A physics problem.

[Turkz]

I am working out of Halliday and Resnick's 7th edition Fundamentals of Physics. On page 26, Sample problem 2-7, a man goes over Niagara Falls in a steel ball. The author(s) claim that once he is in free fall, he is unaware of his increasing speed because the acceleration during the fall was constant. It is only when he hits the water that he notices a change in speed due to a change in acceleration.

Now I disagree. The man should be aware of his changing velocity in both cases, constant or otherwise. I can give several examples of similar circumstances where you most certainly will notice your changing velocity.

For instance in your car. If you are traveling at a constant velocity and don't look out a window. You would not be able to tell the difference between 20mph or 50mph. Press down the gas or brake pedal a certain distance and hold it there and you will be pushed back into your seat or lean foward respectively for as long as either pedal is applied.

Numerous amusement parks rides simulate free fall and I guarantee you notice your stomach move up into you throat. A similar situation occurs with elevators which is correctly discussed on pages 18 and 20 Sample Problem 2-2.

I believe the author(s) are confusing a situation with a constant velocity with one with a constant acceleration.

 

[LS20]

the authors are right. ive taken tons of free fall rides, as soon as you drop it feels the same 1/3rd of the way through the drop as it does 2/3rd through the drop, etc.

your example with the car is is misguided. a car will have different acceleration with the gas pedal down. the torque output (providing for acceleration) changes as the engine speed changes. look at a dynograph that plots torque curves. also, as the car is accelerating, it encounters more and more aero resistance. so no, cars do not accelerate with constant rates

 

[thesurge]

Think about this. At constant velocity, you cannot tell a change in position (imagine your in black space at constant velocity).

 

[3NF]

I think what the author is trying to say is that you aren't going to notice anything, unless there is a change in acceleration (force). The change in acceleration with respect to time is known as "jerk".

Jerk

 

[dighn]

I think the question is badly worded. You definitely can feel constant acceleration. It's just that in the case of free fall, the accelerating force is applied to every part of your body so you feel nothing. But when you hit the water, the reverse acceleration force is only applied to some parts so you do feel a force.

 

[drinkmorejava]

The author is right, various sensory inputs like feeling the wind brush past you aside, you wouldn't be able to tell. It's probably a lot easier to think of a scenerio where you would be able to tell than not though.

 

[LS20]

Originally posted by: dighn
I think the question is badly worded. You definitely can feel constant acceleration. It's just that in the case of free fall, the accelerating force is applied to every part of your body so you feel nothing. But when you hit the water, the reverse acceleration force is only applied to some parts so you do feel a force.

do you feel anything when youre sitting on a couch?

 

[yhelothar]

It does seem quite counter-intuitive.

 

[91TTZ]

You can feel when you're falling, since your body expects to be experiencing 1g at all times. You'll know when you're falling. It'll be the same sensation that astronauts get.

 

[Fenixgoon]

if the man is inside a steel ball, the interior surface of the ball does not move with respect to the man, therefore from his perspective, he is not moving.

 

[dighn]

Originally posted by: LS20

Originally posted by: dighn
I think the question is badly worded. You definitely can feel constant acceleration. It's just that in the case of free fall, the accelerating force is applied to every part of your body so you feel nothing. But when you hit the water, the reverse acceleration force is only applied to some parts so you do feel a force.

do you feel anything when youre sitting on a couch?

I feel the pressure on my ass it's not unlike being pushed into the seat in an accelerating car

 

[PowerEngineer]

Halliday and Resnick... oh, the memories! Resnick was actually my instructor for freshman physics.

But to your question, I'm thinking the authors are right. As long as you and your surroundings are all accelerating at the same rate, then your speed relative to your surroundings will be unchanged (although both you and your surroundings are increasing speed with reference to an outside reference). In fact, only by giving in to acceleration will you ever not feel it. For instance, you feel your weight right now because the floor, chair, or whatever is opposing the acceleration of earth's gravity. When you drop in a steel ball over Niagra Falls, you're letting gravity have it's way for the short fall; by letting it accelerate you without opposition, you feel "weightless".

The problem with your car example is that the force that is accelerating the car is not also working directly on you. Your body wants to stay at its initial speed -- until the car seat forces it to move faster with the car.

Your "stomach move" on free-fall amusement rides is caused because your stomach (and other internal organs) are used to being pulled down by gravity into the bottoms of their available spaces; in free-fall they are weightless and can float around (very disturbing sensation!). What you're feeling is due to the change in acceleration, not the change in speed. Once the acceleration stops changing (and you are weightless), there'll be no sensation to tell you that your speed is increasing.

 

[91TTZ]

Originally posted by: Fenixgoon
if the man is inside a steel ball, the interior surface of the ball does not move with respect to the man, therefore from his perspective, he is not moving.

That is completely incorrect.

Are you telling me that when astronauts are inside the space shuttle, they can't tell when they're in 0 g? Your body can feel it. It can detect equilibrium, and expects to have 1 g being exerted in the proper direction.

He won't be able to tell whether he's in the first couple of seconds of freefall or if he's in orbit, but he will be able to feel a change in acceleration, which requires movement (or someone took away gravity, good luck with that)

 

[WHAMPOM]

The steel ball , the air inside, the man inside all move at or accelerate at the same speed. Essentially the same as freefall in a vacuum, till he hits bottom and enertia catches up to him.

 

[LS20]

confirm all your hypotheses by jumping off tall buildings

 

[91TTZ]

Originally posted by: Turkz
I am working out of Halliday and Resnick's 7th edition Fundamentals of Physics. On page 26, Sample problem 2-7, a man goes over Niagara Falls in a steel ball. The author(s) claim that once he is in free fall, he is unaware of his increasing speed because the acceleration during the fall was constant.

If you know you're on Earth and all of a sudden you feel the sensation of 0G, you have to expect that you're moving. That's because you have to make an assumption based on what's realistic or not.

Sure, it's possible that you were instantly teleported into orbit and you'll feel that 0G sensation forever, but that's not at all likely. So you can expect that you're falling, which on Earth requires you to be picking up speed towards the Earth. Since you know what there's not unlimited distance, you can expect to quickly decelerate pretty soon.

 

[WHAMPOM]

Originally posted by: 91TTZ

Originally posted by: Fenixgoon
if the man is inside a steel ball, the interior surface of the ball does not move with respect to the man, therefore from his perspective, he is not moving.

That is completely incorrect.

Are you telling me that when astronauts are inside the space shuttle, they can't tell when they're in 0 g? Your body can feel it. It can detect equilibrium, and expects to have 1 g being exerted in the proper direction.

He won't be able to tell whether he's in the first couple of seconds of freefall or if he's in orbit, but he will be able to feel a change in acceleration, which requires movement (or someone took away gravity, good luck with that)

Boy! Are you mixed up>

 

[91TTZ]

Originally posted by: WHAMPOM


Boy! Are you mixed up>

No, you're the one that's mixed up.

You're trying to tell us that the guy can't determine whether he's changing speed or not since he can't see outside and from his visual perspective, he's not moving.

I'm saying that he'll be able to feel the acceleration, which on Earth means that he's moving. If you just had a camera showing what he sees, you'd never be able to tell. If you had a G meter and knew he's on Earth, you'd be able to tell. That's because on Earth, the only way to experience 0G's is to be falling.

 

[Fenixgoon]

Originally posted by: WHAMPOM

Originally posted by: 91TTZ

Originally posted by: Fenixgoon
if the man is inside a steel ball, the interior surface of the ball does not move with respect to the man, therefore from his perspective, he is not moving.

That is completely incorrect.

Are you telling me that when astronauts are inside the space shuttle, they can't tell when they're in 0 g? Your body can feel it. It can detect equilibrium, and expects to have 1 g being exerted in the proper direction.

He won't be able to tell whether he's in the first couple of seconds of freefall or if he's in orbit, but he will be able to feel a change in acceleration, which requires movement (or someone took away gravity, good luck with that)

Boy! Are you mixed up>

we KNOW the man is moving because the ball is falling, and he is inside the ball. however, because his surroundings do not move (what he literally SEES), he does not feel as if he is moving, though he knows he is.

when you are driving a car - from your perspective, the surroundings are moving at X MPH relative to you, and you are stationary. we know, though, that you are in fact moving. we simply changed frames of reference.

edit: i used HRW for my physics classes too, fwiw

 

[Turkz]

Originally posted by: LS20
the authors are right. ive taken tons of free fall rides, as soon as you drop it feels the same 1/3rd of the way through the drop as it does 2/3rd through the drop, etc.

If the ride was long enough (just a few seconds would do it) your free fall may have reached some sort of terminal velocity during the middle of it. At which point there would be no acceleration.

Originally posted by: LS20
your example with the car is is misguided. a car will have different acceleration with the gas pedal down. the torque output (providing for acceleration) changes as the engine speed changes. look at a dynograph that plots torque curves. also, as the car is accelerating, it encounters more and more aero resistance. so no, cars do not accelerate with constant rates

I agree that it would be hard to mantain a constant acceleration with a gas pedal. But in a short enough time period it would be approximately constant and the example still valid. I was using a car so it would be easy to relate to but a rocket would do just as well. That is why they have inertial dampeners on the Starship Enterprise.

 

[Turkz]

Originally posted by: thesurge
Think about this. At constant velocity, you cannot tell a change in position (imagine your in black space at constant velocity).

At constant velocity you certainly can determine your position is changing. If you are in a car moving at 20mph and you pass a house on the side of the road. First that house was in front of you and then it is behind you. Relatively speaking if it was just you and the house you can't tell which one is really moving. You could use either frame of reference. In this example I am using the house since you are passing it at 20 mph.

If you were the absolutely the only thing in the universe this would be true (black space as you put it), because there would be nothing to compare your position to.

 

[Turkz]

Originally posted by: 3NF
I think what the author is trying to say is that you aren't going to notice anything, unless there is a change in acceleration (force). The change in acceleration with respect to time is known as "jerk".

Jerk

That is exactly the point I am constesting.

 

[opticalmace]

Turkz: The authors are correct, because this is based on observation. Certainly he knows that he is inside a steel ball, and knows he is on Earth, and is going down a waterfall. With that information, and his previous knowledge of gravitation on Earth, he knows his velocity will increase until he hits the water.

However, based on observation from his perspective only during the freefall, it is impossible to determine increasing velocity. What the authors are saying is that if he were magically born into a steel ball in this situation, he would be unable to determine if the ball had no velocity, in space, or if it were under constant acceleration, towards another body. He is weightless in both cases.

Ultimately, since he got into the ball, he personally knows that he is going to go down the waterfall.
From an observer's standpoint within a steel ball in which weight is not felt, however, increasing velocity cannot be determined.

BTW it's sample problem 2-6.

 

[Chaotic42]

Originally posted by: Turkz
once he is in free fall, he is unaware of his increasing speed because the acceleration during the fall was constant.

It's been a while since my last physics class, but that seems to be the key there. Once he is in free fall, his acceleration is constant. You only feel jerk, you don't feel and change during constant acceleration. That is, once his free body diagram only has a down arrow of magnitude g, he will not feel an increasing "falling feeling", even if he accelerates to 20Km/s.

 

[Savij]

Force = Mass x Acceleration. You feel the force. Your guts feel the force. You notice when the force changes. Ever been in a centrifuge? You don't notice much unless you try to apply force and lift your self up.

The only part of your body that (can) act as an (crappy) accelerometer is your inner ear, but it has a habit of adjusting to the situation it's in. When you spin yourself around you get used to it and then can't stand up because your brain has adjusted to the new acceleration.

What you feel when you get dropped is the force changing throughout your body. Your butt no longer has force applied to it. In turn, your inner organs lose that upward force and feel the push and pull of your body adjusting to not having the upward forces acting upon it. As soon as the forces reach equilibrium you have freefall. At that point you have a constant acceleration and you no longer feel the force changing.

dF/dA = 1M since your acceleration is constant...the forces on your body are not changing...

Also consider this: If you were accelerating at 100Gs in a vacuum by being pushed forward in a seat you would be very uncomfortable if not dead.

If you were accelerating at a 100Gs towards a black hole of a sufficient magnitude and a large enough distance to negate the length and width of your body you would be perfectly comfortable since everything in your body would be uniformly accelerated relative to everything else in your body. You really only notice the linear acceleration when your body has to struggle against its own mass.