Calculating the Force of a Hard Stomp in Newtons

Have you ever wondered just how much force is generated by a hard stomp? In this article, we will explore the physics behind stomp force and provide you with a simple method to estimate this force using basic physical principles.

Estimation of Force

Estimating the force of a stomp requires understanding the basics of physics. The force generated during a stomp can vary based on the mass of the stomper and the acceleration of the foot. We can use Newton's second law of motion to calculate this force, which states that F m a, where:

F is the force in Newtons (N) m is the mass in kilograms (kg) a is the acceleration in meters per second squared (m/s2)

Force Calculation

Let's go through an example calculation to understand how to determine the force of a hard stomp.

Example Calculation

Assumptions:

Assume the person weighs 70 kg. The foot might accelerate downward at around 10 m/s2, which is a rough estimate. Actual acceleration could be higher.

Using these values, we can calculate the force as follows:

F 70 kg x 10 m/s2 700 N

Therefore, a hard stomp could generate a force of approximately 700 Newtons or more, depending on the person's weight and the acceleration of the stomp. In practice, the actual force could be higher if the stomp is particularly forceful or involves a rapid downward motion.

Dynamic Amplification and Springiness

Assuming a really heavy person, the weight falls on one foot at a time. Depending on the springiness of the floor, a dynamic amplification factor of 2 can be considered. In this case:

150 kgf x 2 x g 3 kN (approximately)

Here, kgf stands for kilogram-force, which is equivalent to the weight of 1 kg on Earth (9.8 N).

Rough Estimation Using Energy Balance

Another method involves using the principle of energy balance. For instance, if a person weighing 80 kg drops their heel by 2 cm (0.02 m), the energy transferred can be calculated as:

mgh 80 kg x 9.8 m/s2 x 0.02 m 1.568 J ( joules )

This energy would be converted into kinetic energy. If the kinetic energy is dissipated in 1/20 second, the momentum change can be calculated as:

mdv/dt 80 kg x 0.4 m/s x 20 s 640 N

This rough estimation gives us an idea of the force involved in the stomp.

Springiness and Material Factors

The actual force generated during a stomp depends on several factors, including the springiness of the floor, the type of shoes, and the body's anatomy. For argument's sake, let's assume all the energy is absorbed by the shoe soles. The Young's modulus for shoe soles is around 0.6 MPa.

Using the equations:

F/A Y Delta y/y

m g h F Delta y

And solving for Delta y and equating both equations, we can solve for F:

F sqrt{(m g h A Y)/y}

Substituting the values, we can estimate the force:

n mass of stomping person 70 kg

n g 9.8 N/kg

n h distance stomping person’s center-of-gravity drops during stomp 0.5 m

n A surface area of stomping area 0.01 m2

n Y Young's modulus of shoe sole 600,000 N/m2

n y initial thickness of shoe sole 0.02 m

After performing the calculation, the force is estimated to be approximately 14,000 Newtons.

Conclusion

The force of a hard stomp can vary widely based on several factors. Understanding the physics and applying basic principles of motion and energy can help estimate this force. Whether you're a fitness enthusiast, a sports scientist, or simply curious about human movement, this article provides valuable insights into the force generated during a stomp.