Halliday, Resnick & Walker — Kinetic Energy and Work: Problem 30

In Fig. 7.4.1a, 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 \( \vec{F} \) 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 Fig. 7.21. The scale of the figure’s vertical axis is set by \( K_s = 4.0\text{ J} \). (a) What is the magnitude of \( \vec{F} \)? (b) What is the value of \( k \)?