# B Feeling Forces (like feeling gravity while in free-fall)

#### JLT

Summary
Question: Imagine you are a tennis ball thrown up into a vacuum on earth. Constant acceleration, you slow down, stop, then turn around and fall down. If you have no eyes, can you feel when you stop and turn around? The force is constant - just gravity. The acceleration is constant. Your direction is not constant. Can you feel change in direction? Going up vs. coming down?
a = (change in magnitude of velocity) + (change in direction of velocity)

→ Can you feel when you change direction? Even if force and acceleration are constant?
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#### JT Smith

Tennis balls don't have any feelings.

You or I wouldn't be able to tell. But it's at least theoretical possible that a device would be able to sense the difference in tidal force as a function of altitude. Or maybe I'm wrong.

#### Nugatory

Mentor
If you have no eyes, can you feel when you stop and turn around? The force is constant - just gravity. The acceleration is constant. Your direction is not constant. Can you feel change in direction? Going up vs. coming down?
You won't feel any change in direction. You're in free fall, and it's no different than floating in a spaceship in orbit around the earth .
(You might still be able to feel a change in the direction of air resistance, but we can also imagine doing the experiment in a vacuum and then there's no air resistance to feel).

#### JLT

Tennis balls don't have any feelings.

You or I wouldn't be able to tell. But it's at least theoretical possible that a device would be able to sense the difference in tidal force as a function of altitude. Or maybe I'm wrong.
Yes, just a thought experiment - so pretend you don't have bodily fluids sloshing around, just a homogeneous point mass with each point undergoing the same constant acceleration.

Can you model the top point as rotational motion? Perhaps consider r→0,
a = (change in magnitude of velocity) + (change in direction of velocity)
a=(dVet)/dt
a=(dV/dt)et+V(det/dt)
a=rαet+V((det/dθ)(dθ/ds)(ds/dt)
a=rαet+V((en)(1/r)(V)
a=rαet+(v^2/r)en
or
a=rαet+r ω^2)en

or throw in a parabolic path, variable r gives:
a=(d^2r/dt^2 -r ω^2)en + (rα+2(dr/dt)ω)et

Could you feel the different parts of acceleration - which piece is changing magnitude, and which is changing direction? Even if they add up to something constant?

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#### Nugatory

Mentor
Could you feel the different parts of acceleration - which piece is changing magnitude, and which is changing direction?
No, you won’t feel anything, and that is because there’s nothing to feel. The directly measurable physical fact is that the distance between the tennis ball and the surface of the earth is changing. The acceleration of the ball is just an artifact of our arbitrary choice to consider the surface of the earth to be stationary; we could just as well explain the changing separation by saying that the ball is at rest while the surface of the earth is accelerating.

It would be different if we were to strap a rocket engine onto your back. You would feel the tension in the straps as they accelerated you along with the rocket; that tension can be directly measured and tells us that you are the one that’s really accelerating. But with gravity there’s nothing to feel because everything is moving together. (Gravity is unique this way, and that’s the basis of Einstein's theory of general relativity - off-topic here).

#### JLT

You won't feel any change in direction. You're in free fall, and it's no different than floating in a spaceship in orbit around the earth .
(You might still be able to feel a change in the direction of air resistance, but we can also imagine doing the experiment in a vacuum and then there's no air resistance to feel).

Forces can be felt - accelerometer, we can detect a mass tugging on a spring. Moment of inertia - we can detect resistance to change in rotational as well as translational velocities

Seems like there should be a way to create something that could distinguish between acceleration created by changing the magnitude vs. changing the direction.

How about two tennis balls, connected by a spring, let one have an initially faster velocity than the other as you throw both of them in the air. That could detect change in direction - but I guess you would need two balls, not just one. ... A human with stomach fluids sloshing around , might be able to feel it, but a homogeneous object could not feel it?

#### JLT

No, you won’t feel anything, and that is because there’s nothing to feel. The directly measurable physical fact is that the distance between the tennis ball and the surface of the earth is changing. The acceleration of the ball is just an artifact of our arbitrary choice to consider the surface of the earth to be stationary; we could just as well explain the changing separation by saying that the ball is at rest while the surface of the earth is accelerating.

It would be different if we were to strap a rocket engine onto your back. You would feel the tension in the straps as they accelerated you along with the rocket; that tension can be directly measured and tells us that you are the one that’s really accelerating. But with gravity there’s nothing to feel because everything is moving together. (Gravity is unique this way, and that’s the basis of Einstein's theory of general relativity - off-topic here).

You feel gravity though - an accelerometer in a complete void, just one object surrounded by nothing, and the spring is not stretched out. If there are two objects, those masses attract one another, you can feel it - could detect the other object with an accelerometer, right? Th moon tugs at the ocean etc. you can measure the tides - can't wrap my head around gravity I guess.

Rocket engine + human - if there are two objects, you can feel tugging between the two.

#### Nugatory

Mentor
Seems like there should be a way to create something that could distinguish between acceleration created by changing the magnitude vs. changing the direction
The distinction you are looking for is between “coordinate acceleration” and “proper acceleration”; that’s why I pointed you at that other thread. Introductory physics classes often gloss over this distinction and just say “acceleration”, but they are different things and the difference matters.

Proper acceleration is what an accelerometer measures and what you can feel. All rotations involve some proper acceleration, so can always be felt if you are sensitive enough (you and I cannot feel the rotation of the earth, but a Foucault’s pendulum will).
Gravity does not produce proper acceleration, which is why your tennis ball feels nothing.

#### JLT

“coordinate acceleration” and “proper acceleration”;
Thanks, I'll go study those.

#### Nugatory

Mentor
you can measure the tides - can't wrap my head around gravity I guess.
Tidal forces are caused by differences in the force of gravity in different places. Even the tennis ball could, in theory, detect a tidal force (as @JT Smith suggested in #2 above):
Newton’s law says the Earth’s gravitational force on a mass $m$ is $Gm_Em/r^2$ where $m_E$ is the mass of the earth and $r$ is distance to the center of the earth. But the distance to the top of the tennis ball is greater than the distance to the bottom of the tennis ball, so the force on the top is slightly less (it’s the difference between dividing by $r^2$ and $(r+R)^2$ where $R$ is the diameter of the tennis ball) and the ball will stretch as the bottom tries to accelerate more quickly towards the earth than the top. This stretching force could in theory be detected by a sensitive enough device.

But note that:
1) point particles cannot feel tidal effects because these effects need a difference in force between two nearby points - and a point particle is only at one point.
2) the tidal force the tennis ball feels is completely unrelated to the acceleration you asked about in the first post of this thread.

#### Mister T

Gold Member
If you were a passenger in a car that coasts up a ramp and then back down, you would feel no different at the turning point when the car changes direction. However, if the the driver were to slam on the brakes at that instant you would be able to feel that. The reason is because the braking causes the acceleration to change.

#### jrmichler

A practical application of this is the Vomit Comet (search the term). Here's one of many good links: https://www.space.com/37942-vomit-comet.html.

The airplane flies a parabolic path such that the vertical component of acceleration is 32.2 ft/sec^2, and they fine adjust the throttles along the path to compensate for air drag. The airspeed is continuously changing, so the engine thrust also must be changed accordingly. The result is that the airplane flies a path identical to that of the OP's tennis ball in vacuum. And, since the airplane is much larger than a tennis ball, the people inside can directly experience what the OP is trying to imagine.

"Feeling Forces (like feeling gravity while in free-fall)"

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