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A particle that can move along the x-axis experiences an interaction force Fx=(3x2−5x)N where x is...

A particle that can move along the x-axis experiences an interaction force Fx=(3x2−5x)N where x is in m. Find an expression for the system's potential energy. Express your answer in terms of the variables x and the constant of integration C, where C is in joules.

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Answer #1

force=F=-dU/dx where U is potential energy

dU=-Fdx

dU=-(3x^2-5x)dx=(5x-3x^2)dx

Integrating both sides we get

U=2.5x^2-x^3+C J

where C is constant of integration

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