6.2 In class we noted that the potential energy of a spring is given by Vsp(2) = k(z – zo)² /2, where zo is the spring's equilibrium point and k the spring constant. Now consider an object of mass m (not attached to the spring) that drops from rest, from a height z; > 2o, onto the spring (which is initially in equilibrium at its rest length). Both the gravitational force and the spring force now contribute to the potential energy, initial final E Z. - 2. Vgrav Vgrav + Vsp if z < z0. if z > z0 V(2) = { (1) (a) Sketch (by hand, but carefully) a potential energy diagram for V(z) as a function of height z. (b) Include (and mark) the object's initial energy in the sketch of part (a), then include a horizontal line for the object's conserved total energy E. Also mark the turning point zf for z < 20. (c) Calculate the turning point position zf where the object momentarily comes to rest." (d) Your graph of part (a) should have an equilibrium point. Mark this equilibrium point in your graph, then calculate its position, zeq · (Is it a stable or unstable equilibrium?) (e) Now return to the object that you dropped from height z;. At what height z will it reach its maximum speed? No calculation needed – refer to your graph of part (a) to explain in a sentence or two. Optional [1 bonus pt.] Calculate this maximum speed.
6.2 In class we noted that the potential energy of a spring is given by Vsp(2) = k(z – zo)² /2, where zo is the spring's equilibrium point and k the spring constant. Now consider an object of mass m (not attached to the spring) that drops from rest, from a height z; > 2o, onto the spring (which is initially in equilibrium at its rest length). Both the gravitational force and the spring force now contribute to the potential energy, initial final E Z. - 2. Vgrav Vgrav + Vsp if z < z0. if z > z0 V(2) = { (1) (a) Sketch (by hand, but carefully) a potential energy diagram for V(z) as a function of height z. (b) Include (and mark) the object's initial energy in the sketch of part (a), then include a horizontal line for the object's conserved total energy E. Also mark the turning point zf for z < 20. (c) Calculate the turning point position zf where the object momentarily comes to rest." (d) Your graph of part (a) should have an equilibrium point. Mark this equilibrium point in your graph, then calculate its position, zeq · (Is it a stable or unstable equilibrium?) (e) Now return to the object that you dropped from height z;. At what height z will it reach its maximum speed? No calculation needed – refer to your graph of part (a) to explain in a sentence or two. Optional [1 bonus pt.] Calculate this maximum speed.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![6.2 In class we noted that the potential energy of a spring is given by
Vsp (2)
and k the spring constant. Now consider an object of mass m (not
attached to the spring) that drops from rest, from a height z; > z0;
onto the spring (which is initially in equilibrium at its rest length).
Both the gravitational force and the spring force now contribute to
the potential energy,
initial
final
k(z – zo)²/2, where zo is the spring's equilibrium point
E Zo
Z=0
Vgrav
Vgrav + Vsp if z < zo.
if z > z0
V (2) =
(1)
(a) Sketch (by hand, but carefully) a potential energy diagram for V(2) as a function of height z.
(b) Include (and mark) the object's initial energy in the sketch of part (a), then include a horizontal
line for the object's conserved total energy E. Also mark the turning point zf for z < zO.
(c) Calculate the turning point position zf where the object momentarily comes to rest."
(d) Your graph of part (a) should have an equilibrium point. Mark this equilibrium point in your
graph, then calculate its position, zeg · (Is it a stable or unstable equilibrium?)
(e) Now return to the object that you dropped from height z;. At what height z will it reach its
maximum speed? No calculation needed – refer to your graph of part (a) to explain in a sentence or
two. Optional [1 bonus pt.] Calculate this maximum speed.
"If you find two possible solutions, explain which solution you should choose. Is there a setup for which the other
solution would be a physical solution, too?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc99cc4f-9438-44d8-9b43-49724a6b39cf%2Ff5a7e426-4f8d-4f84-acc0-56c56f7926a3%2F9jy45j_processed.png&w=3840&q=75)
Transcribed Image Text:6.2 In class we noted that the potential energy of a spring is given by
Vsp (2)
and k the spring constant. Now consider an object of mass m (not
attached to the spring) that drops from rest, from a height z; > z0;
onto the spring (which is initially in equilibrium at its rest length).
Both the gravitational force and the spring force now contribute to
the potential energy,
initial
final
k(z – zo)²/2, where zo is the spring's equilibrium point
E Zo
Z=0
Vgrav
Vgrav + Vsp if z < zo.
if z > z0
V (2) =
(1)
(a) Sketch (by hand, but carefully) a potential energy diagram for V(2) as a function of height z.
(b) Include (and mark) the object's initial energy in the sketch of part (a), then include a horizontal
line for the object's conserved total energy E. Also mark the turning point zf for z < zO.
(c) Calculate the turning point position zf where the object momentarily comes to rest."
(d) Your graph of part (a) should have an equilibrium point. Mark this equilibrium point in your
graph, then calculate its position, zeg · (Is it a stable or unstable equilibrium?)
(e) Now return to the object that you dropped from height z;. At what height z will it reach its
maximum speed? No calculation needed – refer to your graph of part (a) to explain in a sentence or
two. Optional [1 bonus pt.] Calculate this maximum speed.
"If you find two possible solutions, explain which solution you should choose. Is there a setup for which the other
solution would be a physical solution, too?
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