# Direction of motion under the influence of friction

• sachin
In summary, the assumption made is that there will be kinetic friction acting on the left and equal and opposite friction acting on the right, so the block will move to the right keeping the center of mass moving with velocity mv/(m + M) to the right. If A stops, then B will move with higher speed to keep the velocity of the center mass constant.
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 ?

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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.)

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

sachin said:
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.

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

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

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.

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yes,hope the common velocity will be greater than the initial velocity v of A.
Doc Al said:
I assume you mean: If A stops relative to Block B. (They end up moving with a common velocity.)

sachin said:
yes,hope the common velocity will be greater than the initial velocity v of A.
No. Hint: You already calculated the final common velocity.

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.

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

sachin said:
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.

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

## 1. What is friction and how does it affect the direction of motion?

Friction is a force that opposes motion between two surfaces in contact. It acts in the opposite direction of the applied force and can cause an object to slow down, change direction, or stop altogether.

## 2. How does the amount of friction affect the direction of motion?

The amount of friction depends on the nature of the surfaces in contact and the force pressing them together. Generally, the greater the friction, the more it will oppose the direction of motion.

## 3. Can friction ever cause an object to change direction?

Yes, friction can cause an object to change direction if the force of friction is greater than the applied force in the original direction. This is often seen in situations where an object is sliding on a curved surface.

## 4. How does the direction of motion change when there is no friction?

When there is no friction, an object will continue to move in a straight line at a constant speed in the direction of the applied force. This is known as Newton's First Law of Motion.

## 5. How can we reduce the effect of friction on the direction of motion?

One way to reduce the effect of friction is by using lubricants, such as oil or grease, to create a slippery layer between two surfaces. Another way is by using smoother surfaces or reducing the force pressing the surfaces together.

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