Two forces, of magnitudes F_1 and F_2, act in opposite directions on a block, wh

Question

Two forces, of magnitudes F_1 and F_2, act in opposite directions on a block, which sits atop a frictionless surface, as shown in the figure. Initially, the center of the block is at position x_1. At some later time, the block has moved to the right, and its center is at a new position, x_f. Find the work done on the block by the force of magnitude F_1 as the block moves from x_i to x_f. Express your answer in terms of F_1 x_i, and x_f. Find the work done on the block by the force of magnitude F_2 as the block moves from x_1 to x_f. Express your answer in terms of F_2, x_i, and x_f. What is the net work done on the block by the two forces? Express your answer in terms of F_1, F_2, x_i, and x_f. Determine the change in kinetic energy, K_f - K_i of the block as it moves from x_i to x_f. Express your answer in terms of F_1, F_2, x_i and x_f.

Explanation / Answer

a) we know, workdone = scalar product of force and displacement

W1 = F1.d

= F1*d*cos(0)

= F1*(xf - xi)

b) W2 = F2.*d

= F2*d*cos(180)

= F2*(xf - xi)(-1)

= -F2*(xf - xi)

c) net workdone = W1 + W2

= F1*(xf - xi) - F2*(xf - xi)

= (F1-F2)*(xf - xi)

d) use work-energy theorem

change in kinetic energy = net workdone

kf - ki = (F1-F2)*(xf - xi)

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