A 68 kg person rides at a speed of 7.2 m/s on a bicycle that hasa mass of 8.1 kg. Each wheel is a hoop of radius 0.33 m and mass 1.4 kg (the mass of the wheels is included in the mass of the bicycle, and I= MR2for a hoop). (a)(2 points) At what angular speed are the wheels rotating? (b)(6 points) What is the total kinetic energy of the bicycle and rider? (c)(2 points) Assuming any friction is negligeable, if the cyclist coasts up a ramp (with an initial speed of 7.2 m/s), what vertical distance will the center of mass of the bicycle-rider system rise before the bike comes to rest?

Aseries circuit consists of a resistor with r = 20 ? , a capacitor with c = 0.01 f, and a decaying battery with e = 300e? 5t. if the initial charge is 0, find the charge as a function of time t

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?

Compare the horizontal displacement of the two balls as they travel to the ground. what do you observe?