The graph in the figure shows the magnitude of the net horizontal force Fx on a

Question

The graph in the figure shows the magnitude of the net horizontal force Fx on a 25-kg package as a function of the position x of the package. Just before the force was applied, the package was originally sliding at 6.0 m/s in the +x direction on a smooth horizontal floor. Find the x component of the velocity of the package just after the force has stopped in each of the following cases. (a) The force is applied in the same direction as the original velocity of the box. (b) The force is applied in the opposite direction to the original velocity of the box.

Please show all work. The answer to a) +8.2 m/s and b) +2.0 m/s.

13) The graph in the figure shows the magnitude of the net horizontal force Fx on a 25-kg package as a function of the position x of the package. Just before the force was applied, the package was originally sliding at 6.0 m/s in the +x direction on a smooth horizontal floor. Find the x component of the velocity of the package just after the force has stopped in each of the following cases (a) The force is applied in the same direction as the original velocity of the box. b) The force is applied in the opposite direction to the original velocity of the box. F, (N) 200 150 100 50 x (m) 0 2.0 4.0 6.0

Explanation / Answer

Apply work energy. Work by F is area under graph

W = 0.5*200*(6.0-2.0) = 400 J

(a) W = change in K.E

400 = 0.5*25*(V2 - 62)

V = 8.25 m/s

(b) -400 = 0.5*25*(V2 - 62)

V = 2 m/s

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