A Force Fx acts on a particle.  The force is related to the position of the particle by the formula Fx = 5.6*x^3 N. Find the work done by this force on the particle as the particle moves from...

A Force Fx acts on a particle.  The force is related to the position of the particle by the formula Fx = 5.6*x^3 N. Find the work done by this force on the particle as the particle moves from x=0.6m to x=17m.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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A force Fx acts on a particle.  The force is related to the position of the particle by the formula Fx = (5.6)*x^3 N.

As the particle moves from point x = 0.6 m to x = 17 m, the force changes. The work done by a force is the product of the force and the distance over which it acts. If the force acts on the particle for an infinitesimally small distance dx, the work done is 5.6*x^3 dx.

Integrating 5.6*x^3 dx from x = 0.6 to x = 17 gives the required work done.

The integral is equal to 5.6*17^4/4 - 5.6*0.6^4/4

=> 116929.21 J

The work done by the force Fx over the distance x = 0.6 to x = 17 is 116929.21 J.

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