The only force acting on a 1.9 kg body as it moves along the x axis varies as sh

Question

The only force acting on a 1.9 kg body as it moves along the x axis varies as shown below. The scale of the figure's vertical axis is set by Fs 4.6 N. The velocity of the body at x -0 is 4.3 m/s. 0 (a) What is the kinetic energy of the body at x 3.0 m? -4.3 (b) At what value of x will the body have a kinetic energy of 8.0 J? (c) what is the maximum kinetic energy attained by the body between x = 0 and x-5.0 m? Work is equal to the change in kinetic energy. Work can be found by the graphical integration of a force with respect to distance. When is such work negative?

Explanation / Answer

a) we know, Workdone = are aunder F-x curve

= (1/2)*1*4.6 + (1/2)*1*(-4.6) + (3-2)*(-4.6)

= -4.6 J

using work-energy theorem,

W = KEf - KEi

KEf = W + KEi

= -4.6 + (1/2)*1.9*4.3^2

= 13 J

b)

using work-energy theorem,

W = KEf - KEi

(1/2)*1*4.6 + (1/2)*1*(-4.6) + (x-2)*(-4.6) = 8.0 - (1/2)*1.9*4.3^2

==> x = 4.1 m

c) the body gains maximum kinetic energy at x = 1

W = KEf - KEi

KEf = W + KEi

= (1/2)*1*4.6 + (1/2)*1.9*4.3^2

= 20 J

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