A force with an x-component acts on a mass with a strength that varies only with

Question

A force with an x-component acts on a mass with a strength that varies only with the position x of the mass on the x-axis, according to |F(x)|= Ax^2. The sign of the force is negative when x is positive and positive when x is negative, indicating that the force always attracts the mass toward the origin. Compute the work done by this force when A = 1595 N/m^2 and the mass moves along the x-axis as follows. (a) from x = -7.0 cm to the origin _____ J (b) from x = -5.0 cm to +5.0 cm (c) from x = +4.0 cm to +2.0 cm 0.298 J (d) from x = -2.0 cm to -3.0 cm -0.01 J

Explanation / Answer

F(x) = Ax^2

integration of F with respect to x give work

W = Ax^3/3

(a) force is positive when x is negative

x1 =0 to x2 = -7 cm

W = -1595*0.07^3/3

W = -0.182 J

(b) from x = -5 cm to x = 5 cm

W = (1595/3) (0.05^3 - 0.05^3)

W = 0 J

(c) from x = 4 cm to x = 2 cm

W = (1595/3) (0.02^3 - 0.04^3)

W = -0.0298 J

(d) from x = -2 cm to x = -3 cm

W = (1595/3) (-0.03^3 + 0.02^3)

W = -0.01 J

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