Newtons law of cooling states that if an object with temperature t(t) at time t is in a medium with temperature tm the rate of change of t at time t is proportional to t(t) − tm, thus t satisfies a differential equation of the form t 0 = −k(t − tm) here k > 0, since the temperature of the object must decrease if t > tm, or increase if t < tm. well call k the temperature decay constant of the medium. (a) a thermometer is moved from a room where the temperature is 70f to a freezer where the tem- perature is 12f . after 30 seconds the thermometer reads 40f. what does it read after 2 minutes? (b) an object is placed in a room where the temperature is 20c. the temperature of the object drops by 5c in 4 minutes and by 7c in 8 minutes. what was the temperature of the object when it was initially placed in the room?

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?

Awater balloon launcher uses an elastic band with a spring constant of 115 n/m to use thee launcher you stretch thee band back with a balloon n it the water balloons have a mass of 1.3 kg a) if you stretch the band by 0.8 m, what elastic force will the band exert? b) with the band stretched 0.8 m, how much elastic potential energy is stored in the spring? c) if you release the band, it pushes forward. what is the kinetic energy of the balloon when it reaches the natural length of the band? d) what is the speed of the balloon when it reaches the natural length of the band?

Rank the six combinations of electric charges on the basis of the electric force acting on q1. define forces pointing to the right as positive and forces pointing to the left as negative. rank positive forces as larger than negative forces. q1,q2,q3 = positive(+) q1 = + q2 = + q3 = - q1 = + q2= - q3= + q1= - q2= + q3= + q1= + q2= - q3= - q1,q2,q3 = negative