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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. 2ro 3ro Aro a. 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, b. 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. 2r. Зго 4ro The particle is released from rest at r=r,/2 c. In terms of U, and m, determine the speed of the particle when it is at r = r,. d. 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. Brieflv and aualitativelv describe the motion of the particle over a long period of time. e. (c) velocity of the particle at r0 when released from r0/2 ΔΚΕ-Δυ %3D mv² =U -U(r.) /2) (r, / 2) (ro -2a [r% =b] %3D Substitute for 'a' (U, /2) n? U, v=, Privacy - Terms

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. 2ro 3ro Aro a. 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, b. 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. 2r. Зго 4ro The particle is released from rest at r=r,/2 c. In terms of U, and m, determine the speed of the particle when it is at r = r,. d. 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. Brieflv and aualitativelv describe the motion of the particle over a long period of time. e. (c) velocity of the particle at r0 when released from r0/2 ΔΚΕ-Δυ %3D mv² =U -U(r.) /2) (r, / 2) (ro -2a [r% =b] %3D Substitute for 'a' (U, /2) n? U, v=, Privacy - Terms

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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. 2ro 3ro Aro a. 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, b. 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. 2r. Зго 4ro The particle is released from rest at r=r,/2 c. In terms of U, and m, determine the speed of the particle when it is at r = r,. d. 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. Brieflv and aualitativelv describe the motion of the particle over a long period of time. e.
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. 2ro 3ro Aro a. 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, b. 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. 2r. Зго 4ro The particle is released from rest at r=r,/2 c. In terms of U, and m, determine the speed of the particle when it is at r = r,. d. 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. Brieflv and aualitativelv describe the motion of the particle over a long period of time. e.
(c) velocity of the particle at r0 when released from r0/2 ΔΚΕ-Δυ %3D mv² =U -U(r.) /2) (r, / 2) (ro -2a [r% =b] %3D Substitute for 'a' (U, /2) n? U, v=, Privacy - Terms
Transcribed Image Text:(c) velocity of the particle at r0 when released from r0/2 ΔΚΕ-Δυ %3D mv² =U -U(r.) /2) (r, / 2) (ro -2a [r% =b] %3D Substitute for 'a' (U, /2) n? U, v=, Privacy - Terms
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