Answer :
Final answer:
The work done by the crane to lift a 2,500 kg load is equal to the gravitational potential energy gained by the load. By using the formula W = mgh and knowing the work (W) is 196,000 J, we can calculate that the load was lifted approximately 8 meters high.
Explanation:
The student is asking about the work done by a crane to lift a load, which is a problem related to mechanical work and energy in physics. The work-energy principle tells us that the work done on an object is equal to the change in its mechanical energy. Since the crane in this scenario is lifting the load straight up against the force of gravity, the work done by the crane is equal to the gravitational potential energy gained by the load.
The formula for gravitational potential energy is
U = mgh,
where U is the potential energy, m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s² on Earth), and h is the height. We know from the question that the work done (W) is 196,000 J and the mass of the load (m) is 2,500 kg. We need to find the height (h).
Using the formula for work done, which is W = mgh, we can solve for h:
- 196,000 J = 2,500 kg × 9.8 m/s² × h
- h = 196,000 J / (2,500 kg × 9.8 m/s²)
- h = 196,000 J / 24,500 kg·m/s²
- h ≈ 8 meters
Thus, the load was lifted approximately 8 meters high by the crane.
