A sled weighing 60.0 N is pulled horizontally across snow so that the coefficient of kinetic friction between sled and snow is 0.100. A penguin weighing 70.0 N rides on the sled, as in Figure. If the coefficient of static friction between penguin and sled is 0.700, find the maximum horizontal force that can be exerted on the sled before the penguin begins to slide off.

It turns out that now the penguins travel on sled, and not only that, also they wear hats for the cold. I can tell you honestly, I don't know what physicists smoke when they occur such problems. But our work here is not be the DEA and find that. Our job is to resolve the problem.
What do I do? What do I do?!! It is what our brain begins to think when we see a problem of physics. This particular problem is part of an area called dynamic where the forces are studied. for solve, you must first run a Free Body Diagram (FBD). where we draw all forces from the center of mass.
performing FBD analysis on the penguin we have two forces the resulting force of the sled (F_result) and the force of friction between the penguin and sled (f_r-penguin). As before but apply it on the sled we have the force F and the friction between the sled and snow (f_r-sled).
Viewing all this in graphical form with the following image.

Having organized our problem we will solve. Wonder what is the minimum force F before the penguin slides ?. This is easy! if the penguin slides off that means that the resultant force is greater than the friction force between the penguin and sled. It is the minimum force before sliding equal to the force of friction between the penguin and sled.
Already we understood? a part of me says no ... Let's see do we have the friction force between the penguin and sled? the answer is yes. We got the weight of the penguin (as there is no vertical movement the weight is equal to the normal of the penguin on sled) and the friction coefficient. Who is the resultant force? is the subtraction between the force F and friction between the sled and snow.
viewing all this writting in equations in the following image:

It was easy! The problems that include friction are all equal just change the target to find (it can be a force, coefficient of friction, angle, etc.) to solve just have to remember that the friction force always opposes the motion.
That's all for this post! See you in the next! if you like our work share it with your friends. Until next time! and remember that physics is very easy! ;)