Question

At a construction site a crane lifts a steel beam with a mass of 330 kg.

With the beam being held still at a height of 40 m, the crane breaks and the beam falls to the ground. Assuming no air resistance, how much total energy will the beam have just as it hits the ground?

Answer 1

The total energy of a 330 kg steel beam just as it hits the ground after falling from 40 m with no air resistance is 129,360 joules (J), derived from its initial potential energy which converts entirely into kinetic energy.

Step-by-step explanation:

The student has asked for the total energy a steel beam of mass 330 kg will have just as it hits the ground after falling from a height of 40 m, assuming no air resistance.

This situation involves understanding the concepts of potential and kinetic energy as the beam falls. When the beam is held still at a height of 40 m, it has gravitational potential energy which can be calculated using the formula potential energy (PE) = mass (m) × gravity (g) × height (h).

Given that the standard acceleration due to gravity is 9.8 m/s², and ignoring air resistance, this potential energy will convert entirely into kinetic energy (KE) at the moment the beam hits the ground. The PE of the beam at 40 m is therefore 330 kg × 9.8 m/s² × 40 m.

PE = 330 × 9.8 × 40 = 129,360 joules (J)

Since energy is conserved, and there is no air resistance to dissipate any energy, the KE just as the beam hits the ground will also be 129,360 J. Thus, this is the total energy of the beam upon impact.