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A skier is pulled by a rope exerting a horizontal force T=[T] KN at a distance h= [h] cm above the centre of mass (see figure). The skier's body is modelled as one rigid body with a mass m= 80 kg with mass moment of inertia of /=15 kg m² about the centre of mass located above the ski boots. The kinetic friction coefficient between snow and ski is 0.1. The distance d=1 m is between the boot location on the skier and the centre of mass (see figure). Note that load T can cause the skier to slide or tip. Include all handwritten solutions and free-body diagrams. Show all your workings; final results without working will not receive marks. Assume g = 10 m/s². A. Determine the equations to solve the dynamics of a sliding skier at the centre of mass. Justify all assumptions in the used equations. List all unknown variables and number the equations. Solve the equations and analyse the correctness of the sliding assumption. B. Determine the critical load T which causes the skier to tip over during motion. Justify the choice of tipping point. C. Determine the equations to solve the dynamics of a skier on the verge of tipping at an assumed force T-3 kN. List all unknown variables and number the equations. Do not solve the equations. D. Now the situation changes; the skier is holding the rope below the skier's centre of mass at a distance of h=-[h] cm. Determine the critical load T causing the tipping over of the skier.

A skier is pulled by a rope exerting a horizontal force T=[T] KN at a distance h= [h] cm above the centre of mass (see figure). The skier's body is modelled as one rigid body with a mass m= 80 kg with mass moment of inertia of /=15 kg m² about the centre of mass located above the ski boots. The kinetic friction coefficient between snow and ski is 0.1. The distance d=1 m is between the boot location on the skier and the centre of mass (see figure). Note that load T can cause the skier to slide or tip. Include all handwritten solutions and free-body diagrams. Show all your workings; final results without working will not receive marks. Assume g = 10 m/s². A. Determine the equations to solve the dynamics of a sliding skier at the centre of mass. Justify all assumptions in the used equations. List all unknown variables and number the equations. Solve the equations and analyse the correctness of the sliding assumption. B. Determine the critical load T which causes the skier to tip over during motion. Justify the choice of tipping point. C. Determine the equations to solve the dynamics of a skier on the verge of tipping at an assumed force T-3 kN. List all unknown variables and number the equations. Do not solve the equations. D. Now the situation changes; the skier is holding the rope below the skier's centre of mass at a distance of h=-[h] cm. Determine the critical load T causing the tipping over of the skier.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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A 65 T 100 B d A skier is pulled by a rope exerting a horizontal force T=[T] kN at a distance h= [h] cm above the centre of mass (see figure). The skier's body is modelled as one rigid body with a mass m= 80 kg with mass moment of inertia of /=15 kg m² about the centre of mass located above the ski boots. The kinetic friction coefficient between snow and ski is 0.1. The distance d=1 m is between the boot location on the skier and the centre of mass (see figure). Note that load T can cause the skier to slide or tip. Include all handwritten solutions and free-body diagrams. Show all your workings; final results without working will not receive marks. Assume g = 10 m/s². A. Determine the equations to solve the dynamics of a sliding skier at the centre of mass. Justify all assumptions in the used equations. List all unknown variables and number the equations. Solve the equations and analyse the correctness of the sliding assumption. B. Determine the critical load T which causes the skier to tip over during motion. Justify the choice of tipping point. C. Determine the equations to solve the dynamics of a skier on the verge of tipping at an assumed force T=3 kN. List all unknown variables and number the equations. Do not solve the equations. D. Now the situation changes; the skier is holding the rope below the skier's centre of mass at a distance of h=-[h] cm. Determine the critical load T causing the tipping over of the skier.
Transcribed Image Text:A 65 T 100 B d A skier is pulled by a rope exerting a horizontal force T=[T] kN at a distance h= [h] cm above the centre of mass (see figure). The skier's body is modelled as one rigid body with a mass m= 80 kg with mass moment of inertia of /=15 kg m² about the centre of mass located above the ski boots. The kinetic friction coefficient between snow and ski is 0.1. The distance d=1 m is between the boot location on the skier and the centre of mass (see figure). Note that load T can cause the skier to slide or tip. Include all handwritten solutions and free-body diagrams. Show all your workings; final results without working will not receive marks. Assume g = 10 m/s². A. Determine the equations to solve the dynamics of a sliding skier at the centre of mass. Justify all assumptions in the used equations. List all unknown variables and number the equations. Solve the equations and analyse the correctness of the sliding assumption. B. Determine the critical load T which causes the skier to tip over during motion. Justify the choice of tipping point. C. Determine the equations to solve the dynamics of a skier on the verge of tipping at an assumed force T=3 kN. List all unknown variables and number the equations. Do not solve the equations. D. Now the situation changes; the skier is holding the rope below the skier's centre of mass at a distance of h=-[h] cm. Determine the critical load T causing the tipping over of the skier.
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