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```Exercise (3)
(Circular Motion)
1.
H
A
B
30 m
20 m
Terminal
platform
The diagram shows part of the route of a roller-coaster in an amusement park.
The cart descends from H, completes a circular loop A and moves to B. If the cart
of passengers is to complete the central circular track safely, what is the minimum
velocity of the cart at the bottom of the circular track A?
(Assume that there is no
friction between the cart and the track.)
2.
A
30o
B
A smooth conical container rotates about the axis AB as shown. A marble remains
at rest relative to the container at a radial distance r from the axis. If the velocity
of the marble is v, Find v²
.
3. Assuming the Earth to be a perfect sphere, what would its angular velocity of
rotation have to be for an object at the equator to be weightless (i.e. to give a
spring balance reading of zero)?
(Radius of the Earth = 6.4  106 m.)
4.
A
10 m
B
C
A sphere is projected downwards from A with a speed of 10 m/s at an angle of
30º to the horizontal.
The sphere rebounds from the ground, first at B and then
at C. If the collisions are perfectly elastic, find the horizontal distance BC .
1
```
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