In this blog post, we’ll examine the proverb “hitting a rock with an egg” through the engineering concept of fatigue failure, and together reflect on the meaning of “impossibility”—something we’ve always taken for granted.

Is the saying “hitting a rock with an egg” really an undeniable truth?

Chul-soo, an engineering student, and Young-hee, a humanities student, are walking across campus. Chul-soo, who doesn’t have a girlfriend, vows to Young-hee that he’ll definitely find a girlfriend who looks just like IU this semester. Hearing this, Young-hee says that Chul-soo’s idea is like trying to crack a rock with an egg. Chul-soo then grins and asks, “So, nothing’s impossible, right?” Young-hee points out Cheol-su’s naivety and asks how it could possibly be possible to crack a rock with an egg.
Most people who hear this conversation would think Cheol-su is wrong and Young-hee is right. We often use the expression “You might as well try to crack a rock with an egg” when talking about impossible tasks or reckless challenges. But does this proverb really refer to something that is absolutely impossible?
According to common sense, it is impossible to break a hard rock with an egg. Most people would assume that no matter how many eggs you throw, the rock wouldn’t even get a scratch.
So, let’s hear the counterargument from Cheol-su, the engineering student.

To understand fatigue failure, you must first understand stress and strain

To understand failure in the context of structural mechanics, it is necessary to first examine the concept of the stress-strain curve. When force is gradually applied to an object, its deformation increases accordingly, and the internal stress resisting this deformation gradually grows. A graph with strain on the horizontal axis and stress on the vertical axis is called a stress-strain curve.
Although the shape of the stress-strain curve varies from material to material, the properties of materials are often explained using the stress-strain curve of steel as a reference.
In the initial stage when a force is first applied to an object, stress and strain maintain a nearly linear proportional relationship. The limit of this region is called the proportional limit, and the slope of the straight line is called the modulus of elasticity. When force is applied within this range, the object undergoes only elastic deformation, so it returns to its original shape when the force is removed.
Once the proportional limit is exceeded, the yield point is reached. If a load greater than the yield point is applied, plastic deformation occurs, meaning the object does not fully return to its original state even after the force is removed. If the stress continues to increase beyond this point, the material reaches its ultimate strength, which represents the maximum strength the material can withstand. If this limit is exceeded, the material eventually reaches the fracture point and breaks; this is commonly referred to as the failure of the object.
Therefore, based solely on the concept of the stress-strain curve, applying a force below the ultimate strength to an object will not cause the material to fail. However, we can easily find examples in our daily lives that contradict this. A water droplet falling on the same spot over a long period of time can gradually erode even solid rock, and structures designed with sufficient safety margins can sometimes become damaged over time due to repeated loading. In other words, even a force smaller than the ultimate strength can eventually lead to failure if applied repeatedly.
So, what principle explains this phenomenon?

Even Small, Repeated Forces Can Ultimately Destroy a Material

In structural mechanics, this phenomenon describes how the strength of a material gradually decreases as the number of cycles increases when a metal material or structure is subjected to repeated stress or fluctuating stress that continuously changes in magnitude. Even if the stress is very small at first, repeated application over a long period causes microscopic cracks to form within the material; these cracks gradually grow, eventually leading to failure. This phenomenon is called fatigue failure.
Fatigue failure is a concept of great importance in various engineering fields, including mechanical engineering, civil engineering, and aerospace engineering. In fact, structures such as automotive parts, bridges, railroad tracks, and aircraft fuselages often sustain damage not because they are subjected to a single, extremely large force, but because fatigue accumulates through the process of being subjected to relatively small forces countless times.
Thus, in fatigue failure, even forces that do not reach a material’s maximum strength can eventually cause failure if applied repeatedly. In other words, a material’s strength is not determined solely by the magnitude of the force but is also influenced by the number of cycles and the duration of exposure.

Is it possible to calculate how an egg could break a rock?

If so, let’s consider how much time it would actually take to destroy a rock with an egg.
Let’s assume the egg has a mass of approximately 60 g and collides with the rock at a speed of about 50 km/h (approximately 14 m/s). Furthermore, if we assume that all of the egg’s momentum is transferred to the rock, we can calculate the impact force that a single egg exerts on the rock.
Momentum is defined as the product of an object’s mass and velocity, and impulse refers to the change in momentum over a given time interval. Assuming the egg strikes the rock for about 0.1 seconds, the average force transferred to the rock is calculated to be approximately 9 N.
However, simply obtaining this value does not mean we can immediately calculate fatigue failure. In structural mechanics, the concept of stress is considered more important than that of force alone. Stress is the force divided by the area over which it acts; it is a physical quantity that indicates how much force is actually acting per unit area. Therefore, to analyze fatigue failure, we must consider not only the magnitude of the force but also how concentrated that force is over a given area.
The strength of the rock gradually decreases as repetitive stress continues to act on it, in accordance with the fatigue failure phenomenon described earlier. Using this principle and making some simple assumptions, calculations show that it would take a very long time for the rock to reach failure. According to the calculation conditions in the original text, if an egg were thrown continuously at one-second intervals, it is estimated that it would take approximately 700 years for the rock to reach fatigue failure. Of course, this calculation is merely a theoretical example based on various idealized assumptions, and the actual results can vary significantly depending on the type of rock, the manner of the egg’s impact, the point of impact, and environmental factors such as weathering.
Ultimately, from an engineering perspective, it is difficult to conclusively state that “hitting a rock with an egg” is absolutely impossible. Even if it is practically almost impossible to achieve, the core of fatigue failure theory is that even hard materials can be destroyed when small, repeated forces accumulate over a long period of time.

The True Meaning Behind the Proverb “Hitting a Rock with an Egg”

The world may be like a massive rock filled with seemingly impossible tasks, and we may be like eggs that seem easily breakable. In such a world, people often choose the comfort of resignation and surrender over relentless effort. Those who take on impossible challenges are sometimes labeled as foolish, and it is common to envy only the results of successful people rather than the effort they put in.
However, if we judge everything solely by its outcome, it would be difficult to even begin challenges that initially seem impossible. In fact, countless advancements in human history have stemmed from the repeated efforts of people who tenaciously tackled seemingly impossible problems.
When viewed from an engineering perspective, the key point of the proverb “hitting a rock with an egg” is not whether the egg breaks the rock immediately. What holds greater significance is the fact that even a small force, when applied persistently and repeatedly, can ultimately bring about change.
This mindset is particularly crucial for engineers who must research new technologies and pioneer new fields. An attitude of not giving up easily and consistently pursuing even small attempts serves as the driving force behind technological advancement and can be the starting point for solving seemingly impossible problems. Ultimately, what fatigue failure demonstrates is not just the properties of materials, but also the power of change brought about by repetition and persistence.