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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

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

International Edition---engineering Mechanics: Statics, 4th Edition
International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:Andrew Pytel And Jaan Kiusalaas
Chapter9: Moments And Products Of Inertia Of Areas
Section: Chapter Questions
Problem 9.46P
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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:

 

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. 

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
Transcribed Image Text: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
Transcribed Image Text:x(t) = L sin² t πι 2 tend
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