# How do we determine the forces present in the free body diagram of a system including multiple objects?

The particular example I'm working on is the following: assume we have a man pushing a sled, where the man doesn't slip because he is wearing ice cleats, and the sled experiences a frictional force from the ground. They're accelerating at a constant rate.

On a free body diagram, the man's horizontal forces would include his push force and the normal force due to the sled (smaller in magnitude). The sled's diagram would include the normal force due to the man, and the frictional force (smaller in magnitude).

In a combined system with both man and sled, would we simply add all of these forces to find the net force of the system? And thus, the system's net force would basically be the man's push force minus the sled's friction?

I thought that a system's internal forces should cancel out, but what are these internal forces in this case? Since the frictional force and push force do not cancel...

• If the system is just the man and the sled then the "push force" and friction aren't internal forces since they involve interactions between parts of your system and things that are not part of the system. If you want those forces to also be internal then you would need to include the Earth as part of your system. – Aaron Stevens Apr 12 at 1:33

## 2 Answers

Consider any two bodies, A and B. If body A exerts a force on body B, then body B exerts an equal force, in the opposite direction, on body A.

So when you have multiple bodies in a free body diagram, the forces any two bodies cancel each other out when you add up the forces.

If your free body diagram includes the man and the sled, then the external horizontal forces would be the friction on the sled, and the horizontal push of the ground on the man's feet.

What I infer from the question is that the man is not slipping backwards. The whole system is accelerating forward. If that is the case then there must be an net external force along the surface on the system (man + sled) in the direction of acceleration. Since man is wearing ice cleats(I don't know what they are, assuming they prevent slipping) he is pushing the surface backward and by third law of newton there must be a reaction force on man in the opposite direction(forward). Subtracting the friction force which is acting on the sled gives the net external force on the system due to which the system accelerates.