Olympic cross country ski champion, Henrik Henrikson, is using a new ski wax, Gripola,
that is supposed to stop his ski from slipping backwards when he pushes off against the snow (it gives him a
coefficient of static friction between the ski and the snow of 0.20). While skiing, he applies a 1200 N force,
directed downwards and backwards, at an angle of 70 to the horizontal (see figure). Based on this
information, what is: a) the magnitude of the normal reaction force (FR) between the ski and the snow, b)
the magnitude of the force trying to cause sliding (FSLIDE) between the ski and the snow, and c) what is the
magnitude of the limiting value of friction (FLIM)?
To find the answers to these questions, we will use the given information and some basic principles of physics.
a) The normal reaction force (FR) is the force exerted by the snow on the ski, perpendicular to the ski surface. It can be found using the vertical component of the applied force.
Given:
Force applied = 1200 N
Angle with the horizontal = 70 degrees
Using trigonometry, we can find the vertical component of the applied force:
Vertical component = Force applied * sin(angle)
= 1200 N * sin(70 degrees)
≈ 1164.94 N
Therefore, the magnitude of the normal reaction force (FR) between the ski and the snow is approximately 1164.94 N.
b) The force trying to cause sliding (FSLIDE) between the ski and the snow can be found using the horizontal component of the applied force.
Horizontal component = Force applied * cos(angle)
= 1200 N * cos(70 degrees)
≈ 406.31 N
Therefore, the magnitude of the force trying to cause sliding (FSLIDE) between the ski and the snow is approximately 406.31 N.
c) The limiting value of friction (FLIM) can be found using the coefficient of static friction and the normal reaction force.
FLIM = Coefficient of static friction * FR
= 0.20 * 1164.94 N
≈ 232.99 N
Therefore, the magnitude of the limiting value of friction (FLIM) is approximately 232.99 N.
Note: It's important to mention that these calculations assume that the ski is on a horizontal surface and the force is applied in that direction.