Question

The potential energy of an object is given by U(x)=8x2-x4, where U is in joules and x is
in meters
a) Determine the force acting on this object.
b) At what positions is this object in equilibrium?
c) Which of these equilibrium positions are stable and which are unstable?

Answer 1

Answer:

The potential energy of an object is given by U(x)=8x2-x4, where U is in joules and x is

in meters

a) Determine the force acting on this object.

b) At what positions is this object in equilibrium?

c) Which of these equilibrium positions are stable and which are unstable?

Answer 2

Archimedes' principle is named after Archimedes of Syracuse, who first discovered this law in 212 BC.[4] For objects, floating and sunken, and in gases as well as liquids (i.e. a fluid), Archimedes' principle may be stated thus in terms of forces:

Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object

—with the clarifications that for a sunken object the volume of displaced fluid is the volume of the object, and for a floating object on a liquid, the weight of the displaced liquid is the weight of the object.[5]

hope it helps ( ╹▽╹ )