Friction force direction question

[SidewaysA]

Homework Statement

Block A slides on a frictionless ramp, as shown (in the attachment). At the instant, the block is moving up the ramp with speed V. Block B rests on top of A, and does not slip, due to friction between A and B. What is the direction of the friction force acting on B?

Homework Equations

F=ma

The Attempt at a Solution

In order for the block B to move it has to have a net force on it, so I assume that the only way for this to happen is if the frictional force is directed up the ramp?

 

[ehild]

In order for the block B to move it has to have a net force on it, so I assume that the only way for this to happen is if the frictional force is directed up the ramp?

The force of friction acts along the plane of contact between the blocks. This plane is horizontal, so the force of friction has to be horizontal, but it can be directed to the right or to the left. Which one?
There is also a vertical force that rises block B. Where does it come from?

ehild

 

[SidewaysA]

In order to move to the left, it'd have to have a force of friction to the direction of the left. However, wouldn't that imply that it'd accelerate instead of going at constant speed? I assumed that in order for block B to not fall off, it'd have to have the same speed/acceleration. In this case, is the normal force on B not equal to the force of gravity on B?

 

[ehild]

In order to move to the left, it'd have to have a force of friction to the direction of the left. However, wouldn't that imply that it'd accelerate instead of going at constant speed? I assumed that in order for block B to not fall off, it'd have to have the same speed/acceleration. In this case, is the normal force on B not equal to the force of gravity on B?

You do not need force for moving with constant velocity. The blocks move with some acceleration, and the force is needed to accelerate them. The blocks move upward on the slope, but what is the direction of acceleration?
Block B has both horizontal and vertical components of acceleration. The resultant of the normal force and gravity has to be equal to its vertical acceleration times mass.
But friction is only involved in the horizontal component of acceleration: is the direction to the right or to the left?

ehild

 

[SidewaysA]

The direction of the frictional force would have to be towards the left.

 

[ehild]

That would mean acceleration upward along the slope. What is the acceleration of an object along a slope if you give an initial upward push to it? Imagine a ball kicked so as it stays on the ground. It will move upward, but will it move with increasing speed?

ehild

 

[SidewaysA]

So the speed is to the left, but the acceleration is to the right in this case?

 

[NascentOxygen]

Is there any clue in the question to suggest the masses are being acted on only by gravity?

 

[ehild]

So the speed is to the left, but the acceleration is to the right in this case?

Yes, it is.

ehild