Problem 160 — Getting the short end of the stick can have weighty consequences, as this month’s problem by Peter Masterson of Newmarket, N.H., demonstrates.
“Why, it’ll be no trouble at all,” sang Finagel J. Wurme. The occasion was a client demonstration of the Lee Key Hydraulic Co.’s new pulleys. Lucius Bluff had constructed a mechanism (see figure) on which he would apply a 10-lb upward force to lift 100 gal water. Wurme had offered to make the lever for the apparatus.
The day of the demonstration dawned. Wurme was seized with a violent fit of hiccups as he handed the 40-ft long lever to Bluff.
The diameter of the large pulley is 25 ft, and the diameter of the small, 4 ft. Neglect stresses and bending in the lever, and the lever’s weight. Take 8.336 lb as the weight of 1 gal water. Also neglect the weight of the bucket and frictional forces in the pulley. If the pivot is 6 ft from the end of the lever to which the pulley rope is attached, what should be the distance from the pivot to where the 10-lb force is applied? Will a 40-ft lever suffice?
Solution to last month’s problem 159 — You are an expert on target marketing if you answered 143 ft. Here are the logistics:
We know the velocity of the buckets is 30 fps. Since Velocity x Time = Distance, in order to find the distance the bucket must be from the point under the target, we need to know the total time from the firing of the slingshot to when the ball hits the belt.
