According to Wikipedia, the Skeleton is a winter sliding sport in which a person rides a small sled, known as a skeleton bobsled, down a frozen track while lying face down and head-first. The sport and the sled may have been named from the bony appearance of the sled. Like the bobsleigh, the race begins with a running start from the opening gate at the top of the course. The maximum combined mass of the athlete + sled is 115 kg for men and 92 kg for women.
In 2002, Park City, Utah hosted the Winter Olympics. The skeleton track at Park City is 1340 m long with a vertical drop of 103.9 m. Elite racers can reach speeds of over 130 km/h. If a female Olympic athlete starts at the top of the track with a speed of 20.0 mph (8.9408 m/s) and finishes with a speed of 87.77 mph (36.111 m/s), how much of the ice was melted on the track during the descent? You may assume that the ice is at the freezing point. Find the force of friction and the coefficient of kinetic friction for this situation.
a) By work energy theorem,
work done by all forces = change in kinetic energy
mgh + work done by friction = 0.5mv^2 - 0.5mu^2 where v is final velocity and u is initial velocity
92*9.8*103.9 + work done by friction = 0.5*92*36.111^2 - 0.5*92*8.9408^2
work done by friction = - 37369 J
heat generated = 37369 J
Heat of ice = M*L where M is mass of ice and L is latent heat of fusion
37369 = M*334e3
M = 37369/334e3
= 0.11188 kg answer
b) Force of friction = work done/distance = 37369/1340 = 27.887 N
Coefficient of friction u = friction/normal
= 27.887/[mg] as normal will be approximately mg
= 27.887/[92*9.8]
= 0.031
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