# Velocities of two blocks to be in contact with each other in a curved path

The figure shows a small block of mass m which is given a velocity v on the horizontal part of a bigger block of mass M slides on the bigger block,all the surfaces are frictionless and the curved part is semicircular,

the question asks to find the velocity of the bigger block when the smaller block reaches the point A.

the solution to the question is as follows,

as there is no external force in the horizontal direction, the linear momentum of the system will be conserved along the horizontal direction,

At the point A the net velocity of the smaller block wirh respect to the bigger block is only upward,

so its horizontal relative velocity wrt the bigger block is 0, so both blocks move to the left with the same velocity v',

so $$m v = ( m v' + M v') = ( m + M ) v'$$

$$v' = mv/(m + M )$$

this solves the problem, my concern is,

for any other point in the curve,for the blocks to be in contact,will the horizontal velocities of both blocks be the same ?

Will the process and answer remain the same for any other point in the curved path or it will change,if it changes how will it change.

this is the question number 29 of chapter 9 from the book "concepts of physics" by h.c verma from the section center of mass,linear momentum and collision.

Remember that momentum of the whole system must be conserved. The questions you should ask are:

What is the starting momentum of the small block.

What is the momentum of the small block when it is at Point A.

The difference in those two (change in momentum of the smaller block) must have been transferred to the large block.

Now that you have the larger block's momentum at that time, what speed does that correspond to for the large block?

To answer your other question, no there is no reason for the horizontal speeds to be the same at the contact surface asv there is no friction.

• can we work on conservation of energy,I dnt know where to use conservation of energy,most of the times its used for a system but work energy theorem talks about a single body,if we can use energy conservation here then how to know it should be used. Aug 21, 2022 at 8:16
• Conservation of energy does not really help you solve the problem in this case. It just tells you $0.5mv^2=0.5mv'^2+0.5MV'^2$, which has infinite possible answers (remember all velocities are total, including vertical). Sometimes momentum or energy alone constrains the answer, sometimes you need both together. It all depends on the situation. Aug 22, 2022 at 18:10