The device in Figure P22.37 is a so-called Newton's cradle. When you raise steel sphere 1 and then release it, its momentum is transferred to the other four steel spheres, and this momentum transfer causes sphere 5 to rise. When it falls, momentum is again transferred through the row of spheres, and sphere 1 rises and falls, and so on. Imagine modifying the device by positioning a charged wire in such a way that every time each end steel sphere rises, it touches the wire and acquires 10 units of charge. You lift sphere 1 and allow it to touch the wire for the first time and acquire 10 units of charge. You release the sphere and it hits the others, transferring its momentum and causing sphere 5 to rise. Sphere 5 touches the charged wire, descends, hits the row of spheres, and transfers its momentum so that sphere 1 rises again and touches the wire for the second time. If the net charge distributes uniformly over all balls, how many units of charge does sphere 1 carry \((a)\) just before it touches the wire this second time and \((b)\) just before it touches the wire after one more round of this momentum-transfer motion?

Data from Figure P22.37

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