4. According to Newton’s law of cooling, if an object at temperature T is immersed in a medium having the constant temperature M, then the rate of change of T is proportional to the difference of temperature M − T. This gives the differential equation dT dt = k(M − T). (a) Solve the differential equation for T. (b) A thermometer reading 100◦F is placed in a medium having a constant temperature of 70◦F. After 6 min, the thermometer reads 80◦F. What is the reading after 20 min?

Dinate system, and a charge q = - 2.00 nc is placed s2 10 n> c. (a) what is the change in electric potential energy when the dipole moment of a molecule changes its orientation with respect to es from parallel to perpendicular? (b) at what absolute temperature t is the average translational kinetic energy 32 kt of a molecule equal to the change in potential energy calculated in part(: abovethistemperature,thermalagitationprevents the dipoles from aligning with the electric field.) placed in a uniform electric field e with magnitude 1.6 * 6 on the positive x-axis at x = 4.00 cm. (a) if a third charge q3 = +6.00 nc is now placed at the point x = 4.00 cm, y = 3.00 cm, find the x- and y-components of the total force exerted on this charge by the other two. (b) find the magnitude and direction of figure p21.62 ll uu 21.55 . torque on a dipole. an electric dipole with dipole moment ps is in a uniform external electric field es. (a) find the orientations of the dipole for which the torque on the dipole is zero. (b) which of the orientations in part (a) is stable, and which is unstable? (hint: consider a small rotation away from the equi- librium position and see what happens.) (c) show that for the stable orientation in part (b), the dipole’s own electric field tends to oppose the external field. 21.62 ..

If a simple machine reduces the strength of a force, what must be increased?

Suppose a diode consists of a cylindrical cathode with a radius of 6.200×10^−2 cm , mounted coaxially within a cylindrical anode with a radius of 0.5580 cm . the potential difference between the anode and cathode is 260 v . an electron leaves the surface of the cathode with zero initial speed (v initial=0). find its speed vfinal when it strikes the anode.