Answers to homework problems: Chapter 7 5) Impulse = Change in momentum = m * v_1 - m * v_2 = 0.35 kg * 4 m/s - 0.35 kg * (-21 m/s) = = 8.75 kgm/s 15) Linear momentum is conserved i.e., total initial momentum =total final momentum total initial momentum = (m(spaceship) + m(rocket)) * v(initial) total final momentum = m(spaceship) * v(spaceship) + m(rocket) * v(rocket) (4 10^6 kg + 1.3 10^3 kg) * 230 m/s = 4 10^5 kg * 0 + 1.3 10^3 kg * v ====> v = 4001.3 10^3 * 230 / 1.3 10^3 = 7.07 10^5 m/s 33) see example 8 There are two unknowns v_1 and v_2 after the collision ==> we need two equations. These are p[rovided by the conservation of momentum and conservation of energy. a) elastic collision m_1 * v_1 + m_2 * v_2 = m_1 * v_0 + m_2 * 0 1/2 m_1 * v_1^2 + 1/2 m_2 * v_2^2 = 1/2 m_1 m_1 * v_0^2 + 0 the solution is goven by v_1 = (m_1-m_2)/(m_1+m_2)*v_0 = (5.0-7.5)/(5.0+7.5)*2 m/s = -0.4 m/s v_2 = 2m_1/(m_1+m_2)*v_0 = 2*5.0/(5.0+7.5)*2 m/s = 1.6 m/s b) inealstic collision here, both balls stick together after the collision i.e., have the same velocity ===> we have only one unknown and we need only one equation. Conservation of linear momentum will do. total initial momentum = 5 kg * 2 m/s + 7.5 kg * 0 = 10 kg m/s total final momentum = (5 kg + 7.5 kg) * v ====> v= 10 kg m/s / 12.5 kg = 0.8 m/s 41) We can use the center of Earth as an origin of one dimensional reference frame In this reference frame the position of Earth is 0 and the position of the moon is equal to the distance between the Earth and the moon. position of center of mass is x_cm = (m_Earth * 0 + m_moon * distance)/(m_Earth+m_moon) = = (7.35 10^22 kg * 3.85 10^8 m/(5.9810^24 kg + 7.35 10^22 kg) = = 4.67 10^6 m