figure shows a smooth horizontal track ,a part of which is a vertical circle of radius 1.0 m . a block of mass 0.1 kg is pushed against a spring of spring constant 300 N/m fixed at one end.the initial compression of the spring so that the block presses the track with the force of 1.0 N when reach the point p
a. 0.1 m
b. 0.2 m
c. 0.3 m
d. 0.4 m
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Answer:
Figure shows a smooth track, a part of which is a circle of radius r. A block of mass m is pushed against a spring of spring constant k fixed at the left end and is then released. Find the initial compression of the spring so that the block presses the track with a force mg when it reaches the point P where the radius of the track is horizontal.
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ANSWER
Given, N=mg
From the figure, the force of gravity and the centripetal force remains balanced on the topmost point.
R
mv
2
=mg
thus,
⇒v
2
=gR
For compression at point P, the block must be pushed with some amount of energy, this energy can be called as total energy.
∴Total energy at point A=energy at p
2
1
kx
2
=
2
1
mv
2
+mgR
⇒
2
1
kx
2
=
2
mgR+2mgR
(because v
2
=gR)
⇒x
2
=
k
3mgR
⇒x=
k
3mgR