decrease the potential energy? Use something about in your answer! d.x (c) Contrast the cases between 2 centimeters stretched and 3 centimeters stretched: where will stretching the spring by a further little bit cause the greater increase in potential energy stored in the spring?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The potential energy is the measure of the net work done by or on the body. The spring potential energy is the potential energy stored due to the deformation of an elastic spring and this elasticity is due to the stretched spring. The elasticity is the ability of a solid-state matter to come back to its equilibrium position or original position after any kind of external force is acted on it. It is also known as Elastic potential energy. The potential energy here is caused due to the displacement of the spring from its equilibrium position to another position and this potential energy is equal to the net work done due to the stretching of the spring. It also resembles the same mechanics of the oscillation of a simple pendulum, where due to the external force, the object moves from its equilibrium position to its maximum ends and the periodic motion continues till it comes back to the equilibrium position to rest. 

Question

(21) When a spring is stretched to x centimeters from its equilibrium point at x = 0, a
potential energy of U = kx² is stored in the spring, where U has units of Joules and
k is a positive constant.
dU
(a) What should the units of
be?
dx
(b) When the string is stretched so that x > 0, does further stretching increase or
dU
decrease the potential energy? Use something about
in your answer!
dx
(c) Contrast the cases between 2 centimeters stretched and 3 centimeters stretched:
where will stretching the spring by a further little bit cause the greater increase
in potential energy stored in the spring?

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