A uniform solid ball rolls smoothly along a floor, then up a ramp inclined at 33.0°. It momentarily stops when it has rolled 1.70 m along the ramp. What was its initial speed?

The equation that describes a transverse wave on a string is y = (0.0120 m)sin[(927 rad/s)t - (3.00 rad/m)x] where y is the displacement of a string particle and x is the position of the particle on the string. the wave is traveling in the +x direction. what is the speed v of the wave?

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?

Madison pushes with a 210-n horizontal force on a 24-kg crate of coffee resting on a warehouse floor. the force of friction on the crate is 74 n. what is the acceleration?