- #1
Tanya Sharma
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Homework Statement
A symmetric block of mass M1 with a groove of hemisphere shape of radius R rests on a smooth horizontal surface in contact with the wall as shown in the figure. A small block of mass m2 slides without friction from the initial position .Find the maximum velocity of the block M1.Describe the motion of both the blocks M1 and m2. ( M1=100 Kg m2=10kg R=5m g=10m/s2).
Homework Equations
The Attempt at a Solution
Initially m2 is is at 1 and slides down to 2 .Since M1 has a wall towards its left side ,the wall exerts a force on M1 till m2 reaches 2 because m2 pushes against M1.So momentum of two block system can not conserved till m2 reaches 2.Afterwards , momentum can be conserved taking initial momentum when m2 is at 2.
Velocity of m2 at 2 can b found using conservation of energy between points 1 and 2.
Loss of potential energy = Gain in Kinetic energy
velocity of m2 at 2 = 10m/s
Now I have a doubt here when block m2 moves from 2 to 3...If we consider only m2 then kinetic energy of m2 at 2 should completely convert in Potential energy at 3 which gives the height to which the block rises i.e R. This means block m2 moves back and forth between 1 and 3.
But if conservation of momentum is applied then as block m2 moves from 2 to 3 the block M1 also moves ie when m2 reaches 3 then M1 is moving and m2 is at rest w.r.t M1
Applying conservation of energy
Loss in Kinetic energy of m2 =Gain in potential energy of m2 + gain in kinetic energy of (M1+m2).
This gives height to which block m2 rises less than R .
Why two different results...
Where am I getting it wrong?