Cart 1 of mass \(m=0.50 \mathrm{~kg}\) fastened to a spring of spring constant \(k=14 \mathrm{~N} / \mathrm{m}\) is pushed \(15 \mathrm{~mm}\) in from its equilibrium position and held in place by a ratchet (Figure 15.27). An identical cart 2 is launched at a speed of \(0.10 \mathrm{~m} / \mathrm{s}\) toward cart 1 . The carts collide elastically, releasing the ratchet and setting cart 1 in motion. After the collision, cart 2 is immediately removed from the track.

(a) What is the maximum compression of the spring?

(b) How many seconds elapse between the instant the carts collide and the instant the spring reaches maximum compression?

Data from Figure 15.27

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