Like many things in life Newton's Second
Law can be applied to snowboarding. The two forces that snowboarders
encounter are those of gravity and friction. When a snowboarder is
going down a hill or mountain he uses the force of gravity and the
decreased friction of the snow to reach top speeds. By applying
Newton's Second Law of F=ma you can calculate speed and acceleration of
a snowboarder going down a hill.
clip art from clker.com
clip art from clker.com
The
figure above shows a free body diagram for a snowboarder going down a
hill at an angle θ. The gravitational force points down and has a
magnitude of MG, where M=mass of the snowboarder and G=Gravity (9.81
m/s²). The force along the plane of the hill is given by mgsinθ
and the normal force is shown equal to mgcosθ. Friction is equal to the
coefficient of kinetic friction (uk) times the normal force, so in this
situation the force of friction would be: Fk=-ukmgcosθ (minus sign
meaning the force in the negative x-direction). So for the total force
in the x-direction we get:
1) mgsinθ-ukmgcosθ=ma
1) mgsinθ-ukmgcosθ=ma
Solving for acceleration: 2) a= g(sinθ-ukcosθ)
If you wanted to solve for the
velocity of the snowboarder you could use the kinematic equation of
vf²=vi²+2a(xf-xi)
Solving for vf (final velocity)
vf=√vi²+2a(xf-xi)
Solving for vf (final velocity)
vf=√vi²+2a(xf-xi)
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