# Stress/strain within an object experiencing a single applied force

If I push an object in space, will any strain/stress happen within the object, though there is only 1 force rather than a pair of opposite forces on the object?

Can be any (even if trivial) stress/strain under the effect of a single force?

• Please add only relevant tags to your question. There is absolutely no relevance of quantum mechanics here, so I don't know why you added that tag. – user191954 Sep 10 '18 at 9:39
• Sorry !! Wasn't sure what quantum mechanics is 😅 – Mr. Bean Sep 10 '18 at 11:46

## 2 Answers

Yes, any force you apply will result in acceleration of the body (F=MA). A non-rigid body will also deform.

This is exactly what's happening when a rocket engine fires up. Depending on how large the push (force) applied and how small the object (mass), the acceleration could range from tiny to huge, as in "squish" to delicate human bodies.

• +1 To add, in the reference in which the body is stationary, an "inertial force" equal to mass times acceleration in the direction opposite to acceleration may be thought of as acting on the body. – Deep Sep 10 '18 at 6:19
• First of all let me thank you for your answer. However, I don't think the example of the rocket engine is valid; that is why I said that the object is in space. In the example you mentioned there might be air pressure or other reaction forces at play (which makes these examples "a pair of forces" examples rather than "single force" examples. Thanks again ! – Mr. Bean Sep 10 '18 at 8:06
• You mention something about the rigidity of the object but I want a general answer. I think if there is stress/strain it won't matter whether it is rigid or non-rigid object. The stress/strain will be there but in lesser magnitudes in the case of rigid objects (at least that's what I think) – Mr. Bean Sep 10 '18 at 8:09
• Commenting on DEEP: let me verify whether or not I understand you; do you mean the F=ma of the particles inside the object that are yet to be reached by the applied force is the other force that act against the applied force causing stress/strain. Did you mean something else. Please let me know. Thanks for your comment. – Mr. Bean Sep 10 '18 at 8:16
• Mr Bean, your comment of "I don't think the example of the rocket engine is valid; that is why I said that the object is in space", and "you mentioned there might be air pressure or other " confuses me as no such constraints were made. I can't help but wonder if you are assuming the common misunderstanding that "rockets push against air"? – user10216038 Sep 10 '18 at 15:33

Start by thinking about an object in a gravitational field - for example, anything on the earth's surface.

Even if the object is not moving, there is a distributed force (gravity) acting on every particle of the body. Those forces are balanced by an internal stress distribution in the body, which has nothing to do with whether the body is rigid or flexible.

For example if the object was a rectangular box resting on a horizontal plane, the stress caused by the gravitational force (i.e. "weight") varies linearly from zero at the top to a maximum value at the base, and the stress at the base is counterbalanced by the reaction force from whatever the object is resting on.

In some situations (for example civil engineering structures like bridges or buildings) these might the most significant stresses in the structure. In other mechanical engineering situations, they may be negligible compared with other stresses and strains in the structure, and therefore they might be ignored when designing or analysing the structure's behaviour.

Now, consider your object in space with a force acting on it. The force will cause the body to accelerate. But if we think about the motion in a coordinate system attached to the body, that "acceleration" looks exactly the same as a gravitational force. If the object is a spaceship with no windows to view what was outside, there is no way for the crew inside to know whether the ship is accelerating, or whether it is sitting on the ground in a gravitational field.

So, there is definitely a stress field in the accelerating body. The amount of strain corresponding to the stress depends on the elastic properties of the body. For a rigid body, the strains and deformations will be zero (that's what "rigid" means!) For a very flexible material, the strains may be big enough to make a large change to shape of the object.

• If rigid means the ELASTIC strains and deformations are zero then I don't think there is an absolutely rigid material in existence – Mr. Bean Sep 10 '18 at 11:50
• Also I think that stress is not the cause of strain. Force is. I think as strain increases stress increases (but not necessarily the other way around) yet force is the only cause here. (Maybe I am wrong here) – Mr. Bean Sep 10 '18 at 11:59
• To be honest, I don't understand your last 2 paragraphs (where the real answer begins). Regardless, I am relieved to know that there is stress-strain with only a single force applied. – Mr. Bean Sep 10 '18 at 12:02