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Chapter 10: Q10Q (page 410)
What is it about analyzing collisions in the center-of-mass frame that simplifies the calculations?
The velocity of the system does not change while analyzing collisions in the center of the mass frame which also simplifies the calculation.
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A beam of high-energy 蟺 鈭� (negative pions) is shot at a flask of liquid hydrogen, and sometimes a pion interacts through the strong interaction with a proton in the hydrogen, in the reaction , where X + is a positively charged particle of unknown mass. The incoming pion momentum is 3 GeV/c (1GeV = 1000 MeV = 1 脳 109 electron-volts). The pion is scattered through , and its momentum is measured to be 1510 MeV/c (this is done by observing the radius of curvature of its circular trajectory in a magnetic field). A pion has a rest energy of 140 MeV, and a proton has a rest energy of 938 MeV. What is the rest mass of the unknown X+ particle, in ? Explain your work carefully. It is advantageous to write the equations not in terms of v but rather in terms of E and p; remember that .
Consider a head-on collision between two objects. Object 1, which has mass , is initially in motion, and collides head-on with object 2, which has massand is initially at rest. Which of the following statements about the collision are true?
(1).
(2).
(3) If, then.
(4) If, then the final speed of object 2 is less than the initial speed of object 1.
(5) If, then the final speed of object 1 is greater than the final speed of object 2.
Redo Problem P21, this time using the concept of the center-of-momentum reference frame.
A car of mass 2300 kg collides with a truck of mass 4300 kg, and just after the collision the car and truck slide along, stuck together, with no rotation. The car鈥檚 velocity just before the collision was鉄�38, 0, 0鉄﹎/s, and the truck鈥檚 velocity just before the collision was鉄ㄢ垝16, 0, 27鉄﹎/s. (a) Your first task is to determine the velocity of the stuck-together car and truck just after the collision. What system and principle should you use? (1) Energy Principle (2) Car plus truck (3) Momentum Principle (4) Car alone (5) Truck alone (b) What is the velocity of the stuck-together car and truck just after the collision? (c) In your analysis in part (b), why can you neglect the effect of the force of the road on the car and truck? (d) What is the increase in internal energy of the car and truck (thermal energy and deformation)? (e) Is this collision elastic or inelastic?
What happens to the velocities of the two objects when a high-mass object hits a low-mass object head-on? When a low-mass object hits a high-mass object head-on?
A projectile of massmoving with speed in the +xdirection strikes a stationary target of masshead-on. The collision is elastic. Use the Momentum Principle and the Energy Principle to determine the final velocities of the projectile and target, making no approximations concerning the masses. After obtaining your results, see what your equations would predict if, or if. Verify that these predictions are in agreement with the analysis in this chapter of the Ping-Pong ball hitting the bowling ball, and of the bowling ball hitting the Ping-Pong ball.
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