A roller coaster is designed such that riders experience "weightlessness...

Q.A roller coaster is designed such that riders experience "weightlessness as they go round the top of a hill whose radius of curvature is 20 m. The speed of the car at the top of the hill is between

AIPMT/NEET 2008| W.P.E Q 3 | In case of vertical circular motion , we require a minimum velocity at lowest position of circle to complete the circle. For any value of velocity greater than this , particle can easily complete its circular motion and at the minimum value of this velocity , normal force ( in other cases it could be tension force ) becomes zero .Even at zero normal reaction force ( in other cases it could be tension force ) particle will not fall towards the centre since it will has some velocity So it will cross that weightlessness . you must know about this if you had subscribed my channel because I already posted these conditions in my twisted qus videos with solution of Q 3 Aipmt/Neet 2004. Only difference , tension force was mentioned instead of normal force.

In this case Mechanical energy will remain conserved because normal will always act perpendicular to displacement i.e direction of velocity so its work done will be zero. Gravity is a conservative force and there is no non-conservative force present .

Conservation of Mechanical Energy

The work-energy theorem, shows that the change DKE in a body’s kinetic energy is equal to the net work done on it :
 DKE = Wnet
Consider separately the work Wc done by conservative force and the work Wnc done by nonconservative forces. Then
DKE = Wc+ Wnc
We’ve defined the change in potential energy DU as the negative of the work done by conservative forces. So we can write
DKE = – DU + Wnc
or DKE + DU = Wnc
We define the sum of the kinetic and potential energy as the mechanical energy. Then Equation shownthat the change in mechanical energy is equal to the work downe by non-conservative forces.
i.e. DE = Wnc
D \E = 0 if Wnc= 0
Thus if work done by non-conservative forces is zero the mechanical energy of the system is unchanged.
This called law of conservation of mechanical energy. It may also be written as
DU + DK E = 0
or DU = – DKE
or U + K E = constant
or Uin + K Ein = Uf + K Ef

We will take initial position at lowest position , where speed is given as ‘ u ‘ and final position where string will be perpendicular to vertical.

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