How Can a Stationary Top Block Accelerate with the Bottom Block?

[DavidOB18]

Homework Statement

A lighter block lies on top of a heavier block. There is static friction between the 2 blocks. You apply a force to the bottom block. Find the maximum horizontal force that can be applied.

Relevant Equations

Accelerations are the same

I know the answer but don't understand the concept. The solution says the accelerations are the same but if the top block is at rest how can it be accelerating. I know you can view both blocks as the same system but can you not study them independently. Any help would be appreciated.

 

[PeroK]

Homework Statement: A lighter block lies on top of a heavier block. There is static friction between the 2 blocks. You apply a force to the bottom block. Find the maximum horizontal force that can be applied.
Homework Equations: Accelerations are the same

I know the answer but don't understand the concept. The solution says the accelerations are the same but if the top block is at rest how can it be accelerating. I know you can view both blocks as the same system but can you not study them independently. Any help would be appreciated.

What does "accelerating" mean? How can you tell if something is accelerating or not?

 

[DavidOB18]

Acceleration is the rate of change if velocity with time but I think the velocity is 0 so there is no acceleration.

 

[PeroK]

Acceleration is the rate of change if velocity with time but I think the velocity is 0 so there is no acceleration.

Okay. So, both blocks are at rest? No force, no acceleration, so what's the problem?

 

[DavidOB18]

In the problem you apply a force to the bottom block with the lighter block on top and both accelerate.

 

[PeroK]

In the problem you apply a force to the bottom block with the lighter block on top and both accelerate.

That sounds straightforward. The blocks move together.

 

[DavidOB18]

Yes but I don't understand how the top block remains at rest but is accelerating at the same time

 

[PeroK]

Yes but I don't understand how the top block remains at rest but is accelerating at the same time

It can't. It's being pulled along by the first block.

How is the second block any different from the first? The first block is "at rest" relative to itself but accelerating relative to the ground. The second block is at rest relative to itself and the first block, but accelerating relative to the ground.

Also, there is no fundamental difference between the second block and the molecules that make up the first block. You could look at the first block as a large number of particles, all bound together in some way and all being pulled along together. The second block is another set of particles.

The only difference is that the bond between the blocks is only friction and will give way long before the blocks themselves are torn apart by pure acceleration.

 

[DavidOB18]

OK I get it now, thank you for your help.

 

[PeroK]

OK I get it now, thank you for your help.

I'll answer the question you didn't:

How can you tell if something is accelerating or not?

You can tell if something is accelerating if it is subject to an unbalanced force. Or, in other words, if the sum of forces on it is non-zero.

The second block in this case has balanced forces in the vertical direction (gravity and the normal force), but a single unbalanced force in the horizontal direction. Therefore, it is accelerating in the horizontal direction.

(Newton's first law, in fact!)