Write in clearly the letter of the selected answer. No other marks will be used

Question

Write in clearly the letter of the selected answer. No other marks will be used to assign credit. A body moving along the x axis is acted upon by a force F_x that varies with x as shown. How much work is done by this force as the object moves from x = 3 m to x = 10 m? -2 J -10 J +10 J -26 J -38 J A force acting on an object moving along the x axis is given by F_x = (10 x - 20 x^2) N where x is in m. How much work is done by this force as the object moves from x = -1 m to x = +6 m? + 14 J + 36 J + 30 J + 42 J - 42 J

Explanation / Answer

1)

work = force * distance

and also for force-distance graph

work = area of graph

work = (6 - 3)*(-8) + (1/2)*(8-6)*(-8) + (1/2)*(9-8)*(4) + (10-9)*4 = - 26 J

2)

Force = F = (10*x - 2*x^2) N

Work = integration of F.dx from -1 to +6

work = [10*x^2/2 - 2*x^3/3](-1 , +6) = [5*(6)^2 - (2/3)*(6)^3 - 5*(-1)^2 + (2/3)*(-1)^3] = 30 J

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