Help, the last equation given to me on previous question was incorrect and I took a 0 % on my assignment !!!
A mountain-climber friend with a mass of 82 kg ponders the idea of attaching a helium-filled balloon to himself to effectively reduce his weight by 25% when he climbs. He wonders what the approximate size of such a balloon would be. Hearing of your physics skills, he asks you. Share with him your calculations that find the volume of the balloon.
To calculate the volume of the balloon needed to reduce the weight of the mountain climber by 25%, we can use the concept of buoyancy. The upward buoyant force exerted on an object in a fluid is equal to the weight of the fluid displaced by the object. In this case, the fluid is air, and the balloon filled with helium will displace an equivalent volume of air.
Here are the steps to find the volume of the balloon:
1. Calculate the weight of the mountain climber:
The weight of the mountain climber is given as the product of his mass (82 kg) and the acceleration due to gravity (9.8 m/s^2). Therefore, the weight is:
Weight = mass * acceleration due to gravity = 82 kg * 9.8 m/s^2
2. Calculate the reduced weight of the mountain climber:
Since the balloon is supposed to reduce the weight of the climber by 25%, we can find the reduced weight by taking 75% of the original weight calculated in step 1. Thus:
Reduced weight = 0.75 * Weight
3. Calculate the weight of the displaced air:
As per Archimedes' principle, the weight of the displaced air is equal to the buoyant force acting on the balloon. Since the buoyant force equals the reduced weight calculated in step 2, the weight of the displaced air is:
Weight of displaced air = Reduced weight
4. Calculate the volume of the balloon:
The weight of the displaced air is equal to the weight of the air that would occupy the same volume as the balloon. Using the relationship between density (ρ), mass (m), and volume (V) where ρ is the density of air, we have:
ρ * V = Weight of displaced air
Rearranging the equation, we find:
V = Weight of displaced air / ρ
5. Find the density of air:
The density of air varies slightly with factors like altitude and temperature. However, at sea level and room temperature, we can use an approximate value of 1.2 kg/m^3.
6. Substitute values and calculate the volume:
Substitute the values of the weight of displaced air (obtained in step 3) and the density of air (1.2 kg/m^3) into the equation obtained in step 4 and calculate the volume.
By following these steps, you can determine the approximate size of the balloon needed to reduce the weight of the mountain climber by 25%.