A block of mass m placed on a smooth floor is connected to
a fixed support with the help of a spring of force constant k.
It is pulled by a rope as shown in the figure. Tension T of the
rope is increased gradually without changing its direction,
until the block losses contact the floor. The increase in rope
tension T is so gradual that acceleration in the block can be
neglected.
(a) What is the necessary tension in the rope so that the block looses contact with the floor?
(b) What is the extension in the spring, when the block looses contact with the floor?
a fixed support with the help of a spring of force constant k.
It is pulled by a rope as shown in the figure. Tension T of the
rope is increased gradually without changing its direction,
until the block losses contact the floor. The increase in rope
tension T is so gradual that acceleration in the block can be
neglected.
(a) What is the necessary tension in the rope so that the block looses contact with the floor?
(b) What is the extension in the spring, when the block looses contact with the floor?
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Tension in the string has 2 components
Tsinx and Tcosx
where x is the angle at which block leaves contact
for the block to leave contact from the surface
weight of the block=Tsinx
mg=Tsinx
mg/sinx=T
extension in the spring = Tcosx
kx=Tcosx
x=Tcosx/k
=(mg/sinx)cosx/k
=mgcotx/k
The necessary tension in the rope so that the block loses contact with the floor is mg/sinθ
The extension in the string when the block loses contact with the floor is (mgcotθ)/k