11. a mass weighing 64 pounds stretches a spring 0.32 foot. the mass is initially released from a point 8 inches above the equilibrium position with a downward velocity of 5 ft/s. (a) find the equation of motion. (b) what are the amplitude and period of motion? (c) how many complete cycles will the mass have completed at the end of 3 seconds? (d) at what time does the mass pass through the equilibrium position heading downward for the second time? (e) at what times does the mass attain its extreme displacements on either side of the equilibrium position? (f) what is the position of the mass at t 5 3 s? (g) what is the instantaneous velocity at t 5 3 s? (h) what is the acceleration at t 5 3 s? (i) what is the instantaneous velocity at the times when the mass passes through the equilibrium position? (j) at what times is the mass 5 inches below the equilibrium position? (k) at what times is the mass 5 inches below the equilibrium position heading in the upward direction?

An asteroid is discovered in a nearly circular orbit around the sun, with an orbital radius that is 2.47 times earth's. what is the asteroid's orbital period, its "year," in terms of earth years?

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 ..

Determine the maximum r-value of the polar equation r =3+3 cos 0