Part A: The Ski Lift A ski lift is installed at a ski resort to pull skiers up a slope (Figure 1 below). The slope has a constant inclination of a = 7°, a length L = 930 m and the friction coefficient between the snow and the skis is μ = 0.04. When lifting a skier, the bar connecting the skier to the aerial steel rope remains inclined by ẞ = 26° (with respect to the normal to the slope) and is subject to a time-varying tension T. For this exercise consider a skier of mass m = 80 kg. β Bar Skier m Slope x Figure 1 - Ski Lift Schematic Aerial rope x(t) = L sin² t πι 2 tend
1. Draw a FBD of the skier during the lifting process. Ensure you include all forces and a coordinate system.
2. Obtain the equation of motion of the skier as a function of the only unknowns x (and/or its derivatives) and T (ie express all other quantities numerically).
3. The skier starts their journey up the ski lift at t = 0, and they reach the top of the slope at tend=224 s. The skier’s position, x, as a function of time, t, over this time period is given by:
(image of expression)
Obtain the analytical expression of the tension with respect to time and compute the maximum tension value.
Note: The coordinate x is parallel to the slope (in the same direction as the motion of the skier) as marked in the diagram above.
4. Determine an equation for the power exerted from the bar onto the skier with respect to time.
5. Using the power equation, determine how much energy is imparted from the bar to the skier during the lift.
6. The skier then reaches the top of the peak and proceeds to ski down the slope as per the image below.
(Image of Slope)(1.3km in length)
The slope has a length of and is at an incline of . The skier starts at rest at the top of the slope. What coefficient of friction is required between the skis and the snow to bring the skier to rest at the bottom of the slope? You may assume that the kinetic and static coefficients of friction are the same and the skier creates the same level of friction between their skis and the snow the whole way down.
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