A small solid metal sphere, with a mass m and radius r, is placed on the inclined section of the metal track shown below, such that its lowest point is at a height h above the bottom of the loop. The sphere is the released from rest, and it rolls on the track without slipping. In your analysis, use the approximation that the radius r of the sphere is much smaller than both the radius R of the loop and the height h. (Use the following as necessary: M, R, and g for the acceleration of gravity.) Solid sphere of mass m and radius r<< R. R (a) What is the minimum value of h (in terms of R) such that the sphere completes the loop? hmin = for R »r (b) What are the components of the net force on the sphere at the point P if h = 3R? Use above the horizontal section of the track.) coordinate system where the +x-direction is to the right and the +y-direction is up. (Assume point P has a height R
A small solid metal sphere, with a mass m and radius r, is placed on the inclined section of the metal track shown below, such that its lowest point is at a height h above the bottom of the loop. The sphere is the released from rest, and it rolls on the track without slipping. In your analysis, use the approximation that the radius r of the sphere is much smaller than both the radius R of the loop and the height h. (Use the following as necessary: M, R, and g for the acceleration of gravity.) Solid sphere of mass m and radius r<< R. R (a) What is the minimum value of h (in terms of R) such that the sphere completes the loop? hmin = for R »r (b) What are the components of the net force on the sphere at the point P if h = 3R? Use above the horizontal section of the track.) coordinate system where the +x-direction is to the right and the +y-direction is up. (Assume point P has a height R
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Transcribed Image Text:A small solid metal sphere, with a mass m and radius r, is placed on the inclined section of the metal track shown below, such that its lowest point is at a height h above the bottom of the loop. The sphere is then
released from rest, and it rolls on the track without slipping. In your analysis, use the approximation that the radius r of the sphere is much smaller than both the radius R of the loop and the height h. (Use the
following as necessary: M, R, and g for the acceleration of gravity.)
Solid sphere of mass m
and radius r<< R.
h
R
P
(a) What is the minimum value of h (in terms of R) such that the sphere completes the loop?
hmin =
for R » r
(b) What are the components of the net force on the sphere at the point P if h = 3R? Use a coordinate system where the +x-direction is to the right and the +y-direction is up. (Assume point P has a height R
above the horizontal section of the track.)
Efy =
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