Sphere a, of mass 0.600 kg, is initially moving to the right at 4.00 m/s. sphere b, of mass 1.80 kg, is initially to the right of sphere a and moving to the right at 2.00 m/s. after the two spheres collide, sphere b is moving at 3.00 m/s in the same direction as before.
(a) what is the velocity (magnitude and direction) of sphere a after this collision?
(b) is this collision elastic or inelastic?
(c) sphere b then has an off-center collision with sphere c, which has mass 1.60 kg and is initially at rest. after this collision, sphere b is moving at 19.0∘ to its initial direction at 1.60 m/s. what is the velocity (magnitude and direction) of sphere c after this collision?
(d) what is the impulse (magnitude and direction) imparted to sphere b by sphere c when they collide?
(e) is this second collision elastic or inelastic?
(f) what is the velocity (magnitude and direction) of the center of mass of the system of three spheres (a, b, and c) after the second collision? no external forces act on any of the spheres in this problem.

Chapter 23, problem 075 the figure shows a geiger counter, a device used to detect ionizing radiation (radiation that causes ionization of atoms). the counter consists of a thin, positively charged central wire surrounded by a concentric, circular, conducting cylindrical shell with an equal negative charge. thus, a strong radial electric field is set up inside the shell. the shell contains a low-pressure inert gas. a particle of radiation entering the device through the shell wall ionizes a few of the gas atoms. the resulting free electrons (e) are drawn to the positive wire. however, the electric field is so intense that, between collisions with gas atoms, the free electrons gain energy sufficient to ionize these atoms also. more free electrons are thereby created, and the process is repeated until the electrons reach the wire. the resulting "avalanche" of electrons is collected by the wire, generating a signal that is used to record the passage of the original particle of radiation. suppose the radius of the central wire is 24 âµm, the inner radius of the shell 2.3 cm, and the length of the shell 14 cm. if the electric field at the shell's inner wall is 2.8 ă— 104 n/c, what is the total positive charge on the central wire?