In Figure (a), a block of mass m lies on a horizontal frictionless surface and i

Question

In Figure (a), a block of mass m lies on a horizontal frictionless surface and is attached to one end of a horizontal spring (spring constant k) whose other end is fixed. The block is initially at rest at the position where the spring is unstretched (x = 0) when a constant horizontal force in the positive direction of the x axis is applied to it. A plot of the resulting kinetic energy of the block versus its position x is shown in Figure (b). The scale of the figure's vertical axis is set by Ks = 2.4 J and the scale of the figure's horizontal axis is set by xmax = 4.4 m.

Explanation / Answer

Given Max. Kinetic energy = Ks = 2.4J

at ends when there is no kinetic energy,As total energy is conserved there will be potential energy = 2.4J

So, (1/2) K x (Xmax)2 = 2.4 ==> (1/2)K x 4.42 = 9.68K = 2.4 ==> K = 0.248 N/m

So, F = K x (Xmax) [as initially on applying F force the system was at equlibrium at Xmax]

==> F = 0.248 x 4.4 = 1.091 N

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