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Chapter 10: Q. 62 (page 259)

A particle that can move along the x-axis experiences an interaction force $F_{x} = (3 x^{2} - 5 x) N,$ where x is inm. Find an expression for the system’s potential energy.

Short Answer

Expert verified

Expression for potential energy is $U (x) = \frac{5 x^{2}}{2} - x^{3}$

Step by step solution

01

Given information

The interactive force is given as

$F_{x} = (3 x^{2} - 5 x) N$

02

Explanation

$F_{x} = (3 x^{2} - 5 x) N U (x) = - \int F_{x} dx = - \int (3 x^{2} - 5 x) dx = - \int 3 x^{2} dx + \int 5 xdx = - 3 [\frac{x^{3}}{3}] + 5 [\frac{x^{2}}{2}] U (x) = - x^{3} + \frac{5 x^{2}}{2} U (x) = \frac{5 x^{2}}{2} - x^{3}$

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Most popular questions from this chapter

The lowest point in Death Valley is $85 m$ below sea level. The summit of nearby Mt. Whitney has an elevation of $4420 m$ . What is the change in potential energy when an energetic $65 k g$ hiker makes it from the floor of Death Valley to the top of Mt. Whitney?

A particle moving along the x-axis is in a system with potential energy $U = 10 / x J$ , where x is in m. What is the x-component of the force on the particle at $x = 2 m, 5 m, a n d 8 m$ ?

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The maximum energy a bone can absorb without breaking is surprisingly small. Experimental data show that the leg bones of a healthy, 60 kg human can absorb about 200 J. From what maximum height could a 60 kg person jump and land rigidly upright on both feet without breaking his legs? Assume that all energy is absorbed by the leg bones in a rigid landing

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