# Can a system experience more force at any point than the applied force?

I was solving a problem where the applied force on a ponit (A) of a member was 40kN. After solving the forces for a given point, it showed that point (B) is experiencing 59kN total force. (See figure)

This feels counter intuitive to me in a sense that why would any point in the system experience more force than the applied force?

Can I please have a brief explanation highlighting my misconception or misunderstanding? • Of course applied forces can be magnified. For example, that's the whole point of a lever. – knzhou May 6 at 12:48

## 3 Answers

People are mentioning levers, but it is important to see here that you actually have one. Your setup is similar to a claw-hammer or so: a rigid object with three points $$A,B,C$$ in a line in that order, such that $$C$$ is lying against some surface and thus acts as a center of rotation, some force is connected at the other end, $$A$$, and the force is amplified on the “nail” that is wrapped by the claw in between those points exists at $$B$$.

Lesson: it is very tempting to take $$B$$ as a pivot, or a center of rotation, but the choice of what you select as your center of rotation is actually very arbitrary, and the physics of torques works well no matter what you choose. If you have multiple places that are stationary on an object, even if one of them seems more correct than the other, sometimes it is helpful to imagine the other as the pivot and see if that looks interesting.

For example, very often to figure out the force direction on a point of contact, it is helpful to imagine what would happen if that point was not there. The bottom hinge of a door pushes the door out from the frame and is under compression; the top hinge pulls it in towards the frame and is under tension. I can say this very confidently because I can say “if that top hinge weren't there it would rotate around the bottom hinge away from the frame” and “if that bottom hinge weren't they it would rotate around the top hinge into the frame.” This freedom is very helpful.

• To be fair, taking B for the pivot is more than just temping for this case. B is the pinned joint, so by definition in analyzing these mechanisms, it can only pivot. – JMac May 6 at 13:55
• Thank you very much for your tip! – Ahmed Afif Khan May 6 at 16:52

Sure, a system can have higher force acting on part of it than applied force.

An obvious example is a lever (which seems relevant to the setup here).

Archimedes is often quoted as saying:

"Give me a place to stand and with a lever I will move the whole world"

This seems to be in reference to the principle of levers, where you can apply less force over a longer distance to get an output of more force over less distance. Energy is still conserved.

There are many physical systems that do similar things. For example, gears can convert a torque at a specific angular velocity to a higher torque with lower angular velocity, or vice versa.

The general topic is often called mechanical advantage.

It seems to me you are mixing up force and energy, and only the latter is conserved.

• Thank you for highlighting that. But I didn’t really want to appear messing up these two concepts. I was aware of that when I was posting the question. In short what I've understood from the answers here is, Energy is always conserved, as a result momentum due to the force is always conserved. The only thing that is varying here is force, which is varying due to the location of the pivot point. – Ahmed Afif Khan May 6 at 17:03