Phys 313 Quiz 6

A proton is fixed at x = 0. Another proton is held at x = 1 m, and then released.

Question 1

Is the acceleration of the second proton constant as it moves from x = 1 m to x = 2 m?

   Answer:   no, the acceleration decreases

Question 2

Write an expression for the acceleration of the second proton when it is at x = x0, some point between x = 1 m and x = 2 m.

                         k * q1 * q2     k * e * e
   Answer:    Force  =  -----------  =  ----------
                            r^2            x0^2

                         F        k * e^2
              accel  =  ---   =  -----------
                         m        x0^2 * m

Question 3

Which of these is closest to the time for the proton to reach x = 2 m?

      A: 1 s     B:  5 s     C: 10 s     D: 50 s

   Answer:  The maximum acceleration occurs when the proton is at x = 1 m,
            and has magnitude 0.14 m/s^2.  If the proton accelerated at
            this (high) rate for the entire journey, it would take

                                2 * 1 m 
                     t  = sqrt(-----------)   =  3.8 sec 
                                0.14 m/s^2

            The minimum acceleration occurs when the proton is at x = 2 m,
            and has magnitude 0.034 m/s^2.  If the proton accelerated at
            this (low) rate for the entire journey, it would take

                                2 * 1 m 
                    t  = sqrt(-----------)   =  7.6 sec 
                              0.034 m/s^2

            Since the actual acceleration varies between these two limits,
            the time it takes to make the journey must between the two
            limits.

            B = 5 seconds is closest.