Consider a beam of electrons in a vacuum, passing through a very narrow slit of width 2.00μm. the electrons then head toward an array of detectors a distance 0.9090 m away. these detectors indicate a diffraction pattern, with a broad maximum of electron intensity (i. e., the number of electrons received in a certain area over a certain period of time) with minima of electron intensity on either side, spaced 0.521 cm from the center of the pattern. what is the wavelength λ of one of the electrons in this beam? recall that the location of the first intensity minima in a single slit diffraction pattern for light is y=lλ/a, where l is the distance to the screen (detector) and a is the width of the slit. the derivation of this formula was based entirely upon the wave nature of light, so by de broglie's hypothesis it will also apply to the case of electron waves.

Tafari worked one summer on a ship that set weather buoys in the ocean. he watched how one of the buoys moved in the water. describe which parts of the wave would cause the buoy to bob up and down. which wave property determined how fast the buoys bobbed in the water? he observed that when the wind blew harder, the ocean waves were larger, and the buoys moved away from the ship. what effect, if any, did the waves have on how far the buoys moved? explain your answer.

During physical science, ms. greene challenged her students to produce an energy transformation. james and jill wrapped a 4-inch nail with a coil of fifty turns of wire. they connected one end of the coil to one terminal of a knife switch. they connected the other terminal of the knife switch to the battery. finally, they connected the end of the coil to the other terminal of the battery. james held the tip of a 1-inch nail near the flat end of the 4-inch nail. jill closed the knife switch quickly and then opened it. the 1-inch nail was pulled toward the 4-inch nail. what is the best explanation of why the nail moved? a) electrical energy was converted to mechanical energy in the 1-inch nail. b) the 4-inch nail became an electromagnet and the magnetic force attracted the 1-inch nail. c) the electric current in the 4-inch nail was converted to mechanical energy in the 1-inch nail. d) the 4-inch nail had a positive charge and the 1-inch nail had a negative charge. opposites attracted.

The 10-kg double wheel with radius of gyration of 125mm about o is connected to the spring of stiffness k = 600 n/m by a cord which is wrapped securely around the inner hub. if the wheel is released from rest on the incline with the spring stretched 225 mm, calculate the maximum velocity v of its center o during the ensuing motion. the wheel rolls without slipping