A 100kg steel beam falls from rest from a height of 20m, Find its impact speed.
To find the impact speed of the steel beam, we can make use of the principle of conservation of energy. According to this principle, the total mechanical energy of the system remains constant throughout the motion, neglecting any losses due to air resistance or other factors.
The mechanical energy of the system at the top of the height (initial position) is given by the potential energy (PE) of the beam, and at the point of impact (final position) it is given by the kinetic energy (KE) of the beam.
The potential energy at the initial position (PEi) can be calculated using the formula:
PEi = m * g * h
Where:
m is the mass of the beam (100 kg)
g is the acceleration due to gravity (9.8 m/s²)
h is the height from which the beam falls (20 m)
Substituting the values into the formula, we have:
PEi = 100 kg * 9.8 m/s² * 20 m
= 19600 N·m (or Joules)
According to the conservation of energy, this potential energy is converted entirely into kinetic energy (KE) at the final position. The kinetic energy is given by the formula:
KE = (1/2) * m * v^2
Where:
m is the mass of the beam (100 kg)
v is the impact speed of the beam (unknown)
Substituting the values into the formula, we have:
19600 N·m = (1/2) * 100 kg * v^2
Rearranging the equation to solve for v, we get:
v^2 = (2 * 19600 N·m) / 100 kg
v^2 = 392 m²/s²
Taking the square root of both sides, we find:
v = √392 m/s
Therefore, the impact speed of the steel beam falling from a height of 20 meters is approximately 19.8 m/s.