Question

procedure
pre - lab procedure:

1. what are the forces acting on a tied balloon attached to a string? draw a free body diagram.
2. the balloon is now untied and traveling down the string. what are the forces acting on the balloon as it travels down the string? draw a free - body diagram.
3. balloon demo: which balloon will reach the end of the string first: the larger or smaller balloon? explain your answer.

Explanation:

Step1: Forces on tied balloon

The forces acting on a tied balloon attached to a string are the force of gravity ($F_g = mg$) pulling it downwards, the buoyant force ($F_b$) acting upwards (due to the air it displaces), and the tension force ($T$) in the string acting upwards to keep it in place. A free - body diagram would have an arrow pointing down for $F_g$, and two arrows pointing up for $F_b$ and $T$.

Step2: Forces on untied balloon moving down the string

When the balloon is untied and moving down the string, the force of gravity ($F_g$) still acts downwards, the buoyant force ($F_b$) acts upwards, and there is also a frictional force ($F_f$) acting upwards along the string opposing its motion. The free - body diagram would have an arrow down for $F_g$, and two arrows up for $F_b$ and $F_f$.

Step3: Balloon race analysis

The smaller balloon is likely to reach the end of the string first. This is because the smaller balloon has less air inside it, so it has less mass. According to Newton's second law $F = ma$, for a given net force (the difference between the gravitational force and the buoyant force minus friction), a smaller mass ($m$) will result in a larger acceleration ($a$). So, the smaller balloon will accelerate more and reach the end of the string faster.

Answer:

1. Forces: Gravity ($F_g$) down, Buoyant force ($F_b$) up, Tension force ($T$) up. Free - body diagram: Downward arrow for $F_g$, upward arrows for $F_b$ and $T$.
2. Forces: Gravity ($F_g$) down, Buoyant force ($F_b$) up, Frictional force ($F_f$) up. Free - body diagram: Downward arrow for $F_g$, upward arrows for $F_b$ and $F_f$.
3. The smaller balloon will reach the end of the string first because it has less mass and will accelerate more for a given net force according to $F = ma$.