Final answer:
A force diagram for a helium-filled balloon would involve downward gravitational force due to the balloon's weight, an upward buoyant force due to the displacement of air, and possibly an upward tension force if the balloon is tethered.
Step-by-step explanation:
Force Diagram for a Helium-Filled Balloon
To draw a force diagram for the helium-filled balloon in question, you need to consider the forces acting upon the balloon. The main forces include the gravitational force acting downwards due to the weight of the balloon, the buoyant force acting upwards caused by the displacement of air, and the tension force if the balloon is tied to a string.
The gravitational force (weight) can be calculated by multiplying the mass of the balloon (234 kg) by the acceleration due to gravity (around 9.81 m/s2). This would result in a force with a magnitude of approximately 2295.74 newtons (N) directed downwards.
Meanwhile, the buoyant force can be found by calculating the weight of the air displaced by the balloon, which is the volume of the balloon multiplied by the density of the air and then by gravity. For a volume of 324 m3 and a density of 1.29 kg/m3, the buoyant force is approximately 4055.24 N directed upwards. Since the balloon floats, we can infer that the buoyant force must exceed the gravitational force.
If the balloon is tied down, there's also a tension force in the string pointing upwards, balancing out the net force to keep the balloon stationary. In a simplified scenario without wind or other disturbances, these are the primary forces that need to be considered in such a force diagram.