ME1520 C Term 1999

Homework 5-8

5. DUE TUESDAY, 25 APRIL A skier weighing 80 kg is sliding straight down a hill with a slope of 15 degrees. Consider dynamic friction coefficients from 0.01 to 0.1. Assuming that all the water in the snow is in the form of ice before the skier slides over it, what are the thickest the average layers of liquid water could be at the tail of the ski, if the ski is 65mm wide? And, what are the smallest slope angles that someone could slide down?

6. A 120 lb., type III skier should have, according to the binding manufacturer’s chart, a forward lean release at 194Nm and a twist release at 50Nm. The boot sole length is 302mm; the AFD extends from 33 to 50mm from the boot toe; the coefficient of friction between the boot and AFD is 0.1. In a forward twisting fall, if the tibia axis is located 250mm from the boot toe and assuming that the tibia is oriented perpendicular to the boot sole, what is the maximum torque that the tibia would see?

7. How much camber should there be in a ski, with a running surface of 170cm, so that when half a 180lb skier’s weight is applied the pressure distribution over the length of the ski is constant? Assume that the ski is resting on a flat, infinitely stiff surface, and that the ski has a constant section modulus (although we know this will not be good for flexing into a uniform arc)- rectangular cross-section of 20mm by 60mm and equivalent elastic modulus of 14,000MPa.

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