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tester [92]
3 years ago
5

A mysterious force acts on all particles along a particular line and always points towards a particular point P on the line. The

magnitude of the force on a particle increases as the cube of the distance from that point, that is, F∝ r3, if the distance from the P to the position of the particle is r. It has been determined that the constant of proportionality is 0.45 N/m3, i.e. the magnitude of the force on a particle can be written as 0.45r3, when the particle is at a distance r from the force center.
Physics
1 answer:
lord [1]3 years ago
7 0

Answer:

       PE = \dfrac{0.45 r^4}{4}

Explanation:

given,

proportionality constant = 0.45

          F∝ r³

         F = k r³

using conservation of energy change in potential energy is equal to work done.

       d (PE) = F. dr

       d (PE) = k r³. dr

integrating both side

     \int {d (PE)} = k \int {r^3} dr

       PE = \dfrac{k r^4}{4} + C

given that at r = 0; PE = 0

       0 = \dfrac{k 0^4}{4} + C

                   C = 0

       PE = \dfrac{k r^4}{4}

       PE = \dfrac{0.45 r^4}{4}

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