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Energy conservation, centripetal acceleration and force, and projectile.

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Energy conservation, centripetal acceleration and force, and projectile.
A circular pipe whose radius R= 10 m, has a frictionless surface. A small frictionless mass placed on its highest point, slides down to a point where it loses contact, then travels in free fall to impact on the ground.
See the diagram in the attachment.

a. Find the angle b from vertical to a
radius from center to the small mass
at the instant it loses contact.
b. For an x,y origin at the point where it
loses contact, find the x and y
coordinates of the impact point on the
ground.
See diagram on the attachment.

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Solution Summary

Energy conservation, centripetal acceleration and force, and projectile are focal topics.

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Solution with explanation.
a. From rest at the highest point, the mass slides down the surface gaining speed. After leaving the starting point but before losing contact, say when the the mass m has described angle c, the two forces on mass m are: mg vertically downward, and normal force N outward along a radius. as shown by Fig. 2 in the problem attachment. At this point, Newton's second law, "Fc = m ac" for the radial direction, is expressed by:
(1) m g ...

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