Spring Clamps
Find the distance of the cushioning spring?
The cable of an elevator of mass M = 1690 kg snaps when the elevator is at rest at one of the floors of a skyscraper. At this point the elevator is a distance d = 31.0 m above a cushioning spring whose spring constant is k = 21100 N/m. A safety device clamps the elevator against the guide rails so that a constant frictional force of f = 11409 N opposes the motion of the elevator. Find the maximum distance by which the cushioning spring will be compressed.
Use (K + U)1 + W outside = (K + U)2…here K1 + K2 = 0..
Set y = 0 when the spring is completely compressed
U1 = m*g*(31 + y) where y is the compression distance
W = -11409*(31 + y)
U2 = 1/2*k*y^2
So m*g*(31 + y) – 11409*(31 + y) = 1/2*k*y^2
So 1/2*21100*y^2 + (11409 – 1690*9.8)y + (-1690*9.8*31 +11409*31) = 0
10550y^2 -5153y – 159743 = 0
y = (5153 +-sqrt(5153^2 – 4*10550*(-159743)))/(2*10550) = 4.14m
Bessey Clippix Spring Clamp Review
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