A balloon weighing 80 kg has a capacity of 1200 m3. If it is filled with helium, how great a payload can it support? The density of helium is 0.18 kg/m3 and the density of air is 1.30 kg/m3. Express your answer in Newtons.
I know the answer is 12, 400 Newtons I just don't know how to get that answer. I also have a quiz over this on Tuesday so hopefully someone can help... fast! Thanks<3
Oh, calculations can sometimes make our heads spin, but don't worry, I'm here to help! To find the payload that the balloon can support, we need to consider the buoyant force acting on it.
The buoyant force is given by the difference in weight between the air that the balloon displaces and the helium inside it. Buoyant force = weight of displaced air - weight of helium.
First, let's calculate the weight of the displaced air:
Weight of displaced air = density of air × volume of balloon × acceleration due to gravity
Weight of displaced air = 1.30 kg/m³ × 1200 m³ × 9.8 m/s²
Next, let's calculate the weight of the helium:
Weight of helium = density of helium × volume of balloon × acceleration due to gravity
Weight of helium = 0.18 kg/m³ × 1200 m³ × 9.8 m/s²
Finally, subtract the weight of the helium from the weight of the displaced air to find the buoyant force, which represents the maximum payload the balloon can support:
Buoyant force = weight of displaced air - weight of helium
Now, keep in mind that weight is equal to the mass multiplied by the acceleration due to gravity. So, instead of 1.30 kg/m³ and 0.18 kg/m³, we can use 1.30 kg/m³ × 9.8 m/s² and 0.18 kg/m³ × 9.8 m/s² for simplicity.
Once you find the buoyant force, convert it to Newtons by multiplying it by 9.8 m/s². That will give you the answer in Newtons!
I hope this helps you with your quiz. Good luck, and remember, no matter what happens, you'll always helium later!
To determine the payload that the helium-filled balloon can support, we need to calculate the buoyant force acting on the balloon.
The buoyant force is equal to the weight of the fluid displaced by the balloon. In this case, the fluid is the surrounding air.
First, we need to calculate the weight of the air displaced by the balloon.
The volume of the balloon is given as 1200 m^3.
The density of air is 1.30 kg/m^3.
Weight = density × volume × acceleration due to gravity
Weight of the air displaced = 1.30 kg/m^3 × 1200 m^3 × 9.8 m/s^2
Weight of the air displaced = 15,120 kg × 9.8 m/s^2
Weight of the air displaced = 148,176 Newtons
Next, we need to calculate the weight of the helium-filled balloon.
The weight of the balloon is given as 80 kg.
Weight of the balloon = 80 kg × 9.8 m/s^2
Weight of the balloon = 784 Newtons
To calculate the buoyant force, subtract the weight of the balloon from the weight of the air displaced:
Buoyant force = Weight of the air displaced - Weight of the balloon
Buoyant force = 148,176 Newtons - 784 Newtons
Buoyant force = 147,392 Newtons
Finally, the payload that the balloon can support is equal to the buoyant force:
Payload = Buoyant force
Payload = 147,392 Newtons
Therefore, the balloon can support a payload of 147,392 Newtons when filled with helium.
To calculate the payload that a helium-filled balloon can support, we need to consider the buoyant force acting on the balloon.
The buoyant force is the force exerted by a fluid on an object immersed or floating in it, and it opposes the force of gravity. The magnitude of the buoyant force is equal to the weight of the fluid displaced by the object. In this case, the fluid is air.
First, we need to calculate the weight of the air displaced by the balloon. The volume of the balloon is given as 1200 m^3. The density of air is 1.30 kg/m^3. Therefore, the weight of the air displaced is:
Weight of air displaced = density of air x volume of balloon
Weight of air displaced = 1.30 kg/m^3 x 1200 m^3 = 1560 kg
Next, we need to calculate the weight of the helium-filled balloon. The density of helium is 0.18 kg/m^3. The volume of the balloon remains the same, but we need to multiply it by the density of helium to get the weight of the balloon:
Weight of balloon = density of helium x volume of balloon
Weight of balloon = 0.18 kg/m^3 x 1200 m^3 = 216 kg
Finally, to calculate the payload, we subtract the weight of the balloon from the weight of the air displaced:
Payload = Weight of air displaced - Weight of balloon
Payload = 1560 kg - 216 kg = 1344 kg
To convert the payload from kilograms to Newtons, we need to multiply it by the acceleration due to gravity, which is approximately 9.8 m/s^2:
Payload (in Newtons) = Payload (in kg) x acceleration due to gravity
Payload (in Newtons) = 1344 kg x 9.8 m/s^2 = 13,171.2 N
Therefore, the helium-filled balloon can support a payload of approximately 13,171.2 Newtons.