A 5450-m^3 blimp circles Fenway Park duing the World Series, suspended in the earth's 1.21-kg/m^3 atmosphere. The density of the helium in the blimp is 0.178 kg/m^3. A) What is the buoyant force that suspends the blimp in the air? B) How does this buotant force compare to the blimp's weight? c) How much weight, in addition to the helium, can the blimp carry and still continue to maintain a constant altitude?
for
A) I got 64626.1N
B) they are equal
C)HELP ME WITH THIS!!!
PS: If I've done the A or B wrong pleas correct me
Thank You
bouyant force= weight of displaced air.
weightair= volume*density*g
= 5450*1.21*9.8
weight of blimp= 5450*.178*g
c) the differerence.
A) It seems like you've calculated the buoyant force correctly. The buoyant force can be calculated using the formula:
Buoyant force = (Air density - Helium density) * Volume * g
Using the given values:
Buoyant force = (1.21 kg/m^3 - 0.178 kg/m^3) * 5450 m^3 * 9.8 m/s^2
Buoyant force ≈ 64626.1 N
So, your calculation for the buoyant force is correct!
B) The weight of the blimp can be calculated using the formula:
Weight = Mass * g
Since the mass is not given, we can calculate it using the density and volume of the blimp:
Mass = Density * Volume
Mass = 0.178 kg/m^3 * 5450 m^3
Mass ≈ 970.1 kg
Now we can calculate the weight:
Weight = 970.1 kg * 9.8 m/s^2
Weight ≈ 9517.98 N
So, the weight of the blimp is approximately 9517.98 N.
Comparing the buoyant force and the weight:
Buoyant force = 64626.1 N
Weight = 9517.98 N
The buoyant force is greater than the weight, indicating that the blimp is being suspended in the air.
C) To calculate how much weight the blimp can carry and still maintain a constant altitude, you need to consider the maximum buoyant force that the blimp can support. This can be calculated by considering the maximum volume of helium the blimp can contain.
To calculate the maximum volume of helium the blimp can contain, divide the maximum buoyant force by the difference in density between air and helium, and by the acceleration due to gravity:
Max Volume of Helium = Max Buoyant force / ((Air density - Helium density) * g)
Substituting the given values:
Max Volume of Helium = 64626.1 N / ((1.21 kg/m^3 - 0.178 kg/m^3) * 9.8 m/s^2)
Max Volume of Helium ≈ 5303.4 m^3
To find the additional weight the blimp can carry, subtract the weight of the helium (assuming it occupies the maximum volume) from the maximum buoyant force:
Additional Weight = Max Buoyant force - (Helium density * Max Volume of Helium * g)
Substituting the values:
Additional Weight = 64626.1 N - (0.178 kg/m^3 * 5303.4 m^3 * 9.8 m/s^2)
Additional Weight ≈ 319852.52 N
So, the blimp can carry approximately 319852.52 N of additional weight and still maintain a constant altitude.
I hope this helps! Let me know if you have any other questions.
To find the weight that the blimp can carry and still maintain a constant altitude, we need to consider the buoyant force equation.
The buoyant force (B) is given by the equation:
B = (density of the fluid) × (volume displaced) × (acceleration due to gravity)
Given:
Density of the atmosphere = 1.21 kg/m³
Volume of the blimp = 5450 m³
Density of helium = 0.178 kg/m³
To find the weight that the blimp can carry, we can set up the equation:
B = (density of the atmosphere) × (volume displaced) × (acceleration due to gravity)
Substituting in the given values:
B = (1.21 kg/m³) × (5450 m³) × (9.8 m/s²)
Simplifying:
B = 63,924.6 N
This is the buoyant force that suspends the blimp in the air.
To find the weight that the blimp can carry in addition to the helium, we subtract the weight of the helium from the total buoyant force.
Weight of helium = (density of helium) × (volume of blimp) × (acceleration due to gravity)
Weight of helium = (0.178 kg/m³) × (5450 m³) × (9.8 m/s²)
Weight of helium = 95,675.8 N
Weight blimp can carry = (total buoyant force) - (weight of helium)
Weight blimp can carry = 63,924.6 N - 95,675.8 N
Weight blimp can carry = -31,751.2 N
Since the result is negative, it means that the blimp cannot carry any additional weight and still maintain a constant altitude.
To find the weight that the blimp can carry in addition to the helium and still maintain a constant altitude, we need to consider the concept of buoyancy.
A) Buoyant Force:
The buoyant force is the force exerted on an object immersed in a fluid (in this case, the blimp in the atmosphere). It is equal to the weight of the fluid displaced by the object. So, to calculate the buoyant force on the blimp, we need to find the weight of the air displaced by the blimp.
Buoyant Force = Weight of Air Displaced
The volume of the blimp is given as 5450 m^3 and the density of the atmosphere is given as 1.21 kg/m^3. Using these values, we can find the weight of the air displaced:
Weight of Air Displaced = Volume of Blimp * Density of Air
= 5450 m^3 * 1.21 kg/m^3
= 6594.5 kg
To convert this weight to newtons, we need to multiply it by the acceleration due to gravity, which is approximately 9.8 m/s^2:
Buoyant Force = Weight of Air Displaced * Acceleration due to Gravity
= 6594.5 kg * 9.8 m/s^2
= 64657.1 N
So, the buoyant force that suspends the blimp in the air is approximately 64657.1 N. Your calculation of 64626.1 N is close, but might be a rounding error in the intermediate steps.
B) Comparison to Blimp's Weight:
To compare the buoyant force with the blimp's weight, we need the weight of the blimp, which is the mass of the blimp multiplied by the acceleration due to gravity.
Weight of Blimp = Mass of Blimp * Acceleration due to Gravity
The density of the helium inside the blimp is given as 0.178 kg/m^3. So, to find the mass of the blimp, we need to multiply the density of helium by the volume of the blimp:
Mass of Blimp = Density of Helium * Volume of Blimp
= 0.178 kg/m^3 * 5450 m^3
= 971.9 kg
Weight of Blimp = Mass of Blimp * Acceleration due to Gravity
= 971.9 kg * 9.8 m/s^2
= 9526.6 N
Therefore, the weight of the blimp is approximately 9526.6 N.
Blimp's Weight is equal to 9526.6 N, which is slightly less than the buoyant force (64657.1 N) calculated earlier. So, the blimp will be in equilibrium and remain suspended in the air.
C) Weight the Blimp can Carry:
To determine how much weight the blimp can carry in addition to the helium and still maintain a constant altitude, we need to calculate the net force acting on the blimp. Since it is maintaining a constant altitude, the net force must be zero.
Net Force = Buoyant Force - Weight of Blimp - Weight of Additional Weight
= 0 (constant altitude)
Rearranging the equation, we can solve for the weight of the additional weight:
Weight of Additional Weight = Buoyant Force - Weight of Blimp
Weight of Additional Weight = 64657.1 N - 9526.6 N
= 55130.5 N
Therefore, the blimp can carry an additional weight of approximately 55130.5 N (which is equal to the buoyant force minus the weight of the blimp) and still maintain a constant altitude.