Potential energy in common problems: there are certain systems that show up again and again in physics, because they are useful models for other phenomena. it is thus to store key equations for these systems in long-term memory. look up or figure out the formula for the potential energy u of the following systems: (a) an object of mass m located a distance y above the ground (which we will assume to be at zero potential energy, for convenienc. if it , assume that y is much smaller than the radius of the earth. (b) a spring with stiffness k that has been displaced from equilibrium a distance δ . (c) a pendulum consisting of a mass m attached to a string of length l, and the string has been pulled back from equilibrium through an angle θ. assume that the string is hanging straight down and the potential energy is zero when θ 0. i want the exact formula for the potential energy of this system, not the quadratic approximation! (d) a satellite of mass m located a distance r from the center of the earth. (e) two point charges ı and g2 separated by a distance r.

Calculate the amount of heat produced when 18000 coulombs of charge is transferred in one hour through a potential difference of 50v

Which changes of state do the labels represent? a: b: c:

Search coils and credit cards. one practical way to measure magnetic field strength uses a small, closely wound coil called a search coil. the coil is initially held with its plane perpendicular to a magnetic field. the coil is then either quickly rotated a quarter-turn about a diameter or quickly pulled out of the field. (a) derive the equation relating the total charge q that flows through a search coil to the magnetic-field magnitude b. the search coil has n turns, each with area a, and the flux through the coil is decreased from its initial maximum value to zero in a time ∆t. the resistance of the coil is r, and the total charge is q = i∆t, where i is the average current induced by the change in flux. (b) in a credit card reader, the magnetic strip on the back of a credit card is rapidly “swiped” past a coil within the reader. explain, using the same ideas that underlie the operation of a search coil, how the reader can decode the information stored in the pattern of magnetization on the strip. (c) is it necessary that the credit card be “swiped” through the reader at exactly the right speed? why or why not?