Answers for Problem Set 9

Chapter 9

(a) The initial center of mass is H / 2
(b) The final center of mass is H / 2
(c) During the draining of the can, the center of mass first drops and then rises back to its original height.
(d) h = [ H sqrt ( M² + M m ) - M H ] / m <= H / 2

16. [My answers agree with previous edition of text]
(a) The car can have moved at most a distance L.
(b) The car moves that far only if its mass is negligible compared to the total mass of the cannonballs.
(c) The car is back at rest, v = 0 .

40. Call the direction of the momentum of the neutrino y and the direction of the momentum of the electron x.
(a) The momentum of the nucleus is
p_Z = - p_neutrino 1_y - p_electron 1_x

| P_Z | = sqrt ( p_neutrino² + p_electron² ) = 1.4 x 10 ^-22 kg m / sec

The angle from the x axis is theta = pi + tan ^-1 ( p_neutrino / p_electron ) = 208^o = 3.63 rad

(b) The kinetic energy of the recoiling nucleus is p_Z² / (2 m ) = 1.59 x 10 ^-19 joule

47. Text answers:

(a) 0.200 v_rel when the stones are thrown simultaneously.

(b) 0.2103 v_rel if m₁ is thrown first.

(c) 0.2095 v_rel if m₂ is thrown first.

55. Proof.