Ahollow steel [e = 30,000 ksi] tube (1) with an outside diameter of 3.250 in. and a wall thickness of 0.375 in. is fastened to a solid aluminum [e = 10,000 ksi] rod (2) that has a 1.750-in.-diameter and a solid 1.125-in.-diameter aluminum rod (3). the bar is loaded as shown. assume l1 = 70 in., l2 = 40 in., l3 = 27 in., r = 35 kips, q = 16 kips, and p = 28 kips. determine (a) the change in length of steel tube (1). (b) the deflection of joint d with respect to the fixed support at a. (c) the maximum normal stress in the entire axial assembly.

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?

Imagine you are standing in the antarctic during the southern hemisphere summer. the sky is clear and blue. there are no clouds in the sky. your shadow is cast on the icy ground. what is the color of the shadow?

The diagram shows a wave. the quantity shown is the amplitude. this quantity is directly proportional to which of these other quantities? a) energy b) frequency c) period d) wavelength