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Fundamentals of Physics | 10th Edition | ISBN: 9781118230725 | Authors: David Halliday; Robert Resnick; Jearl Walker
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A single conservative force F(x) acts on a 1.0 kg particle

Chapter , Problem 41

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QUESTION:

A single conservative force F(x) acts on a 1.0 kg particle that moves along an x axis. The potential energy U(x) associated with F(x) is given by U(x) ! %4x e%x/4 J, where x is in meters. At x ! 5.0 m the particle has a kineticenergy of 2.0 J. (a) What is the mechanical energy of the system? (b) Make a plot of U(x) as a function of x for 0 ( x ( 10 m, and on the same graph draw the line that represents the mechanical energy of the system. Use part (b) to determine (c) the least value of x the particle can reach and (d) the greatest value of x the particle can reach. Use part (b) to determine (e) the maximum kinetic energy of the particle and (f) the value of x at which it occurs. (g) Determine an expression in newtons and meters for F(x) as a function of x. (h) For what (finite) value of x does F(x) ! 0?

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QUESTION:

A single conservative force F(x) acts on a 1.0 kg particle that moves along an x axis. The potential energy U(x) associated with F(x) is given by U(x) ! %4x e%x/4 J, where x is in meters. At x ! 5.0 m the particle has a kineticenergy of 2.0 J. (a) What is the mechanical energy of the system? (b) Make a plot of U(x) as a function of x for 0 ( x ( 10 m, and on the same graph draw the line that represents the mechanical energy of the system. Use part (b) to determine (c) the least value of x the particle can reach and (d) the greatest value of x the particle can reach. Use part (b) to determine (e) the maximum kinetic energy of the particle and (f) the value of x at which it occurs. (g) Determine an expression in newtons and meters for F(x) as a function of x. (h) For what (finite) value of x does F(x) ! 0?

ANSWER:

Step 1 of 9

The given function is

 { potential energy}

When , the kinetic energy of the particle is

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