Tapered beams are used in a variety of applications to save both weight and cost. indeed, we see them in bridges, churches and tree branches. despite their weight savings, the weight of the beam must be consider when designing the structure lest it will fail. consider the illustrated tapered wood beam of length l = 6 m, thickness (into the screen) t = 20 cm, and big and small end heights h b i g = 100 cm and h s m a l l = 50 cm. knowing that the mass density of wood is rho = 700 kg/m 3 , determine the resultant force f r in n and resultant moment m r in nm about the base, i. e. big end, due to the weight of the beam.

In which of the following cases is work being done on an object? question 2 options: pushing against a locked door carrying a box down a corridor pulling a trailer up a hill suspending a heavy weight with a strong chain

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?

Aflask with vinegar in it has a mass of 160 grams. a balloon with baking soda in it has a mass of 40 grams. the balloon is attached to the flask to seal the opening and the vinegar and baking soda mixes. the balloon inflates to a large volume. what will the total mass of the balloon and flask be after the balloon inflates? explain. a) less than 200 grams because the solid baking soda disappears. b) 200 grams, because all the atoms remain in the balloon or flask. c) more than 200 grams because the size of the balloon is so much larger. d) less than 200 grams because gases such as the one in the balloon are lighter than solids and liquids.