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An airplane of a total wing area of 120 m2 is in a level flight at some height. If the pressure difference between the upper and lower surface is 2.5 kPa, then the mass of the airplane is: [Take g = 10 ms-2]
- a)2 x 103 kg
- b)3 x 104 kg
- c)5 x104 kg
- d)7 x 107 kg
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
An airplane of a total wing area of 120 m2 is in a level flight at so...
Step 1: Balance the forces
(P1 - P2)A = mg
Step 2: Calculate the mass
Thus, m = 2.5 × 103 × 12010 = 3 × 104 kg.
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Community Answer
An airplane of a total wing area of 120 m2 is in a level flight at so...
Given:
Total wing area (A) = 120 m^2
Pressure difference (ΔP) = 2.5 kPa
Acceleration due to gravity (g) = 10 m/s^2
To find:
Mass of the airplane
Solution:
1. Calculate the force:
The pressure difference between the upper and lower surface of the wing creates a net force (F) which supports the weight of the airplane.
Using the formula:
F = ΔP * A
Substituting the given values:
F = 2.5 kPa * 120 m^2
F = 300 kN
2. Calculate the weight:
The weight of the airplane is equal to the force acting on it due to gravity.
Using the formula:
Weight (W) = mass (m) * g
Substituting the given value of g:
W = m * 10
3. Equate the force and weight:
Since the net force (F) supports the weight (W) of the airplane, we can equate the two:
F = W
300 kN = m * 10
4. Convert units:
The force is given in kN, so we need to convert it to N to match the unit of weight (N):
300 kN = 300,000 N
5. Solve for mass:
Substituting the value of force (W) into the equation:
300,000 N = m * 10
m = 300,000 N / 10
m = 30,000 kg
6. Answer:
The mass of the airplane is 30,000 kg, which is equivalent to 3 x 10^4 kg. Therefore, option B is the correct answer.
Total wing area (A) = 120 m^2
Pressure difference (ΔP) = 2.5 kPa
Acceleration due to gravity (g) = 10 m/s^2
To find:
Mass of the airplane
Solution:
1. Calculate the force:
The pressure difference between the upper and lower surface of the wing creates a net force (F) which supports the weight of the airplane.
Using the formula:
F = ΔP * A
Substituting the given values:
F = 2.5 kPa * 120 m^2
F = 300 kN
2. Calculate the weight:
The weight of the airplane is equal to the force acting on it due to gravity.
Using the formula:
Weight (W) = mass (m) * g
Substituting the given value of g:
W = m * 10
3. Equate the force and weight:
Since the net force (F) supports the weight (W) of the airplane, we can equate the two:
F = W
300 kN = m * 10
4. Convert units:
The force is given in kN, so we need to convert it to N to match the unit of weight (N):
300 kN = 300,000 N
5. Solve for mass:
Substituting the value of force (W) into the equation:
300,000 N = m * 10
m = 300,000 N / 10
m = 30,000 kg
6. Answer:
The mass of the airplane is 30,000 kg, which is equivalent to 3 x 10^4 kg. Therefore, option B is the correct answer.
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An airplane of a total wing area of 120 m2 is in a level flight at some height. If the pressure difference between the upper and lower surface is 2.5 kPa, then the mass of the airplane is: [Take g = 10 ms-2]a)2 x 103 kgb)3 x 104 kgc)5 x104 kgd)7 x 107 kgCorrect answer is option 'B'. Can you explain this answer?
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