MadSci Network: Physics

Re: 2 skiers at the top of a hill - who finishes first?

Date: Mon Feb 4 19:20:12 2002
Posted By: Renafaye Norby, Faculty, Science Education, Black Hills State Univ.
Area of science: Physics
ID: 1011641204.Ph

Judy, this question has a couple more variables than you mention in your 
If you think about the two skiiers in free fall (like Galileo's 
experiment) they would fall straight down with the same acceleration and 
would land at the same time, ignoring wind resistance.
Coming down a frictionless hill would be the same thing - just a component 
of gravitational force, depending on the angle of the hill, works on the 
skiiers, and the larger weight has a greater force so they both land at 
the same time.  

i.e. F= m1*m2*G/(r^2) = m1*a so a = m2*G/(r^2)  m2 is the earth's mass, G 
is the universal gravitational constant, and r is the distance from the 
mass to the earth's center of mass.

However, there's always some friction between the skis and the hill, and, 
friction is proportional to weight, so if the snow were not real fluffy 
and close to frictionless, the bigger skiier's weight would slow her down.

Go carts in the snow? If the go carts were on a hill where the road is 
smooth, then the mass wouldn't matter if we can ignore friction. They'd 
arrive at the same time. If we can't ignore friction then the heavier cart 
comes in last.
Hope this helps!

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