Suppose that F is the inverse square force field below, where c is a constant. F

Question

Suppose that F is the inverse square force field below, where c is a constant. F(r) = cr/|r|^3 r = Find the work done by F in moving an object from a point P_1 along a path to a point P_2 in terms of the distances d_1 and d_2 from these points to the origin. An example of an inverse square field is the gravitational field F = -(MG)r/|r|^3. use part (a) to find the work done by the gravitational field when the earth moves from aphelion (at a maximum distance of 1.52 Times 10^8 km from the sun) to perihelion (at a minimum distance of 1.47 Times 10^8 km). Use the values m = 5.97 Times 10^24 kg, M = 1.99 Times 10^30 kg, and G = 6.67 Times 10^-11 N middot m^2/kg^2. (Round your answer to two decimal places.) Another example of an inverse square field is the electric force field F = Qr/|r|^3. Suppose that an electron with a charge of -1.6 Times 10^-19 C is located at the origin. A positive unit charge (1 C) is positioned a distance 10^-12 m from the electron and moves to a position half that distance from the electron, use part (a) to find the work done by the electric force field. Use the value epsilon = 8.985 Times 10^9. (Round your answer to the nearest hundred joules.)

Explanation / Answer

a)   Since we need to solve for work done , so we will apply

F = cr / ||r||³

Work = [PP] F•dr = c [PP] r•dr/||r||³


r / ||r||³ = (x,y,z)(x²+y²+z²)¹

= ( {(x²+y²+z² ) }/x, {(x²+y²+z² ) }/y, {(x²+y²+z² ) }/z )

= ((x²+y²+z² )) = where =1/d


So F is conservative and work is change in c from P to P

work done = c/d (c/d) = c/d c/d   answer

For 2nd part you did all correct , just need to calculate correctly

b) - (5.97 * 10^24)(1.99 * 10^30)(6.67 10^-11)(-2:2377 10^-10) = 1.77 * 10^35 J answer

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