Tubing Hill Bumps: Newton's Third Law at Winter Camp

Camp Notes: Trouble at the Bottom of the Hill

1Every January, the eighth graders at Alder Creek Middle School spend three days at Larkspur Winter Camp. Between ski lessons and building snow shelters, the favorite stop is the tubing hill. Riders sit in large, bouncy inflated tubes and slide down a groomed lane to a flat run-out at the bottom, where they coast to a stop. On busy afternoons, a tube sometimes reaches the run-out before the rider ahead has climbed out, and the moving tube bumps into the stopped one. Last year two small campers were jolted hard in bumps like these, so camp director Mr. Teodoro Valsamakis asked the science class to study the problem and recommend a fix.

2To keep everyone safe, no one rode during the tests. Staff strapped sandbag dummies into the tubes, so each tube and its dummy had a total mass of either 40 kg, like a small rider, or 80 kg, like an adult. A staff member let go of the moving tube from a marked spot on the hill, so it reached the run-out at a known speed and slid straight into a tube resting in the lane. Students filmed each bump from the side, next to a row of flags placed 1 m apart, and used the slow-motion video to find each tube's speed just before and just after the bump. Each bump was repeated three times, and Table 1 shows the averages. All speeds point away from the hill unless the table says "back toward hill."

3Mr. Valsamakis gave the class two criteria for a fix. First, in the worst bump the run-out allows, no tube's speed may change by more than 2.0 m/s, because a large, sudden change in speed is what jolts a rider. Second, the hill must still send at least 60 riders down each hour. The class and the staff then tried five options. Rubber slow-down mats are strips laid across the lane just before the run-out; they slow each tube by friction. Bumper rings are soft foam rings fastened around each tube. A longer run-out gives tubes more flat, raked snow to slow down on before they reach the stopped tubes. Table 2 shows the results.