Direction of motion under the influence of friction

[sachin]

Homework Statement

In the figure,a small block A rests on a bigger block B which rests on the ground,there is friction between A and B,but the ground is frictionless.
If the block A is given a velocity v to the right,which way B will move,to the left or to the right ?

Relevant Equations

coefficient of kinetic friction between A and B is non zero.

My assumption says,as A moves to the right,there will be kinetic friction acting on it to the left and equal and opposite friction will act on B to the right,so it should move to the right keeping the center of mass go on moving with velocity mv/(m + M) to the right as there is no net external force acting on the system and

if A stops,then B will move with higher speed to keep the velocity of the center mass constant.

Is my assumption correct ?

 

[Doc Al]

Your thinking is partly correct. If A has an initial velocity to the right, it will exert a friction force on B to the right. If no external forces act on the system, the velocity of the center of mass will remain constant. But what is that velocity? (It's not the initial velocity of block A.)

 

[sachin]

yes,the velocity of center of mass is mv/(m + M ),so B moves to the right ?

 

[Doc Al]

yes,the velocity of center of mass is mv/(m + M ),so B moves to the right ?

Yes. B moves to the right, dragged along by A.

 

[sachin]

have edited the question with velocity of center of mass and some typing errors.

 

[Doc Al]

if A stops

I assume you mean: If A stops relative to Block B. (They end up moving with a common velocity.)

 

[sachin]

just a query,in this picture also the bigger block should go on going to the left if there is friction or not between A and B in the horizontal part,center of mass should go on going to the left,the small block given an intial velocity v to the left.

 

[sachin]

yes,hope the common velocity will be greater than the initial velocity v of A.

I assume you mean: If A stops relative to Block B. (They end up moving with a common velocity.)

 

[Doc Al]

yes,hope the common velocity will be greater than the initial velocity v of A.

No. Hint: You already calculated the final common velocity.

 

[sachin]

equalising mv/(m+M) = (mv1+Mv1)/(m+M)= (m+M)v1/(m+M),
so mv = (m+M)v1,v1 should be less than v,v1 being the common velocity.

 

[Doc Al]

Yes. You calculated the velocity of the center of mass earlier. That's the common velocity, which is less than A's initial velocity.

 

[SammyS]

just a query, in this picture also the bigger block should go on going to the left if there is friction or not between A and B in the horizontal part, center of mass should go on going to the left, the small block given an initial velocity v to the left.

You should include in your post that you are referring here to another thread which you have posted.
https://www.physicsforums.com/threads/applying-the-work-energy-theorem-to-a-system.1045222/

It's also helpful for readers of your thread for you to include a full size version of that image.