An empty rubber balloon has a mass of 0.0100 kg. The balloon is filled with helium at a density of 0.181 kg/m3. At this density the balloon is spherical with a radius of 0.300 m. If the filled balloon is fastened to a vertical line, what is the tension in the line?
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To find the tension in the line, we need to consider the forces acting on the balloon.
1. Weight of the balloon:
The weight of an object is given by the formula: weight = mass × acceleration due to gravity. In this case, the mass of the balloon is 0.0100 kg, and the acceleration due to gravity is approximately 9.8 m/s^2. Therefore, the weight of the balloon is:
weight = 0.0100 kg × 9.8 m/s^2 = 0.098 N
2. Buoyant force:
When the balloon is filled with helium, it experiences an upward buoyant force due to the difference in density between the helium and the surrounding air. The buoyant force is given by the formula: buoyant force = density of fluid × volume of fluid displaced × acceleration due to gravity.
In this case, the density of helium is 0.181 kg/m^3, and the volume of fluid displaced is the volume of the spherical balloon. The volume of a sphere can be calculated using the formula: volume = (4/3) × pi × radius^3. Substituting the values, we get:
volume = (4/3) × pi × (0.300 m)^3 ≈ 0.113 m^3
So, the buoyant force is:
buoyant force = 0.181 kg/m^3 × 0.113 m^3 × 9.8 m/s^2 ≈ 0.200 N
3. Tension in the line:
The tension in the line is the force required to hold the balloon up against the combined weight and buoyant force. Since the balloon is in equilibrium, the tension in the line must balance the weight and buoyant force. Therefore, the tension in the line is:
tension in the line = weight + buoyant force
= 0.098 N + 0.200 N
≈ 0.298 N
Therefore, the tension in the line is approximately 0.298 N.
Tension = Bouyancy force - ballon weight - helium weight.
= [V(air density - helium density) + ballon mass)]*g
V = (4/3) pi R^3
g = 9.8 m/s^2
By multiplying by g, you get the answer in Newtons, which is probably what they want.
For the air density, which you need, they should have told you what Temperature and pressure to assume. Use the STP value.