Graph 2 is reprodaced again below. Two dotted lines have been added to show two
ID: 1769924 • Letter: G
Question
Graph 2 is reprodaced again below. Two dotted lines have been added to show two different possible vales for the total energy of an object moving in this potential energy funetion Et Graph 2 (e) (4 points) Suppose that a particle has total energy Ea (represented by the lower dotted line), and is initinlly loeated at the position marlked ro. Describe how this particle would move over time. How does its speed vary? Is it "trapped" in a certain region, or is it free to escape? Explain how you can tell (d) (4 points) Now suppose that the particle has total energy Es (represented by the upper dotted line), and is initially located at the position mar ked ro. Describe how this particle would move over time, addressing the same issues as in part (c). What, if anything, is different about the particle's behavior in this case? Explain your rensoningExplanation / Answer
(c)
In this case particle's energy doesnt exceed the max. potential energy value. So we can deduce that particle's motion is bounded in this case.
The two points where particle's energy touches PE function will be the 'turning points' of the motion of the particle i.e. particle will move from x0 to one of the turning points and then it will head back towards x0 again and then to the other urning point.
Regarding velocity, it will have maximum velocity at x0 i.e. when radius is smallest (perigee). Particle move slowest when it is farthest i.e. at turning points (aka apogee).
(d)
in this case particle's energy exceeds the PE curve so particle is no longer trapped or bound. It will start from x0 and escape to infinity. There is no contact between PE function and particle's energy line so there are no turning points in this trajectory.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.