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.]
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?
The potential energy of a nitrogen atom in an ammonia (NH3) molecule varies with position as U(x) = x4 - 2ax2 (a is some constant)
a) Give an expression for the force F on the nitrogen atom and sketch F(x).
b) At what positions will the nitrogen atom be in stable equilibrium?
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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