The force of a spring is given by F = −kx, where k is the stiffness of the spring and x is the displacement of the spring from equilibrium. From an earlier activity, we said that the derivative of the potential energy with respect to position is equal to the negative force. Assume that at equilibrium (when x = 0), the spring has no potential energy. (a) Write an initial value problem for solving P E(x). Clearly identify the initial condition.

The force of a spring is given by F = −kx, where k is the stiffness of the spring and x is the displacement of the spring from equilibrium. From an earlier activity, we said that the derivative of the potential energy with respect to position is equal to the negative force. Assume that at equilibrium (when x = 0), the spring has no potential energy. (a) Write an initial value problem for solving P E(x). Clearly identify the initial condition.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter2: Newtonian Mechanics-single Particle

Section: Chapter Questions

Problem 2.47P: Consider a particle moving in the region x > 0 under the influence of the potential where U0 = 1 J...

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The force of a spring is given by F=−kx, where k is the stiffness of the spring and x is the displacement of the spring from equilibrium. From an earlier activity, we said that the derivative of the potential energy with respect to position is equal to the negative force. Assume that at quilibrium (when x= 0), the spring has no potential energy. (a) Write an initial value problem for solving PE(x). Clearly identify the initial condition. (b) Solve the initial value problem for the potential energy of the spring at position x. Clearly show the use of the initial condition to solve for the constant of integration. (c) How much potential energy is in the spring if it is stretched to x = 2 meters and the constant k= 20 Newtons/meter (include units)? (Note that 1 Joule = 1 Newton meter.)
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