As shown in the figure below, a block of mass m starts from rest and slides on a
ID: 1285104 • Letter: A
Question
As shown in the figure below, a block of mass m starts from rest and slides on a frictionless loop-the-loop track with a loop radius of r. Determine the minimum release height h in order for the block to maintain contact with the track at all times. Express your answer in terms of the radius of the loop, r.
As shown in the figure below, a block of mass m starts from rest and slides on a frictionless loop-the-loop track with a loop radius of r. Determine the minimum release height h in order for the block to maintain contact with the track at all times. Express your answer in terms of the radius of the loop, r.Explanation / Answer
let v is the minimum speed.
m*v^2/r = m*g
v^2/r = g
v = sqrt(g*r) --(1)
but we know, v = sqrt(2*g*(h-2*r)) --(2)
from equations 1 and 2, we get
g*r = 2*g*(h-2*r)
r = 2*h - 4*r
h = (5/2)*r
= 2.5*r <<<<<<----------Answer
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