# Total force on upper block in two block system

If a block $$m$$ is placed on another block $$M$$ and a force $$F$$ is applied on bolck $$M$$. Then how many forces are acting on block $$m$$.(Friction is non zero)

The image is taken from this site.

Is pseudo force acting on block $$m$$ or not?

Pseudo-forces only appear if you work in a non-inertial frame of reference.

In this case, you could work in a frame of reference in which the lower block is stationary. Because we know that the lower block is actually being accelerated by the force $$F$$, this must be a non-inertial frame of reference, so pseudo-forces will appear.

In particular, if the upper block does not slip then it is also stationary in this non-inertial frame of reference. In order to "pretend" that the upper block is in equilibrium, we need to introduce a horizontal force that is equal and opposite to the force of friction that the lower block exerts on the upper block. This fictitious force is a pseudo-force - it is only introduced to make the forces on the upper block appear to balance.

As pointed out in other answers, it is actually much simpler to work in an inertial frame of reference, and then you don't need to introduce pseudo-forces at all.

• So, you mean that I need to work w.r.t. ground.Right??? – user75659 Aug 20 at 7:53
• Yes - simples approach is to work in a frame of reference in which the ground is stationary. This is an inertial frame of reference, so you do not need any fictitious forces. – gandalf61 Aug 20 at 9:25

No pseudo-force ever acts on anything. A pseudo-force is - as the name indicates - imaginary and non-existing. It is just a "feeling" or "illusion" of a force. So don't worry about pseudo-forces; just stick to inertial reference frames (references that aren't accelerating), and you never have to worry about them.

In your case, if the bottom block accelerates because of that force $$F$$, then friction - and only friction - acts on the upper block in the horizontal direction. This friction pulls the upper block along with the lower block.

Vertically, there is a normal force as well as gravity, of course. They cancel each other out, so only the friction causes its acceleration.

• So when does pseudo force acts – user75659 Aug 19 at 8:42
• @user75659 They never do. A pseudo-force doesn't exist. – Steeven Aug 19 at 8:44
• You might want to clarify that the friction force will only occur if block $M$ accelerates, which would require that the external force applied to $M$ exceeds the maximum static friction force between $M$ and the bottom surface – Bob D Aug 19 at 8:53
• @BobD Okay, good point. I was assuming from the description, that the system is accelerating. I have added this point to the answer. – Steeven Aug 19 at 8:58
• @Steeven I originally assumed that too until I realized it was never stated or indicated in the diagram – Bob D Aug 19 at 9:05

Three forces act on block $$m$$. (1) the force of gravity acting downward (2) the normal reaction force that block $$M$$ exerts on $$m$$ acting upward and equal to the downward force of gravity and (3) the friction force, if block $$M$$ accelerates, that block $$M$$ exerts on block $$m$$ horizontally in the same direction as as the external force applied to block $$M$$.

An example of a pseudo force is the apparent force you feel pressing you back against your car seat when you accelerate. It’s due to inertia and not some physical object pushing you against your seat. None of the three forces are pseudo forces

Hope this helps