Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei from gold-197 nuclei. The energy of the incoming helium nucleus was 8.00\times 10^{-13}~\text{J}8.00×10 −13 J, and the masses of the helium and gold nuclei were 6.68\times 10^{-27}~\text{kg}6.68×10 −27 kg and 3.29\times 10^{-25}~\text{kg}3.29×10 −25 kg, respectively (note that their mass ratio is 4 to 197). If a helium nucleus scatters to an angle of 120^\circ120 ∘ during an elastic collision with a gold nucleus, what is the final kinetic energy of the helium nucleus?

1point) a skydiver weighing 130 lb (including equipment) falls vertically downward from an altitude of 14,000 ft and opens the parachute after 20 s of free fall. assume that the force of air resistance, which is directed opposite to the velocity, is of magnitude 0.85|v|0.85|v| when the parachute is closed and is of magnitude 17|v|17|v| when the parachute is open, where the velocity vv is measured in ft/s. assume that acceleration due to gravity has magnitude 32 ft/s/s; remember that weight is the product of mass and gravitational acceleration. find the speed of the skydiver when the parachute opens. speed is 150.6121788 ft/s find the skydiver's height when the parachute opens. height is 2338.98591 ft find the limiting velocity vlvl after the parachute opens. (think about whether this should be positive or negative.) vl=vl= 7.647 ft/s

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 ..

Which object is most likely represented by a dot?