The resistance and the magnitude of the current depend on the path that the current takes. The drawing shows three situations in which the current takes different paths through a piece of material. Each of the rectangular pieces is made from the same material whose resistivity is rho = 1.50 x 10^-2 Ω·m, and the unit of length in the drawing is L0 = 5.80 cm. Each piece of material is connected to a 3.00-V battery. Find:

a. the resistance
b. the current in each case.

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.

A58-kg boy swings a baseball bat, which causes a 0.140-kg baseball to move toward third base with a velocity of 38.0 m/s.

Asynthetic fiber used in manufacturing carpet has tensile strength that is normally distributed with mean 75.5 psi and standard deviation 3.5 psi. how is the standard deviation of the sample mean changed when the sample size is increased from n equals 8 to n equals 47