Question

THE ONE-EYED JACK MINE INVESTIGATION

The abandoned One-Eyed Jack Mine is about 31 miles off the main road adjacent to the Salmon River Wilderness area. There is only a rutted dirt track left where the access road used to run. It is so steep that when we hiked up it we had to pause every fifty feet or so to catch our breath. It seemed impossible but 3- 5 miles further we found remnants of the old wagons, the mineshaft, and the mill. The gold ore found in this mine was embedded in quartz and prospectors used the mill to grind up the quartz and rinse it with acid in huge shallow vats that were agitated so that the gold would sink to the bottom and the quartz could be washed away.
One arrangement of equipment we noticed included a circular vat about 18 feet in diameter which must have been connected by a huge belt to a smaller circular drive wheel 10 feet in diameter. The distance between the wheel and the vat was 8 feet. The equipment had been partially pre-fabricated then carried up the hill piece by piece to be re-assembled on the spot. Just the belt to connect the vat to the drive wheel would have been a major burden. We wondered how many times they had to carry new ones up to replace it. Calculate the length of belt needed to go around the drive wheel and the vat.

Answer 1

79.6 feet.

Step-by-step exp

2 x 3.14 x (5 + 9) = 79.6 feet.

Answer 2

The length of the belt needed to go around the drive wheel and the vat is approximately 79.6 feet. This is calculated by using the circumference formula C = 2πr where r is the radius of the wheel (5 feet) and the radius of the vat (9 feet). The total circumference is then 2 x 3.14 x (5 + 9) = 79.6 feet.