Final answer:
The total force F on the helium balloon can be expressed as the difference between the buoyant force Fb and the weight w of the balloon, adjusted for the upward acceleration using Newton's second law. The question involves applying principles of buoyancy and understanding of density differences between helium and air.
Step-by-step explanation:
Buoyant Force and Helium Balloons
The question pertains to the concept of buoyant force in Physics, specifically how it applies to a helium balloon. This involves understanding Archimedes' principle, which states that the upward buoyant force exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces. Due to the density difference between helium and air, a helium balloon experiences a buoyant force that can allow it to float or even ascend in the air.
To express the total force F acting on the balloon in terms of weight (w) and buoyant force (Fb), you can use the equation F = Fb - w. The buoyant force is the weight of the air displaced by the balloon, calculated by multiplying the volume of the balloon (Vb) by the density of air (ρa) and gravity (g). The weight w is the mass of the helium multiplied by gravity. Since the balloon accelerates upward, this means F is the net force taking into account the mass and acceleration of the balloon (m*a).
Thus, F = (ρa*Vb*g) - (m*g + m*a), where m is the mass of helium which is calculated from its density (multiplied by the volume of the balloon), and g is the acceleration due to gravity.