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Name: Shadrack
Status: student
Grade: n/a
Country: USA
Date: Summer, 2011


Question:
When I push against a wall, where does the wall get the energy needed to create the reaction force of that contact? The wall gets its energy from the product of the strain (deformation as a result of pushing) and the wall's modulus of elasticity. Since the modulus of elasticity of the wall is so large the deformation is too small to feel or measure. But where does the energy come from?

Replies:
Hi Shadrack,

Energy is required to do work, which is a force applied across some distance. By leaning against the wall, you are doing work on the wall if the wall strains in response to the load you place upon it. You have put potential energy into the wall just by leaning on it.

Now that you are leaning against the wall and you are at steady state, no energy is required since there is no displacement (strain) happening. You have a force balance now. The wall is pushing back with a force (not energy) resulting from its elastic modulus and strain, which is equal to the force you are pushing on it.

I hope that helps. I think sometimes these questions are hard to answer because there is a tendency to think of force as energy.

Regards, John C. Strong


Shadrack,

If we view a hand pushing a wall from the point of view of energy, the energy comes from your hand. The ability to resist your hand, to make use of this energy, comes from the molecular structure of the wall. A useful model is a structure of little balls connected by very strong springs that can be compressed as well as extended.

Your hand presses on the wall to make it move. The force from your hand moves many of the wall's molecules near the surface, gives them kinetic energy. As these molecules move, they stretch the connections they have with other molecules. The connections absorb some of this energy, transferring it from kinetic to potential. Now, some energy has been stored in the connections and the molecules are moving slower. Some of this potential energy is released to molecules further in. Now, a thicker portion of the surface is moving, but much more slowly than before. More connections absorb energy. Eventually, all of the kinetic energy becomes potential energy within the connections.

Dr. Ken Mellendorf Physics Instructor Illinois Central College


Shadrack,

If we view a hand pushing a wall from the point of view of energy, the energy comes from your hand. The ability to resist your hand, to make use of this energy, comes from the molecular structure of the wall. A useful model is a structure of little balls connected by very strong springs that can be compressed as well as extended.

Your hand presses on the wall to make it move. The force from your hand moves many of the wall's molecules near the surface, gives them kinetic energy. As these molecules move, they stretch the connections they have with other molecules. The connections absorb some of this energy, transferring it from kinetic to potential. Now, some energy has been stored in the connections and the molecules are moving slower. Some of this potential energy is released to molecules further in. Now, a thicker portion of the surface is moving, but much more slowly than before. More connections absorb energy. Eventually, all of the kinetic energy becomes potential energy within the connections.

Dr. Ken Mellendorf Physics Instructor Illinois Central College


The energy comes from you. Pushing on the wall is like compressing a spring. Your push deforms the atomic structure of the wall - it pushes atoms closer together. The harder you push, the closer the atoms get and the harder they push back. When you let go, they release the stored energy by springing back to their original position (assuming you didn't push hard enough to make a permanent dent).

This is a really basic analogy, but it seems to have helped some of my students untangle the concept of reaction force.

R. W. "Mr. A." Avakian


Formally, a static force requires no energy. Energy is "work"; work = force * distance, and in a static situation there is no further motion, no further distance being traversed. In practice, there usually is some energy needed due to elasticity of the structure. But that energy you provide as the wall first deforms, as you gradually increase your initial force on the wall. You are charging up a spring by pushing on the wall. As long as the wall does not break, sag, or cold-flow, that charge is retained and is sufficient energy to push back at you.

If you have intuitive impression that force requires energy, science does not see it that way. Large opposing forces can and do exist with virtually no ongoing energy expenditure (power) and relatively little initial energy stored.

I guess that could be counter-intuitive. Our experience is from our use of our muscles. Our muscles are very inefficient by comparison to ideal static-force structures. Our bodies must expend ongoing effort to maintain a constant force, except for the case of merely resting your weight on something. This is because our muscles are biochemical machines with a great deal of slippage inside their molecular mechanism. I think electric motors also have this problem, unless they include a spring-and-ratchet mechanism (not often done, but could be). Motors with very large-ratio of down-shifting gears (>100) and an elastic element in the output shaft can have a similar stored force effect, because the friction in the gears could stop relaxation of the spring, even when the motor coils are mostly de-energized. If the job is to maintain a static force with little use of power, this kind of mechanism is much more efficient than motors we usually use for things. Such motors are quite feasible, just a little more complicated and expensive and uncommon. Piezo-electric motors tend to have latching mechanisms and elasticity which would make them efficient for this. I guess they are pretty in-efficient and slow for mostly-moving uses, such as pushing a car down the road. Perhaps that is one reason we have experienced few such motors.

Jim Swenson


Hi Shadrack,

I think your confusion might come from the difference between "force" and "energy". An object need not expend energy to exert or experience a force. In this case, the reason is because the object is in a force field. You might be thinking of the effort "you" must expend (with your muscles) to create a force, but not all forces require energy to be used. In particular, when objects are in a force field (such as gravity or buoyancy), the gravitational field, not energy expenditure within the object, is the source of forces between objects.

Consider a simple example: a bowl on a table. Gravity exerts a force on the bowl downward, and the table exerts a force on the bowl upward. The bowl is not moving. While it is possible to deform an object and store energy that way (a rubber band or a hockey stick come to mind), the ability of the table to push back on the bowl is NOT due to energy stored in its deformation (even though there might be some very small microscopic elastic deformation, it is negligible in this example). Energy is defined as a force applied through a distance -- so since the bowl is not moving, its (macroscopic) energy is staying the same. Potential energy is derived from the position of objects in a force field (such as gravity or buoyancy), but the object must move within the field for its potential energy to change. Similarly with kinetic energy -- the object must be moving. In this example we are neglecting chemical energy, heat, etc. In short, the table does not "expend" energy in holding up the bowl.

(I should also clarify that this example is based on a local system -- not universe-scale/relativistic phenomena, nor quantum/microscopic effects.)

Hope this helps, Burr Zimmerman


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