A block A having a mass m A = 3kg is released from rest at the position P shown and slides freely down the smooth fixed inclined ramp. When it reaches the bottom of the ramp it slides horizontally onto the surface of a cart of mass m c = 2kg for which the coefficient of friction between the cart and the block is µ = 
. If h = 6m be the initial height of A, determine the position ‘x’ (with respect to cart) of the box on the cart after it comes to rest relative to cart. (The cart moves on smooth horizontal surface.)
Text Solution
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(6)
Velocity of A after falling height h V A = 
.
Applying momentum conservation
m a V A = (m a + m c ) V
V = 
using work energy theorem.
μ m a g x = 
m a V A 2
2 μ m a g x = (m a + m c ) 
– m a V a 2
2 μ gx. ma = 
2 μ g x = 
2 μ gx = 
⇒ x = 
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