In the figure, block 1 of mass m1 slides from rest along a frictionless ramp from height h = 2.4 m and then collides with stationary block 2, which has mass m2 = 2m1. After the collision, block 2 slides into a region where the coefficient of kinetic friction μk is 0.2 and comes to a stop in distance d within that region. What is the value of distance d if the collision is (a) elastic and (b) completely inelastic?
Height of ramp
Energy of block 1 at that height is (potential energy)
Energy of block 1 at the bottom of ramp is
Conserving the energy of block 1 at two positions,
a) Elastic collision.
Velocity of block 1 before collision is and velocity of block 2 before collision is zero.
Conserving the momentum of the two blocks before and after collision,
---(1)
For elastic collision ----(2)
Solving (1) and (2) and
With velocity block travels a distance with friction coefficient until it stops.
Conserving the energy of mass ,
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b) Inelastic collision
Velocity of block 1 before collision is and velocity of block 2 before collision is zero.
Conserving the momentum of the two blocks before and after collision,
Now both masses together travel a distance until they stop on the frictional surface.
Conserving the energy of mass ,
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In the figure, block 1 of mass m1 slides from rest along a frictionless ramp from...
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