The three equilibrium configurations of a right circular cone and identify them as positions of stable, unstable, or neutral equilibrium.

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(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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Chapter 6, Problem 55P

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To Sketch: The three equilibrium configurations of a right circular cone and identify them as positions of stable, unstable, or neutral equilibrium.

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(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 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.)

A 0.30-kg block slides along a small track with elevated curved ends and a flat central part. The flat part has a length L=144 m. The curved portions of the track have negligible friction, but the flat part of the track has a coefficient of kinetic friction of 0.186. The block is released from rest from a height h=62 cm on the left curved portion of the track. Calculate the maximum height reached by the block on the right curved portion of the track.