In a rollercoaster ride, the vehicle performs a loop-the loop where it turns in

Question

In a rollercoaster ride, the vehicle performs a loop-the loop where it turns in a vertical circle. The maximum velocity of the vehicle will occur at the (bottom, top) of the circle and the minimum velocity of the vehicle will occur at the (bottom, top) of the circle. The force which maintains the motion in a circular path is called the centripetal force where the centripetal acceleration acts (away from, towards) the centre of the circle. The minimum velocity required to successfully complete the full circle will be at the (top. bottom) of the circle when ( cos(theta) = -1, or cos(theta) = +1) and when the normal force between the vehicle and the track tends to (infinity, zero) choices are included in the sentance in (1, 2) format.

Explanation / Answer

From the law of conservation of energy at bottom and top

(½mv²)bottom = mg(2r) +(½mv²)top

So from here we can say velocity will be maximum at the bottom and minimum at the top.

Direction of centripetal force and centripetal acceleration is always directed towards the center of circle.

Minimum velocity required to complete the full circle is at the top of the circle when angle theta is 180° and when angle is 180° then cos(theta) = -1.

At that position N + mg = mv²/r

So in case of v minimum N will be zero.

So normal force between the vehicle and the track tends to zero.

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