In the boxes below, draw the initial momentum, the change in momentum, and the f

Question

In the boxes below, draw the initial momentum, the change in momentum, and the final momentum for each astronaut in the three experiments. The initial momentum is shown for astronaut A. Draw the other vectors using the same scale. Generalize from your results above to answer the following questions: If the net force on a system of two colliding objects is zero, how does the change in momentum of one object compare to the change in momentum of the other object: in magnitude? in direction? Explain how your answers to part f are consistent with Newton's third law and the impulse-momentum theorem (Fnet Delta t = Delta p) for: each astronaut considered separately, and for the system of both astronauts together. Two astronauts, A and B, participate in three collision experiments in a weightless, irictionless environment. In each experiment, astronaut B is initially at rest, and astronaut A has initial momentum pAf = 20 kg-m/s to the right. (The velocities of the astronauts are measured with respect to a nearby space station.) The astronauts push on each other in different ways so that the outcome of each experiment is different. As shown in the figure at right, astronaut A has a different final momentum in each experiment. Determine the magnitude of the final momentum of astronaut B in each experiment. Explain. Rank the three experiments according to the final kinetic energy of astronaut B, from largest to smallest. Explain. Is the total kinetic energy after the collision in experiment 2 greater than, less than, or equal to the total kinetic energy after the collision in experiment 3? (In this case, total kinetic energy means the sum of the kinetic energies of the two astronauts.) Explain. Consider the following statement: "The momentum of the system is conserved in each experiment because there is no net force on the system. If momentum is conserved, then kinetic energy must also be conserved, because both momentum and kinetic energy are made up of mass and velocity. One of the sentences above is completely correct. Discuss the error(s) in reasoning in the other sentence.

Explanation / Answer

Conservation of momentum
Pi = +20 + 0 = +20 kg-m/s
(taking right direction as positive )
1) Pf = Pi
0 + x = +20 (Astronaut B 's Final momentum is 20 k-m/s towards right)
2) -5 + x = +20
   x = +25 (Astronaut B 's Final momentum is 25 k-m/s towards right)
3) +5 +x = +20
   x= +15 (Astronaut B 's Final momentum is 15 k-m/s towards right )

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