Final answer:
To calculate the buoyant force on a 2.00-L helium balloon, Archimedes' principle is applied. The closest correct answer is 0.02 N. The net vertical force, after taking into account the mass of the rubber, is approximately 0.009285 N.
Step-by-step explanation:
To calculate the buoyant force on a 2.00-L helium balloon, we can use Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object. In this case, the fluid is air. Assuming standard conditions, the density of air is approximately 1.225 kg/m3.
First, convert the balloon's volume to cubic meters (m3), which gives 0.002 m3 (since 1 liter equates to 0.001 m3). The weight of the displaced air is calculated by multiplying the volume of the balloon by the density of air and acceleration due to gravity (9.81 m/s2). This gives:
Buoyant Force (Fb) = Volume x Density of air x g
Fb = 0.002 m3 x 1.225 kg/m3 x 9.81 m/s2
Fb ≈ 0.024 N
However, none of the given options exactly match this calculation. Among the provided choices, 0.02 N is the closest one. Therefore, the most likely intended answer would be (b) 0.02 N, assuming that air's density does not depart significantly from the standard conditions.
Now for part (b), we need to find the net vertical force on the balloon once it is let go, disregarding the volume of the rubber. The mass of the rubber is given as 1.50 g, which is 0.0015 kg. The force due to gravity acting on the rubber (Fg) is:
Fg = Mass of rubber x g
Fg = 0.0015 kg x 9.81 m/s2
Fg = 0.014715 N
The net vertical force is then the buoyant force minus the force due to gravity on the rubber:
Net Vertical Force = Fb - Fg
Net Vertical Force = 0.024 N - 0.014715 N
Net Vertical Force ≈ 0.009285 N
The balloon will experience a net upward force and will rise.
Therefore answer is (b) 0.02 N.