Question

A horizontal block 'A' is at rest on a smooth horizontal surface. A small block B, whose mass is half of A, is placed on 'A' at one end and projected along other end with
some speed 'vo'. The coefficient of friction is u. Then
[Assume that the block 'B does not fall from block A]
B
V.
A
Smooth​

Answer 1

Answer:

As there are no external forces acting on the 'A + B' system, its total momentum is conserved. If the masses of A and B are 2m and 2 respectively, and v is the final common velocity, mu=(m+2m)v or v=u/3

Work done against friction = loss in KE =

2

1

mu

2

−

2

1

(3m)v

2

=

2

1

mu

2

−

2

1

(3m)

9

u

2

=

2

1

mu

2

[1−

3

1

]=

3

2

×

2

1

mu

2

The force of friction between the blocks is μmg.

Acceleration of A (to the right) =a

1

=

2m

μmg

=

2

μg

Acceleration of B (to the left) =a

2

=

m

μmg

=μg

Acceleration of A relative to B =a

1

−(−a

2

)=

2

3

μg.