Problem 254: Chocolate challenge
Don’t dought your ability to chip away at this dilemma.
Holiday sales were a bit sluggish this year for Charlie’s Chocolate Chip Cookie Factory. The fourth quarter wasn’t a total disaster, just down about 10% over last year’s figures — it’s unfortunate Charlie can’t say the same about his weight. (Then again, maybe it’s not a good idea to have a skinny guy running a cookie factory.)
It’s a small factory, and although Charlie is a big guy with a big title, he is in charge of many of the tedious, day-to-day operations. His first challenge of the new year, though, is to lift all the leftover 50 lb. chocolate chip bricks onto a conveyor belt that winds back into cold storage. To avoid exerting himself, Charlie has built a simple machine. Oddly, his inspiration came from a device he noticed on a replica of the Santa Maria ship, in Columbus, Ohio. He has constructed a wooden roller (radius of 1.5 ft), with a rope going around the roller and a hook at the end of it, which he can attach to the chocolate bricks one at a time. To turn the roller, Charlie has attached a 4-ft. crank handle, which makes an angle of 45° to the floor, at its starting point. If he applies a force of 50 lb. at an angle directed 20° below horizontal (pushing the handle counterclockwise), will he be able to lift a chocolate brick?