# 2 airplanes same size and shap different mass

2 identical balls of different mass dropped from same height reach the ground at the same time due to the acceleration of gravity being constant.

If I understand correctly the ball with more mass does have a greater force acting on it but due to its greater mass it takes more force to more it and they cancel out.

• Therefore is it correct to say that 2 identical airplanes of different weight only need to equal the acceleration of gravity in other direction to stay in the air?

• But the heavier plane requires more upward force (lift) as it has more mass so is harder to move to equal the same force of upwards acceleration than the lighter airplane?

• The lift has to be equal and opposite to the gravitational attraction $m_{\text{aeroplane}} g$. – Farcher Feb 4 '16 at 9:03
• distance is same for both the balls and so the value of acceleration ($g$). Hence use the equation $$s=ut+\frac 12 at^2$$ and $u$ is zero for both the balls. Hence you can see this equation is independent of the mass. – Anni Feb 5 '16 at 9:43

It is true that the heavier plane needs a greater lift and this is seen in practice. If two planes at equal altitude loose power at the same time and one weighs more than the other they will be able to glide the ...... same distance! One of them descends faster than the other but it glides forward faster to generates more lift.

It seems odd, but one descends faster and simply arrives ahead of the lighter plane. This works within reasonable limits where air speeds are not so different that air friction becomes a limiting effect.

The example of dropping two balls is strictly true only in a vacuum and not a good analogy for the behavior of an airfoil.

• Not steeper, just faster. Both lift and drag are proportional to velocity squared, so their ratio is roughly constant, L/D. The tangent of the descent angle is just D/L. So if Weight is greater, Lift must be greater, so Velocity increases as the square root of Lift, and Drag increases linearly with Lift. So - same angle. For a small plane, the L/D ratio is about 9. For a jet airliner it is more like 25. For a sailplane, 30. – Mike Dunlavey Feb 5 '16 at 12:36
• Yes, of course. Doh! If one was steeper it would never reach the same landing point. – C. Towne Springer Feb 8 '16 at 4:47

well you see the lift has got to do with the mass. Because of the design of the wings of the airplane the speed of wind going above the wing is more than the speed of air going from the bottom of the wing. Therefore from the Bernoulli's equation the pressure above the wing is less than the pressure below the wing. this pressure difference causes the lift.

now suppose the mass of the airplane is $m$ ton and when it moves with a big velocity its wings produced a pressure difference of $P$ because of which the plane moves up with an acceleration of $a$ therefore the equation comes out to be

$$\frac PA- mg = ma$$ where $A$ is the surface area of the wings.

so from this you can see that the lift has got to do with mass. heavier the plane is more lift is required, so plane need more velocity to lift up, so a longer runway!

however the falling balls falls at same time because of the equation $$s=ut+\frac 12 at^2$$ and this equation is independent of mass.

F = MA. The force required to lift a plane is mass times acceleration. Acceleration on earth is around 9.8m/s/s. The mass increase will therefore increase the amount of force it's applying, and therefore the force required to cancel it out. Two balls of the same shape but one has more mass, it will fall at the same speed as the other, but will press harder on your hand when you hold it, and you have to push harder to hold it up. Same with the planes, they will fall at the same speed, but more force is needed to cancel out the force of the heavier plane. Gravity is just the acceleration towards earth, things the same shape will fall at the same speed, but if they have different masses, they exert more force. Force itself is not acceleration.