Randall D. Knight — Dynamics II: Motion in a Plane: Problem 59

Elm Street has a pronounced dip at the bottom of a steep hill before going back uphill on the other side. Your science teacher has asked everyone in the class to measure the radius of curvature of the dip. Some of your classmates are using surveying equipment, but you decide to base your measurement on what you’ve learned in physics. To do so, you sit on a spring scale, drive through the dip at different speeds, and for each speed record the scale’s reading as you pass through the bottom of the dip. Your data are as follows: Speed (m/s): 5, 10, 15, 20, 25 Scale reading (N): 599, 625, 674, 756, 834 Sitting on the scale while the car is parked gives a reading of 588 N. Analyze your data, using a graph, to determine the dip’s radius of curvature.