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.
Copyright © Michael Richmond.
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