A particle of mass 0.50 kg moves along the x-axis with a potential energy whose dependence on x is shown below. (a) What is the force on the particle at x=2.0,5.0,8.0,and 12 m? (b) If the total mechanical energy E of the particle is −6.0 J, what are the minimum and maximum positions of the particle? (c) What are these positions if E=2.0J? (d) If E=16J, what are the speeds of the particle at the positions listed in part (a)?

Identify the arrows that show the correct direction of heat transfer. 66°f 112°f 98°f

Abaseball has a mass of 0.145 kg and approaches a bat at 40.0 m/s. after it is hit, the ball leaves the bat at 50.0 m/s directly back. find the impulse of the bat on the ball. 7.25 kg*m/s 13.1 kg*m/s 5.80 kg*m/s 1.45 kg*m/s

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?