Final answer:
The gravitational potential energy added to the vase is 7.84 J.
Step-by-step explanation:
The gravitational potential energy (PE) of an object can be calculated using the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object. In this case, the mass of the vase is 4 kg and the change in height is 1.4 m - 1.2 m = 0.2 m. The acceleration due to gravity, g, is approximately 9.8 m/s^2. Plugging these values into the formula, we get PE = 4 kg * 9.8 m/s^2 * 0.2 m = 7.84 J.
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