The blocks A and B have equal masses. The surface of A is smooth but that of B has a friction coefficient of 0.1 with the floor. Block A is moving at a speed of 10 m/s towards B which is kept at rest. Find the distance travelled by B if (a) the collision is perfectly elastic and (b) the collision is perfectly inelastic. g=10 m/s2 .
a) In a lab frame of reference,
Velocity of center of mass is given by,
Now, in center of mass frame of reference,
Since, there will be perfectly elastic collision. After collision, they exchange their velocity.
In lab frame of reference,
Deceleration due to the friction = µg
From kinematics we have,
Since the final velocity of B is zero, we get t=10s.
Distance travelled d is given by,
d = VBt - (µgt2)/2
Inserting given values, the distance travelled by block is 50m.
b) After perfectly inelastic collision, both blocks A and B travel as a combined mass.
We get, initial velocity of the combined mass 5m/s.
The friction of the block B will have affect whole body.
Then we have,
d = VABt - (µgt2)/2
Solving the equations, the distance travelled by the body is 12.5m.
Work-Energy Theorem can also be used to find the distance.