Answers to homework problems: Chapter 6 part 2. 48) Impulse Delta(p) = m * v - m * v_0. Since initional velocity v_0 = 0 then 3.0 Ns = 0.25 kg * v ---> v = 12 m/s = 26.85 miles/h 50) Impulse = m * v - m * v_0 = 0.45 kg * 8 m/s - 0.45 * (-2 m/s) = 4.5 Ns 81) This is one dimensional problem. The center of mass will be at some distance x from the smaller mass. It will be at distance (1.5 m-x) from the larger mass. The equation for the center of mass is then 4.0 kg * x - 7.5 kg * (1 - x) = 0 ---> x = 11.25/11.5 m = 0.98 m 88) Center of mass is at the point from which the vectorial sum of the distances to each mass weighted by the value of the mass is zero. a) from symmetry of the problem the cm is located at the center of the square defined by the position of the masses i.e., x = 2 m, y = 2 m b) the situation is still symmetric since the two masses on the opposite corners of the square are the same --> x = 2 m, y = 2 m c) the center of mass is at a point with coordinates x,y . The center of mass equation can be written separaqtely for x and y coordinates BUT all masses have to be included in both equations: m_1 * x + m_2 * x - m_3 * (4-x) - m_4 * (4-x) = 0 m_1 * y - m_2 * (4-y) - m_3 * (4-y) + m_4 * y = 0 ----> 10x = 28 m i.e., x = 2.8 m ----> 10y = 20 m i.e., y = 2.0 m Chapter 7 part 1 10) arc length s = r * theta. Radius of Earth orbit (from back of the book table) r = 1.5 10^8 km theta (4 month = 1/3 year) = 2*pi/3 radians ---> arc length 3.14 10^8 km 28) a) averge angular velocity = total angle/time = = 24 * (2*pi)/(3*60 s) = 0.84 rad/s b) tangential speed v = r * omega = 4.0 m * 0.84 rad/s = 3.36 m/s = 5.0 m * 0.84 rad/s = 4.20 m/s 31) time of one revolution = time/number of revolutions = 60 s/500 rpm = 0.12 s There is a typo in the original syllabus. The problem number should be 43 43) centripetal acceleration = v^2/r = (120 km/h)^2 / 1km = = (120000m/3600s)^2/(1000m) = 1.11 m/s^2 For those who tried the problem 93 93) To orbit Earth a satelite must have a tangential velocity, must be acted on by a centripetal force and must have greater gravitational potential energy than on Earth. Short answer - all of the above!