Agadget of mass 21.85 kg floats in space without motion. because of some internal malfunction, the gadget violently breaks up into 3 fragments flying away from each other. the first fragment has mass m1 = 6.42 kg and speed v1 = 6.8 m/s while the second fragment has mass m2 = 8.26 kg and speed v2 = 3.54 m/s. the angle between the velocity vectors ~v1 and ~v2 is θ12 = 64 ◦ . what is the speed v3 of the third fragment? answer in units of m/s.

If an inclined plane is 5 m long and 2 m high, what is its mechanical advantage? a. 2.5 b. 3 c. 7 d. 10

According to newton’s first law of motion, which force is expected to cause a body to accelerate?

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?