Two bodies, with heat capacities c₁ and c₂ (assumed independent of temperature) and initial temperatures t₁ and t₂ respectively, are placed in thermal contact. show that their final temperature is given by t₁ = (c₁t₁ + c₂t₂)/(c₁ + c₂). if c₁ is much larger than c₂ . show that = t₁ + c₂(t₂ -t₁)/c₁.

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?

What is the measure of how much matter is in an object and that can be measured using a balance? a. height b. volume c. weight d. mass

The diagram shows a boulder rolling down a hill into a valley and then up the opposite hill. at which position does the boulder have the greatest kinetic energy? ab c d