Analyze the net external force acting on the block is the horizontal 31-N force.

Question

Analyze the net external force acting on the block is the horizontal 31-N force. Use the work-Kinetic energy theorem for the block, nothing that its initial kinetic energy is zero: W_ext = delta K = K_i = 1/2 mv^2_1 - 0 = 1/2 mv^2_t Solve for v_t and use W F delta r cos theta for the work done on the block by F: v_t = Squareroot 2 W_ext/m = Squareroot 2 F delta x/m v_t = Squareroot 2(31 N)(8.0 m)/9.3 Kg = 0.91 m/s Finalize you should solve this problem again by modeling the block as a particle under a not force to find its acceleration and then as a particle under constant acceleration to find its final velocity. In a following chapter, we will see that the energy procedure followed above is an example of the analysis model of the nonisolated system. 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

vf = sqrt(2*F*x/m)
vf = sqrt((2*31*8)/9.3)
From the calculation above, Velocity comes out to be, vf = 7.3 m/s

vf = 7.3 m/s
vf = sqrt((2*Fnew*x)/m)
7.3 = sqrt((2*62*x)/9.3)
x = 4.0 m

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