After a particularly cold winter, a chunk of ice sits at the apex of a hemispher

Question

After a particularly cold winter, a chunk of ice sits at the apex of a hemispherical top of a metal silo at a farm in South Dakota. On a warm spring day, the chunk of ice begins to slide down the frictionless surface. If the radius of the cap is R = 15.0 m and the bottom of the cap is at height H = 36.0 m above the ground, find the: (a) height of the chunk of ice, above the ground, at the point that it loses contact with the cap; (b) speed of the chunk of ice at the point that it loses contact with the cap; (c) distance d from the side of the silo where the chunk of ice impacts the ground; (d) speed of the chunk of ice as it hits the ground;

Explanation / Answer

mv2/R=mgcos

mv2/2=mgR(1-cos)

So cos=2(1-cos)

cos=2/3

height from ground=H+Rcos=36+15*2/3 = 46m

b) v=gRcos=10m/s

c) vy=(10sin)2+2g*46=30.5m/s

30.5-10=10t

t=2.05s

10cost=d

d=13.67m

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