The potential energy between two atoms in a particular molecule has the form U(x) = 2.1 x 8 − 5.2 x4 where the units of x are length and the numbers 2.1 and 5.2 have appropriate units so that U(x) has units of energy. What is the equilibrium separation of the atoms (that is the distance at which the force between the atoms is zero)

Ahydroelectric plant takes energy from water and turns it into electrical energy. what are the transformations of energy in the water molecules that are used in the process of generating electricity this way?

Suppose that an electromagnetic wave which is linearly polarized along the x−axis is propagating in vacuum along the z−axis. the wave is incident on a conductor which is placed at z > 0 region of the space. the conductor has conductivity σ, magnetic permeability µ and electric permittivity ε. (a) find the characteristic time for the free charge density which dissipates at the conductor. (b) write the maxwell equations and derive the wave equation for a plane wave propagating in a conductor. (c) find the attenuation distance at which the incident amplitude reduces to e ^−1 of its initial value. (d) find the electric and magnetic fields inside the conductor. 8 (e) find the power loss per area of the incident electromagnetic wave at the surface of conductor.

1. jay fills a wagon with sand (about 20 kg) and pulls it with a rope 30 m along the beach. he holds the rope 25° above the horizontal. the rope exerts a 20-n tension force on the wagon. how much work does the rope do on the wagon?