Analyze: The net external force acting on the block is the horizontal 8.5 N forc

Question

Analyze: The net external force acting on the block is the horizontal 8.5 N force. Find the work done by this force on the block: W = F Delta x = (8.5 N)(9.0 m) = 76.5 J Use the work-kinetic energy theorem for the block and note that its initial kinetic energy is zero: W = K_f - K_i = 1/2 mv_f^2 - 0 Solve for v_f: v_f = Squareroot 2 W/m = Squareroot 2(76.5 J)/7.11 kg It would be useful for you to solve this problem again by modeling the block as a particle under a net force to find its acceleration and then as a particle under constant acceleration to find its final velocity. For the above example, suppose that the magnitude of the force is doubled. Through what displacement will the block travel before reaching the same final speed found above?

Explanation / Answer

if the force is doubles then

W = 2 * 8.5 * x

vf = sqrt(2 * W / m)

4.64 = sqrt(2 * 2 * 8.5 * x / 7.11)

x = 4.502 m

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