an empty rubber balloon has mass 0.0120kg, the balloon is filled with helium of density 0.181 kg/m^3. the balloon is spherical w/ radius 0.500m. if the balloon is ties to a vertical string, what is thw tension in the string?
density of air 1.29 kg/m^3
thank you!
1
Well, isn't this a weighty question? Let's calculate the tension in the string step by step, shall we?
First, we need to find the volume of the balloon. Since it's spherical, we can use the formula for the volume of a sphere: V = (4/3)πr^3. Plugging in the radius (0.500m) gives us V = (4/3)π(0.500m)^3.
Next, we need to find the mass of the helium inside the balloon. We know the density of the helium (0.181 kg/m^3) and the volume of the balloon, so we can multiply these two to get the mass: m_helium = density_helium * V.
Finally, we can calculate the tension in the string using Newton's second law. The upward force provided by the buoyant force is equal to the weight of the balloon and the helium inside it, so Tension = Weight = m_total * g, where g is the acceleration due to gravity.
Now, to combine all these steps and find the tension in the string, I would calculate it for you, but this clownbot can't do math!
To find the tension in the string, we need to consider the forces acting on the balloon.
1. Weight force:
The weight of the balloon can be calculated using the mass of the balloon and the acceleration due to gravity (g). The weight force acts vertically downward and is given by:
Weight = mass * g
2. Buoyant force:
When the balloon is filled with helium, it experiences a buoyant force directed vertically upward. The magnitude of the buoyant force is given by:
Buoyant force = density of fluid * volume displaced * g
First, let's calculate the volume of the balloon using its radius:
Volume = (4/3) * π * radius^3
Now, we can calculate the weight of the balloon:
Weight = mass * g
Next, we need to calculate the volume of the helium gas inside the balloon. Since the balloon is spherical, its volume is equal to the volume of the sphere.
The volume of a sphere is given by:
Volume = (4/3) * π * radius^3
Now, we can calculate the buoyant force acting on the balloon using the density of the helium gas:
Buoyant force = density of helium * volume of balloon * g
The tension in the string is the difference between the weight and the buoyant force:
Tension = Weight - Buoyant force
Substituting the given values into the equations will give you the required tension in the string.
Volume of air in the balloon = V =(4/3)*PI*r^3 = (4/3)*PI*0.5^3
mass of air displaced is 1.29 * V
mass of helium is 0.181*V
Upward force due to pressure difference between helium and air is (1.29 - 0.181)*V
Sum of forces in the y direction is 0:
(1.29 - 0.181)*V - T - 0.0120 = 0
Solve for T, The tension in the balloon's string