An empty rubber balloon has a mass of 0.0120 kg. The balloon is filled with helium at 0 degrees celsuis, 1 atm pressure, and a density of 0.179kg/m^3. The filled balloon has a radius of .5m
a)What is the magnitude of the net force acting on the balloon?
b) What is the magnitude of the buoyant force acting on the balloon?
Please explain!!
To calculate the magnitude of the net force acting on the balloon, we need to consider the forces acting on it:
1. Gravitational force (weight): This force is equal to the mass of the balloon multiplied by the acceleration due to gravity (9.8 m/s²).
Weight = mass × acceleration due to gravity
Given that the mass of the balloon is 0.0120 kg, we can calculate:
Weight = 0.0120 kg × 9.8 m/s² = 0.1176 N
2. Buoyant force: This force is exerted by the surrounding fluid (in this case, air) on an object immersed in it. The buoyant force is equal to the weight of the fluid displaced by the object:
Buoyant force = Density of fluid × Volume of fluid displaced × acceleration due to gravity
To calculate the volume of fluid displaced, we need to know the volume of the balloon. The formula for the volume of a balloon is V = (4/3)πr³, where r is the radius of the balloon.
Given that the radius of the balloon is 0.5 m, we can calculate:
Volume of fluid displaced = (4/3)π(0.5 m)³ = 0.5236 m³
Now we can calculate the buoyant force:
Buoyant force = 0.179 kg/m³ × 0.5236 m³ × 9.8 m/s² = 0.890 N
a) The magnitude of the net force acting on the balloon is the difference between the weight and the buoyant force:
Net force = Weight - Buoyant force = 0.1176 N - 0.890 N = -0.7724 N (downward force)
(Note: The negative sign indicates that the net force is acting downward.)
b) The magnitude of the buoyant force acting on the balloon is 0.890 N.