a .15 kg block is placed at a point on a curved ramp that is at a height of 2.0

Question

a .15 kg block is placed at a point on a curved ramp that is at a height of 2.0 m above the bottom of a track.    It slides with negligible friction down the track around the inside of a loop of radius .60m and leaves the track at a point whose height is .50 m above the bottom of the track.  

The minimum speed the block has at the top of the loop is 2.4 m/s    

Calculate the minimum height above the bottom of the track at which the block can be released and still go around the loop without losing contact with the track.

Explanation / Answer

If you use conservation of energy it is completely independent of the path... even if there's a loop.

mgh =.5mv^2

a) 5.42m/s

b) Weight and normal force both acting downwards

c)minimum speed is when centripetal force = gravity or mv^2/r = mg

v^2/r = g

v^2/.6 =9.8

v= 2.42m/s

d) mgh = .5mv^2 where you we set the top of the circle as the reference level. set v equal to 2.42 and solve h... then add that h to 1.2 to get the height above the bottom of the track

1.5m

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