When a cylindrical steel bar is dropped from a height of 110 m, several factors come into play that determine the impact force when it hits the ground. First, we need to consider the potential energy at the height from which it is dropped and how that energy converts to kinetic energy as it falls.
The potential energy (PE) of the bar at the height of 110 m can be calculated using the formula:
PE = m * g * h
Here, m is the mass of the bar, g is the acceleration due to gravity (approximately 9.81 m/s²), and h is the height (110 m).
Once the bar hits the ground, the kinetic energy (KE) it has gained while falling is equal to that potential energy. The kinetic energy just before impact can be calculated as:
KE = 0.5 * m * v²
where v is the final velocity of the bar just before hitting the ground.
Neglecting air resistance, we can set PE equal to KE to find the impact velocity, which can then be used to determine the force of impact. However, you also mentioned the stress and material properties of the bar, which is important.
The stress experienced by the bar upon impact can be calculated using the formula:
Stress = Force / Area
Assuming the impact force can be represented as equal to the momentum change upon hitting the ground, and knowing the cross-sectional area of the bar (which can be calculated as π * r² where r is the radius of the bar), allows us to determine the level of stress that bar experiences.
In summary, when a cylindrical steel bar is dropped from a significant height, it will fall freely under gravity, gain kinetic energy, and when it impacts the ground, it will exert considerable stress depending on its material properties. Understanding these principles can help in designing bars that can withstand impacts without failing.