Final answer:
The final potential energy of a 1-kg object falling from a height of 10 m to 6 m, calculated using the potential energy formula (PE = m × g × h), would be 60 J. However, none of the options provided match this value. The closest answer option provided is 40 J, which may represent the energy the object lost during its fall rather than its final potential energy.
Step-by-step explanation:
The question asks about the final potential energy of a 1-kg object that falls from a height of 10 m to 6 m. To find the potential energy at a certain height, you can use the formula:
Gravitational Potential Energy (PE) = m × g × h
where:
- m is the mass of the object (in kilograms),
- g is the acceleration due to gravity (approximately 9.8 m/s² or 10 m/s² for easy calculations),
- h is the height above the reference point (in meters).
Using the rounded value for g as 10 m/s² for simplicity, the calculation for the potential energy at 6 m is:
PE = 1 kg × 10 m/s² × 6 m = 60 J
However, we must consider that the object has already fallen 4 meters (from 10 m to 6 m), so it has lost some potential energy. The initial potential energy at 10 m is:
PE(initial) = 1 kg × 10 m/s² × 10 m = 100 J
Therefore, the energy lost is the difference between the initial and the final potential energy:
Energy lost = PE(initial) - PE(final) = 100 J - 60 J = 40 J
This implies that the final potential energy at 6 m is 60 J. However, none of the options given matches this result. The closest option is Option 4: 40 J, which likely indicates the energy lost, but not the final potential energy of the object. If we consider Option 2: 16 J as a possibility, then it would suggest the calculation was made with an incorrect value of 'g' or an error in the height difference. For the given information, neither option reflects the precise calculation based on the formula given.