As a particle moves along an x axis, a force in the positive direction of the ax

Question

As a particle moves along an x axis, a force in the positive direction of the axis acts on it. The figure shows the magnitude F of the force versus position x of the particle. The curve is given by F = a/x2, with a = 9.0 N·m2. Find the work done on the particle by the force as the particle moves from x = 1.0 m to x = 3.0 m by (a) estimating the work from the graph and (b) integrating the force function.

As a particle moves along an x axis, a force in the positive direction of the axis acts on it. The figure shows the magnitude F of the force versus position x of the particle. The curve IS given by F = a x2 with a = 9.0 Nm. Find the work done on the particle by the orce as the part ce moves rom x 1,0 x m , a estimating he won rom the graph and (b) integrating the force function 12 10 8 6 0 x (m) (a) Number Units (b) Number Units

Explanation / Answer

a) Workdone = Area under F-x graph

= (1/2)*(3-1)*9

= 9.0 J

b) Workdone = integral F.dx

= integral a/x^2 dx

= (-a/x) (from x = 1m, to x = 3m)

= -(9/3 - 9/1)

= 6.0 J

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