( a ) ( b ) In Figure (a), a block of mass m lies on a horizontal frictionless s

Question

(a)
(b) 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 F rightarrow 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 = 2.0 J and the scale of the figure's horizontal axis is set by xmax = 4.0 m. What is the magnitude of F rightarrow What is the value of k?

Explanation / Answer

We know that.

Amplitude(a)= xmax/2=4/2=2

Maximum Potential Energy of the spring = 0.5*K*(a^2)

==>2=0.5*k*(2*2)

==>k=1

==>k=1 N/m

Force Applied(F) = K*Amplitude

==> F=1*2

==>F=2 N

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