Table of Contents
Acceleration
Acceleration in an airplane
In an accelerating airplane, passengers feel a tendency toward the back and they are pressed to the back of their seats. Assume that we have a passenger A in front in the business class section and a passenger B all the way to the back. Will they feel different accelerations? And if so can we calculate accelerations for each passenger A and B?
In an accelerating airplane moving forward along a straight path, all passengers experience the same acceleration in magnitude because the airplane is a rigid body. This means that the entire airplane (including everything inside it) is accelerating uniformly as a single object, assuming no significant structural deformation. Thus:
Why the accelerations are the same:
- Newton’s Second Law: \( a = \frac{F}{m} \). Since the plane is moving as a rigid body, each passenger experiences the same external force per unit mass.
- Frame of Reference: Passengers are in the same reference frame (the airplane), so their experienced acceleration is identical in that frame.
Why they feel pressed to the back of their seats:
This sensation of being pushed backward is due to inertia. When the airplane accelerates forward, your body tends to remain at its current velocity (which feels like a force pressing you backward relative to the accelerating airplane).
Possible Misconception:
The only difference between Passenger A (at the front) and Passenger B (at the back) is their relative position inside the airplane, but this does not affect their experienced acceleration under uniform acceleration. If the acceleration varies along the length of the airplane (for example, during rapid turns or if the airplane flexes significantly), small differences might arise, but this is negligible in normal flight conditions.
Can We Calculate the Acceleration?
Yes! Assuming the airplane is accelerating at \( a \) (let’s say \( 5 \, \text{m/s}^2 \)):
- The acceleration experienced by both Passenger A and B is \( a = 5 \, \text{m/s}^2 \).
The acceleration magnitude is uniform throughout the plane. Let me know if you’d like to introduce additional factors like rotational motion or non-rigid motion for more complex cases!
Acceleration an space
- In the weightless environment of space only acceleration counts
- Should we say “matterless” or “massless” environment of space