What happens with Newton's second law when a body is not moving?(a=0)

Reply Sat 17 Oct, 2020 06:24 am
So after encountering a physics problem I had bumped into the following issue.

Let's say I want to push a skyscraper with my hands.
I will push the building with a constant force of F = 10 N let's say
The building of course, it does not move because I am too weak so this theoretically means that the acceleration of the building is 0.

https://postimg.cc/QKGr1R8x here is the drawing that I made for a better visualization of what I am saying

Newton's second law says that :

`The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.`

This means(in my humble opinion), that the building's acceleration is equal to the resulting force divided by its mass.
The resultant force would be F - Ff(friction force)

The thing is that even though I change the force to let's say F = 20N the building will not move, and the building's acceleration will still be 0.

After writing down the forces on the sky scraper object I reached the conclusion that F = µmg, in order for the acceleration be 0 on the X axis.

But this does not feel right, I mean they are clearly not equal. And the formula does not really express the reality. I must have done something wrong, I am sure of that but what though?

My intuition says that the formula should hold as an inequality, thus
the force F shoud be less then the friction force( F < Ff = µmg, m = the mass of the building)

This is my first post. I want to learn physics and understand every detail of it.
I posted a paint showing the steps I took to reach the formulas.

Thanks for reading and I hope you don't laugh at the silliness of the question
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Reply Sat 17 Oct, 2020 08:57 am
1. You might be confusing "moving" with "acceleration". When you say "a=0" that means that it isn't accelerating. Something can be moving but not accelerating. An example of this is when I drive my car down the highway at a constant speed of 65 mph hour. My car is definitely moving. But it is not accelerating (until I hit the gas pedal).

2. The key here is "net force". Sky scrapers are (generally) firmly attached to the ground. Your diagram is correct. When you press on the skyscraper, the skyscraper presses on the ground (i.e. the planet). The ground doesn't give... so it pushes back with the same force. So the net force is 0. When the net force is 0 the building doesn't accelerate.

3. Just to warn you, there is something confusing with Newton's third law. The fact the ground pushes on the building with the same force is not directly related to the third law. Make sure you understand the difference.

4. If we dug up this skyscraper, and put it on frictionless wheels... then you would be able to move it by pushing on it. In this case it would not be attached firmly to the planet, there would be no friction force opposing your push, and the building would accelerate when you pushed on it.
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Reply Sat 17 Oct, 2020 09:09 am

One more thing, You are using the coefficient of static friction. The word "static" means that the object isn't currently in motion, and static friction is a force that resists any motion. In order to resist motion... it has to give the force necessary to ensure that the net force is 0 (or else the building will accelerate).

You can think of the static friction as a maximum. When an object is not in motion, the static friction will provide a "cancelling force" (the amount needed to balance out your force) up until this maximum. At that point the object will start moving.

You can experiment with this easily if you have a book and a table. Put the book on the table... and push gently on the side of the book with your finger (horizontally). You will notice that you can put a certain amount of force on the side of the book without it sliding a bit. This is because the table is providing an equal force on the book (NOTE: this is NOT Newton's third law).

If you put a strong enough force (greater than the maximum static friction) then the book will start sliding.

The building is a bit of a different situation since they dig down and attach the building firmly to the planet. But still, if you could push with enough force, the building would move (please don't do this... it would cause pain to yourself and others).
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