In some diatomic molecules, the force each atom exerts on the other can be approximated by F = − C / r 2 + D / r 3 , where r is the atomic separation and C and D are positive constants, ( a ) Graph F vs. r from r = 0.8 D/C to r = 4 D / C . ( b ) Show that equilibrium occurs at r = r 0 = D/C. ( c ) Let Δ r = r – r 0 be a small displacement from equilibrium, where Δ r ≪ r 0 . Show that for such small displacements, the motion is approximately simple harmonic, and ( d ) determine the force constant. ( e ) What is the period of such motion? [ Hint : Assume one atom is kept at rest.]
In some diatomic molecules, the force each atom exerts on the other can be approximated by F = − C / r 2 + D / r 3 , where r is the atomic separation and C and D are positive constants, ( a ) Graph F vs. r from r = 0.8 D/C to r = 4 D / C . ( b ) Show that equilibrium occurs at r = r 0 = D/C. ( c ) Let Δ r = r – r 0 be a small displacement from equilibrium, where Δ r ≪ r 0 . Show that for such small displacements, the motion is approximately simple harmonic, and ( d ) determine the force constant. ( e ) What is the period of such motion? [ Hint : Assume one atom is kept at rest.]
In some diatomic molecules, the force each atom exerts on the other can be approximated by
F
=
−
C
/
r
2
+
D
/
r
3
, where r is the atomic separation and C and D are positive constants, (a) Graph F vs. r from r = 0.8D/C to r = 4D/C. (b) Show that equilibrium occurs at r = r0= D/C. (c) Let Δr = r – r0 be a small displacement from equilibrium, where
Δ
r
≪
r
0
. Show that for such small displacements, the motion is approximately simple harmonic, and (d) determine the force constant. (e) What is the period of such motion? [Hint: Assume one atom is kept at rest.]
The potential energy of two atoms in a diatomic molecule can be approximated by the Lennard-
Jones potential U(r) = a/r¹² — b/r6, where r is the distance between the two atoms, and a and b
are positive constants.
a) Find the force F(r) on one of the atoms as a function of r.
b) Find the equilibrium distance between the two atoms. Is this equilibrium stable?
c) Suppose the distance between the two atoms is equal to the equilibrium distance found in part
b). What minimum energy must be added to the molecule to break the two atoms apart? (This
is called the dissociation energy of the molecule.)
of a copper wire of uniform cross section and
Ex. 70: find the energy stored per unit volume
of length 1.5 m, when it is stretched to a length
of a copper wire of uniform cross section and
of length 1.5 m, when it is stretched to
length
a
of 1.51 m by a stress of 3 x 102 N/m2.
(a) A cube of Jell-0 6 cm on a side sits on your plate. You exert a horizontal force of 0.20 N on thetop surface parallel to the surface and observe a sideways displacement of 5 mm. What is the shearmodulus of the Jell-O?
(b) A molecule in a microwave oven experiences a torque τ = τ0 sin θ. How much work must bedone to rotate the molecule from θ = 0° to = 180° ?(c) The evolution of a star depends on its size. If a star is sufficiently large, the gravity forcesholding it together may be large enough to collapse it into a very dense object composed mostlyof neutrons. The density of such a neutron star is about 1014 times that of the earth. Suppose thata star initially had a radius about that of our sun, 7 × 108 km, and that it rotated once every 26 days,as our sun does. What would be the period of rotation (the time for 1 rev) if the star collapsed to aradius of 15 km?
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Work and Energy - Physics 101 / AP Physics 1 Review with Dianna Cowern; Author: Physics Girl;https://www.youtube.com/watch?v=rKwK06stPS8;License: Standard YouTube License, CC-BY