# Does force get divided among things?

If I exert a force to more than one thing at a time, will the force be divided among them or all of them will feel the same force? I mean imagine that I have tied up 3 bags of same mass with A rope and I lift the rope up by exerting 90N force on. What is the force each of the bags going to feel? 90N or 30N?

• Please not that, weight is a force you mean mass. – iharob Nov 27 '15 at 17:14

## 2 Answers

Force is not divided, it applied to the first bag, and then the first bag will make a force on the second one, and the second on the third. The first bag feels two forces, the one you apply and the reaction from the second bag, the second bag in turns feels two forces, one from the front bag and one from the rear bag. If the bags are attached trough ropes, the tensions on the ropes will be from front to back: 90N, 60N and 30N.

• they all have the same acceleration – user83548 Nov 27 '15 at 17:16
• yes, I believe both answers complement each other – user83548 Nov 27 '15 at 17:18
• I think I am not clear enough. When you attach three bags with one rope (not in a line) there is no way the first bag can make a force on the 2nd one. Here is an image I made to give you the idea i.imgur.com/B4CkP1c.png – Farhan Fuad Nov 27 '15 at 17:45
• In that setup yes, the force is "splits" in three (your comment in the other answer is correct) – user83548 Nov 28 '15 at 13:33

If all of them feel the same force, they would have an acceleration that would give them a speed and hence a kinetic enegy greater than the work done by the applied force. It would violate the conservation of energy and conservation of linear momentum principles.

The force on each bag will depend on their individual masses, you can compute the acceleration of the system and then

$${\bf{F}}_i = m_i{\bf{a}}$$

such that

$$\sum{\bf{F}}_i = \bf{F}$$

So as you see, it has nothig to do with dividing the force. The right treatment has to consider the whole system and the forces applied to each bag come from the interactions between the parts of the system, as detailed in this answer.

It is the net acceleration of the system that matters. Remeber that there is no acceleration of the center of mass due to the internal forces in any system, if it accelerates it has to be because there are external forces, in this case $\bf{F}$. Any change in the velocity of the system will be reflected by the whole system unless, you could interact individually with each component. But in that case it would be a completely different system.

• I voted up, but I still believe that saying that the force will be divided could be confusing – user83548 Nov 27 '15 at 17:20