CTP-1 In which situation is the magnitude of the total momentum the largest? A) Situation I has larger total momentum B) Situation IIC) Same magnitude total momentum in both situations.Answer: Same magnitude momentum in both situations. Momentum is a vector. In situation II, the momenta are in opposite directions and they partially cancel.CTP-2 A car is sitting on the surface of the Earth and both the car and the Earth are at rest. (Pretend the Earth is not rotating or revolving around the Sun.) The car accelerates to a final velocity. After the car reaches its final velocity, the magnitude of the Earth's momentum is __________ the magnitude of the car's momentum.A) more than B) the same as C) less thanD) Cannot answer the question because the answer depends on the interaction between the Earth and the car. Answer: the same as. The total momentum of the Earth/car system is zero. So if the car acquires a momentum to the right, the Earth must acquire an equal magnitude momentumto the left. |MEvE| = |mcvc |. Since ME>>mc, vE is incredibly tiny compared to vc, but vE is not zero. CTP-3 Suppose the entire population of Earth gathers in one location and, at a pre-arranged signal, everyone jumps up. About a second later, 6 billion people land back on the ground. After the people have landed, the Earth's momentum is..m2m(rest)vm2mvvI:II:A) the same as it was before the people jumped.B) different than it was before the people jumped.C) impossible to know whether the Earth's momentum changed.After the 6 billion people have passed the apex of their jump and are on the way down, the velocity of the Earth is..A) away from the people B) toward the people C) zeroAnswers: Question 1) Same as it was before. The total momentum of the Earth/people system is zero. When the people are moving up(having just jumped), the Earth is recoiling away down. When the people are on the way back down, the Earth is moving upto meet them (due to the mutual gravitational attraction). When the people return to rest, so does the Earth. Question 2) toward the people. The people fall back toward the Earth because of the forceof gravity, but the people exert an equal-sized gravitational attraction on the Earth as the Earth exerts on the people. So the Earth "falls" toward the people. CTP-4 Two masses m1 and m2 are approaching each other on a frictionless table and collide. It is possible that, as a result of the collision, all of the kinetic energy of both masses is converted to heat? A) Yes, all KE can disappear B) No, impossibleAnswer: True. If the masses initially have equal and opposite momenta, so that the total momentum of the system is zero, then it is possible that the masses stick together and stop. In this case, all of the KE is (eventually) converted into heat. A moving mass m1 is approaching a stationary mass m2. It is possible that, as a result of the collision, all of the kinetic energy of both masses is converted to heat?A) Yes, possible. B) No, impossibleAnswer: No. Since the total momentum before the collision is non-zero, the masses cannot be at rest after the collision. Therefore there must be some KE in the system after the collision, in order to satisfy conservation of momentum. CTP-5 Two masses, of size m and 3m, are at rest on a frictionless surface. A compressed, massless spring between the masses is suddenly allowed to uncompress, pushing the masses apart.3m m After the masses are apart, the speed of m is ____ the speed of 3m.A) the same as B) twice C) three timesD) 4 times E) none of theseThe kinetic energy of m is __________ the kinetic energy of 3m.(Hint: If Ptot = 0, then mA|vA| = mB|vB| .)A) the same as B)greater than C) less than While the spring is in contact with both masses, the magnitude of the acceleration of 3m is __________ that of m.A) the same as B) greater than C) less than Answers: Question (1) 3 times. Notation: m1=m and m2=3m. Since the total momentum iszero, we must have m1v1+m2v2 = 0, v1 = –(m2/m1)v2 = –(3m/m)v2 = –3v2. DANGER: Usually the symbol v (no arrow overhead) means the speed and is always positive. In 1D collision problems, the symbol v often represents velocity and can be (+) or (–). Question (2)greater. Since m1|v1| = m2|v2| and |v1| > |v2| , we must have m1|v1|2 > m2|v2|2. Question (3) less than. By Newton's third law, the force from m1 on m2 is equal in magnitude to the force from m2 on m1. F1 = F2, so m1a1 = m2 a2 (here, a means magnitude of acceleration). Since m1=m is less than m2=3m, then a1 > a2, a2 < a1. Same size force on the lighter object will cause greater acceleration.CTP-6 A ball bounces off the floor as shown. The direction of the impulse of the ball,p, is ...A) straight up B) straight down C) to the right D) to the left Answer: straight up. We can see this in two ways.: Method I: Draw a vector diagram showing the vector addition p1 + p = p2 Method II: Since p is in the same direction as Fnet (according to p = Fnett ), the direction of the force from the floor (which is straight up) must be the same as the direction of the impulse p .CTP-7 Consider two carts, of masses m and 2m, at rest on an air track. If you push first one cart for 3 s, and then the other for the same length of time, exerting equal force on each, the momentum of the light cart is _______ the momentum of the heavy cart.A) four times B) twice C) equal toD) one-half E) one-quarterm 3m F for time t F for time t Answer: equal to. According to p = Fnett , if I apply the same force F for the same time interval, the change in momentum is the same.CTP-8 Suppose a tennis ball and a bowling ball are rolling toward you. Both have the same momentum, and you exert the same force to stop each. How do the time intervals to stop them compare?A) It takes less time to stop the tennis ball.B) Both take the same time.C) It takes more time to stop the tennis ball.Answer: both take the same time. Both have the same momentum (the bowling ball must be going very slow and/or the tennis ball is going really fast) and p = Fnett . If we apply the same force to each, it will take the same time to stop both. p1p2pCTP-9 A fast-ball thrown at a batter has a momentum of magnitude | pi | = (0.3kg)(40m/s) = 12 kgm/s. The batter hits the ball in a line drive straight back at the pitcher with momentum of magnitude | pf | = (0.3kg)(80m/s) = 24 kgm/s. What is the magnitude of the impulse |p|? A) | pf | – |