Static and Kinetic Coefficient of Friction Find Force to Move Box & Force to have Constant Velocity

In this problem we have a wooden crate that has a mass of 23 kilograms and is resting on a wood floor. The coefficient of static friction is .58 and the coefficient of kinetic friction is .4. What pull force is required to get the crate to move and what force is needed after it is moving to maintain a constant velocity.
Lets draw all our force arrows in a free body diagram.
First we have the force that we are pulling with which will be marked with a yellow arrow
We then have the normal force from the crate which is mass times the acceleration due to gravity this will be marked with a blue arrow
The floor will be pushing back with an equal but opposite force which is the normal force from the floor which is marked with a purple arrow.
The force pulling on the crate will first be counteracted by the force due to static friction which will be marked with a red arrow
After the static friction is overcome and the crate starts moving the pull force will then be counteracted by the force due to kinetic friction
On the bottom of this slide I have a graph that shows what happens as you increase the force from pulling. So at first the force increases up until the point where we hit the max static friction force after we surpass that the crate begins to move and we now are working against the coefficient of kinetic friction. In most cases the kinetic friction force is less then the static friction force. Of course there are exceptions.
Now to get the force needed to overcome static friction we can take the normal force times the coefficient of static friction to get 130.9 newtons of force for the max static friction.
So if the pull force is less then or equal to the static friction force then the object will not move
If the pull force is greater than the static friction force then the object will begin to move
Once the object starts moving it is being slowed down by kinetic friction which can be found by taking the normal force times the coefficient of kinetic friction. Doing so we are left with a force of kinetic friction of 90.252 newtons.
So if the object is moving and the pull force is less than the force due to kinetic friction the object will decelerate
If the object is moving and the pull force is equal to the force due to kinetic friction then it will maintain a constant velocity.
If object is moving and the pull force is greater than the force due to kinetic friction then the object will accelerate.

Disclaimer
These videos are intended for educational purposes only (students trying to pass a class) If you design or build something based off of these videos you do so at your own risk. I am not a professional engineer and this should not be considered engineering advice. Consult an engineer if you feel you may put someone at risk.

[NoahSonserReal]

Thanks man, I didn't realize the static friction was so simple. Although something tells me that this will continue to get more difficult. I can't wait 😂.