Final answer:
The buoyant force on a helium balloon is greater than its weight if the balloon is floating upward with acceleration; this scenario is backed by Archimedes' principle.
Step-by-step explanation:
When a balloon filled with helium gas, with a density of 0.33 kg/m³, is floating upward with acceleration, it indicates that the buoyant force acting on the balloon is greater than the weight of the balloon. The buoyant force is the force exerted by a fluid that opposes the weight of an object immersed in the fluid. In this case, the fluid is air, with a density of about 1.23 kg/m³. According to Archimedes' principle, the buoyant force on an object in a fluid is equal to the weight of the fluid displaced by the object. Since the balloon is accelerating upward, we can infer that the upward buoyant force must be greater than the downward force of gravity on the balloon, causing a net upward force and, thus, acceleration.
The volume of the balloon (V_b) is given as 0.057 m³. To calculate the buoyant force, we multiply the volume of the displaced air by the density of air and the acceleration due to gravity (approximately 9.81 m/s²). The weight of the balloon can be calculated by multiplying its volume by its density and gravity. If the buoyant force weren't greater than the balloon's weight, the balloon would be in equilibrium or fall, not accelerate upward.