Final answer:
Using the formula GPE = mgh, the gravitational potential energy of a 6.4 kg ceiling fan at a height of 3.5 m above the ground is calculated to be 220.16 J, which corresponds to option A.
Step-by-step explanation:
To calculate the gravitational potential energy (GPE) of a ceiling fan that is 3.5 m above the ground, we use the formula GPE = mgh, where m is the mass in kilograms, g is the acceleration due to gravity (approximately 10 m/s²), and h is the height in meters. For a ceiling fan with a mass of 6.4 kg and a height of 3.5 m above the ground, the GPE can be calculated as:
GPE = 6.4 kg × 10 m/s² × 3.5 m = 224 J.
However, given that the options provided do not include this number, we likely round the acceleration due to gravity to the nearest whole number, which is common in various problems. Thus, using the rounded down gravitational acceleration value of 9.8 m/s², the GPE would be:
GPE = 6.4 kg × 9.8 m/s² × 3.5 m = 220.16 J.
Therefore, the correct answer from the provided options is A. 220.16 J.