Amass weighing 4 pounds is attached to a spring whose constant is 2 lb/ft. the medium offers a damping force that is numerically equal to the instantaneous velocity. the mass is initially released from a point 1 foot above the equilibrium position with a downward velocity of 6 ft/s. determine the time at which the mass passes through the equilibrium position. (use g = 32 ft/s2 for the acceleration due to gravity.)

If an object with an initial temperature of 300 k increases its temperature by 1°c every minute, by how many degrees fahrenheit will its temperature have increased in 10 minutes? (a) 6°f (b) 10°f (c) 18°f (d) 30°f

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?

The star betelgeuse is about 600 light-years away. if it explodes tonight, a. we'll know because debris from the explosion will rain down on us from space.b. we'll know it immediately because it will be brighter than the full moon in the sky.c. we won't know about it until 600 years from now.d. none of the above.