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The question is:
A skier of mass 60kg and initially at rest, slides down from the top fo a frictionless icy hemispherical mountain with a radius of 100m.
a) Draw a free body diagram and write the Newton's Equations at the moment when she is at some point below the top of the mountain.
b) Find the angle 'alpha' with the horizontal surface at which she will lose contact with the mountain surface.
Ok so I have my free body diagram set up with the x-axis being tangent to the mountain, and the y-axis along the radius. The angle alpha is measured from the origin of the circle (mountain) which makes the component of the gravitational force mgcos(alpha) tangent to the circle along the direction of motion (to the right from the top of the mountain in my case). The component mgsin(alpha) is along the radius. The Newtons equations in this case are Fx = mgcos(alpha) and Fy = n - mgsin(alpha). This is as far as I've gotten, I think part b has to do with momentum but I cannot think of a way to link this to mg to solve the problem! Any help would be much appreciated. Thanks
Aidan
A skier of mass 60kg and initially at rest, slides down from the top fo a frictionless icy hemispherical mountain with a radius of 100m.
a) Draw a free body diagram and write the Newton's Equations at the moment when she is at some point below the top of the mountain.
b) Find the angle 'alpha' with the horizontal surface at which she will lose contact with the mountain surface.
Ok so I have my free body diagram set up with the x-axis being tangent to the mountain, and the y-axis along the radius. The angle alpha is measured from the origin of the circle (mountain) which makes the component of the gravitational force mgcos(alpha) tangent to the circle along the direction of motion (to the right from the top of the mountain in my case). The component mgsin(alpha) is along the radius. The Newtons equations in this case are Fx = mgcos(alpha) and Fy = n - mgsin(alpha). This is as far as I've gotten, I think part b has to do with momentum but I cannot think of a way to link this to mg to solve the problem! Any help would be much appreciated. Thanks
Aidan