1995M2. A particle of mass m moves in a conservative force field described by the potential energy function U(r) = a(r/b + b/r), where a and b are positive constants and r is the distance from the origin. The graph of U(r) has the following shape. U. 2ro Зго 4ro In terms of the constants a and b, determine the following. i. The position r, at which the potential energy is a minimum ii. The minimum potential energy U. Sketch the net force on the particle as a function of r on the graph below, considering a force directed away from the origin to be positive, and a force directed toward the origin to be negative. a. b. F The particle is released from rest at r = r,/2 In terms of U, and m, determine the speed of the particle when it is at r= r.. d. c. Write the equation or equations that could be used to determine where, if ever, the particle will again come to rest. It is not necessary to solve for this position. Briefly and qualitatively describe the motion of the particle over a long period of time. e.
1995M2. A particle of mass m moves in a conservative force field described by the potential energy function U(r) = a(r/b + b/r), where a and b are positive constants and r is the distance from the origin. The graph of U(r) has the following shape. U. 2ro Зго 4ro In terms of the constants a and b, determine the following. i. The position r, at which the potential energy is a minimum ii. The minimum potential energy U. Sketch the net force on the particle as a function of r on the graph below, considering a force directed away from the origin to be positive, and a force directed toward the origin to be negative. a. b. F The particle is released from rest at r = r,/2 In terms of U, and m, determine the speed of the particle when it is at r= r.. d. c. Write the equation or equations that could be used to determine where, if ever, the particle will again come to rest. It is not necessary to solve for this position. Briefly and qualitatively describe the motion of the particle over a long period of time. e.
Related questions
Question
Transcribed Image Text:1995M2. A particle of mass m moves in a conservative force field described by the potential energy function U(r) =
a(r/b + b/r), where a and b are positive constants and r is the distance from the origin. The graph of U(r) has the
following shape.
U.
2ro
Зго
4ro
In terms of the constants a and b, determine the following.
i. The position r, at which the potential energy is a minimum
ii. The minimum potential energy U.
Sketch the net force on the particle as a function of r on the graph below, considering a force directed away
from the origin to be positive, and a force directed toward the origin to be negative.
a.
b.
F
The particle is released from rest at r = r,/2
In terms of U, and m, determine the speed of the particle when it is at r= r..
d.
c.
Write the equation or equations that could be used to determine where, if ever, the particle will again come to
rest. It is not necessary to solve for this position.
Briefly and qualitatively describe the motion of the particle over a long period of time.
e.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 6 images
