Why don't heavy objects fall more SLOWLY?

[russ_watters]

Yes...

 

[Drakkith]

If I were to hit a bowling ball with a tennis bat and then a marble, both with the same amount of force won't one travell further than the other.
The marble and the bowling ball are separated on the floor of the craft.

In your spaceship you are accelerating them both at the same time to the same speed. Both of them are accelerating at the same rate and once you reach your maximum velocity both will be traveling at that velocity. Each one takes a different amount of force to accelerate, but since they are both on the floor of the ship at the same time they both have to accelerate at the same rate.

This is kind of similar to hitting both the bowling ball and the marble with the bat at the same time, except that hitting them with the bat has much more complicated physics come into play such as elasticity and such. Imagine you had them both sitting on a catapult at the same time and simply launched them into the air with it. Both would accelerate at the same rate to the same speed.

 

[Buckleymanor]

This is kind of similar to hitting both the bowling ball and the marble with the bat at the same time, except that hitting them with the bat has much more complicated physics come into play such as elasticity and such. Imagine you had them both sitting on a catapult at the same time and simply launched them into the air with it. Both would accelerate at the same rate to the same speed.

Yes if they were both sitting in or on the catapult together the bowling balls mass and the marble mass would each have an influence on each other and the catapult, so they would accelerate at same rate.
If they were separated and on the floor of the spacecraft , or placed on separate seats in the front of car when the craft decelerated or the car crashed and elasticity was 'allowed' to do what it does.
They would still accelerate at the same rate to the same speed.The less massive marble would not have as much elastic effect when first accelerated as the more massive bowling ball.
Thanks.

 

[Drakkith]

If they were separated and on the floor of the spacecraft , or placed on separate seats in the front of car when the craft decelerated or the car crashed and elasticity was 'allowed' to do what it does.
You would be able to tell that the objects are being accelerated and not in a gravitational field.

No, the floor of the spacecraft is like the catapult, accelerating both equally. Same for a car.

 

[Buckleymanor]

Yes I must have been editeing at the same time you were posting thanks.

 

[Buckleymanor]

In your spaceship you are accelerating them both at the same time to the same speed. Both of them are accelerating at the same rate and once you reach your maximum velocity both will be traveling at that velocity. Each one takes a different amount of force to accelerate, but since they are both on the floor of the ship at the same time they both have to accelerate at the same rate.

This is kind of similar to hitting both the bowling ball and the marble with the bat at the same time, except that hitting them with the bat has much more complicated physics come into play such as elasticity and such. Imagine you had them both sitting on a catapult at the same time and simply launched them into the air with it. Both would accelerate at the same rate to the same speed.

To be honest I am haveing trouble trying to understand this.
If you just had the the bowling ball on the floor of the spaceship and you accelerated it to your maximum velocity and then applied the brakes or reverse thrust and measured the distance and the speed it traveled at.
Then you repeated the same experiment with just the marble won't the distances and speeds of the two objects be different.

With respect to this question I posted.

If I were to hit a bowling ball with a tennis bat and then a marble, both with the same amount of force won't one travell further than the other.

And the answer I received from russ_watters

Yes...

If that is the case then won't it be possible to distinguish between acceleration due to gravity and acceleration due to acceleration.

 

[Drakkith]

To be honest I am haveing trouble trying to understand this.
If you just had the the bowling ball on the floor of the spaceship and you accelerated it to your maximum velocity and then applied the brakes or reverse thrust and measured the distance and the speed it traveled at.
Then you repeated the same experiment with just the marble won't the distances and speeds of the two objects be different.

There is no maximum velocity. Your velocity will continue to increase as long as you apply thrust. What you can do is measure the velocity relative to something else, like the Earth, for the amount of fuel you expend. Accelerating the ship with the bowling ball will get you to a lower velocity than with just the marble for the same amount of fuel.

Also, you say we should stop accelerating and apply the brakes. But that IS acceleration, it's just in the negative direction to your current vector. If you applied the same acceleration in both instances both the bowling ball and the marble would be traveling the same speed upon measurement. This is because once you reverse the thrust you are only accelerating the ship, and the motion of the ball and marble relative to the ship would be the same because the ship will accelerate the same in both cases.

And you cannot measure the distance the bowling ball or marble travel. Both will travel to the other side of the ship at the same velocity and hit the wall. Remember that in order to say that acceleration is the same as gravity we cannot "cheat" and look outside to see what is actually going on. We are forced to measure things inside the ship.

 

[TurtleMeister]

To be honest I am haveing trouble trying to understand this.
If you just had the the bowling ball on the floor of the spaceship and you accelerated it to your maximum velocity and then applied the brakes or reverse thrust and measured the distance and the speed it traveled at.
Then you repeated the same experiment with just the marble won't the distances and speeds of the two objects be different.

No. When the spacecraft reverses thrust, whatever objects are sitting on the floor will simply continue traveling at the velocity the spacecraft obtained before it reversed thrust (acceleration has been removed from the objects so Newton's first law applies). While the spacecraft (and the floor of course) will accelerate away from the objects (in the opposite direction).

If I were to hit a bowling ball with a tennis bat and then a marble, both with the same amount of force won't one travell further than the other.

Yes, one will travel faster than the other. But in that case you are hitting the objects separately at different times. That scenario is not analogous to the spacecraft scenario. Ask yourself this question: What would happen if you attached the bowling ball and the marble together and hit them both at the same time? That would be more analogous to the spacecraft scenario. You don't have to even attach them together, just hit them both at the same time.

 

[Buckleymanor]

And you cannot measure the distance the bowling ball or marble travel. Both will travel to the other side of the ship at the same velocity and hit the wall. Remember that in order to say that acceleration is the same as gravity we cannot "cheat" and look outside to see what is actually going on. We are forced to measure things inside the ship.

Correct me if I am wrong but that would only apply if the bowling ball and marble were on board the craft at the same time.If you took the bowling ball up first and measured it's velocity it would be slower than the marbles.

 

[Drakkith]

Correct me if I am wrong but that would only apply if the bowling ball and marble were on board the craft at the same time.

As long as you decelerate the ship at the same rate it doesn't matter if you have one or the other or both.

If you took the bowling ball up first and measured it's velocity it would be slower than the marbles.

Measured its velocity relative to what?

 

[Buckleymanor]

Measured its velocity relative to what?

You accelerate the craft for a given amount of time with maximum thrust with just the bowling ball on board then decelerate for another measured amount of time with maximum reverse thrust.
Then repeat with just the marble on board and then compare the time it took for the marble and bowling ball to leave the floor and hit the far side of the ship.

 

[TurtleMeister]

You accelerate the craft for a given amount of time with maximum thrust with just the bowling ball on board then decelerate for another measured amount of time with maximum reverse thrust.
Then repeat with just the marble on board and then compare the time it took for the marble and bowling ball to leave the floor and hit the far side of the ship.

The time would be the same. The mass of the bowling ball and marble have nothing to do with it (the time period you are talking about). What affects that time interval is the thrust of the rocket and the mass of the spacecraft (minus the bowling ball and marble). As I explained in my previous post, once the spacecraft reverses it's thrust the only thing that accelerates is the rocket. The bowling ball and marble (regardless of whether this exercise is done with them together or separate) will simply obey Newton's first law and "coast" until the other side of the spacecraft accelerates into them.

 

[Drakkith]

You accelerate the craft for a given amount of time with maximum thrust with just the bowling ball on board then decelerate for another measured amount of time with maximum reverse thrust.
Then repeat with just the marble on board and then compare the time it took for the marble and bowling ball to leave the floor and hit the far side of the ship.

It would be equal. In both cases the only thing you are decelerating is the ship, not the marble or bowling ball. So applying maximum thrust would cause both to reach the other side of the ship after an equal amount of time.

 

[Buckleymanor]

It would be equal. In both cases the only thing you are decelerating is the ship, not the marble or bowling ball. So applying maximum thrust would cause both to reach the other side of the ship after an equal amount of time.

Are you sure won't they have different closing velocities.
The marble and the ball would have attained different velocities with the initial acceleration.
Because you are only decelerating the ship the marble would have a greater intial velocity than the bowling ball because the ship would be lighter.

For instance if it were possible to stop the ship the craft that weighed more could not have attained the speed of a lighter craft with the same amount of thrust.

 

[Drakkith]

Are you sure won't they have different closing velocities.
The marble and the ball would have attained different velocities with the initial acceleration.
Because you are only decelerating the ship the marble would have a greater intial velocity than the bowling ball because the ship would be lighter.

For instance if it were possible to stop the ship the craft that weighed more could not attained the speed of a lighter craft with the same amount of thrust.

No, we are measuring the velocity relative to the ship, not an outside source. In such a case the velocity of the ship relative to an outside object is irrelevant, only the acceleration upon braking matters.

 

[Buckleymanor]

No, we are measuring the velocity relative to the ship, not an outside source. In such a case the velocity of the ship relative to an outside object is irrelevant, only the acceleration upon braking matters.

I don't see how that will prevent the lighter object reaching the other side of the ship more quickly.
The ship would have to accelerate at the same velocity for both which it won't becuase it's more massive with one object on board than the other.

 

[Whovian]

I don't see how that will prevent the lighter object reaching the other side of the ship more quickly.
The ship would have to accelerate at the same velocity for both which it won't becuase it's more massive with one object on board than the other.

No, the engine is accelerating the ship, but is not doing any work on the ball until it hits the edge. The ship and its contents are more massive, but it's what the engine is doing work on or accelerating that matters, and it isn't doing either to the ball initially. And aren't we starting to get into the basics of General Relativity here?

 

[Jasso]

I don't see how that will prevent the lighter object reaching the other side of the ship more quickly.
The ship would have to accelerate at the same velocity for both which it won't becuase it's more massive with one object on board than the other.

Ok, let's use some actual formula's for this. Suppose a rocket with an object inside had been constantly accelerated and then instantly reversed the direction of acceleration. At the moment that the acceleration changed, it had a velocity $v_0$, and we label the location as the origin. The distance the base of the rocket travels at a time $t$ later with new acceleration $-a_r$is:

$$d_r = v_0 t - \frac{1}{2} a_r t^2$$.

Now, up till now, the object was in contact with the base of the rocket, so it also had a velocity of $v_0$. However, once it loses contact with the ship, it will keep traveling at that velocity until it makes contact again. So the distance that the object travels in the same time $t$ is simply:

$$d_b = v_0 t$$.

If the chamber where the object is had a length $l$, and $t$ was the time it took for the object to travel to the other end, then the object would have to travel a distance of $d_r + l$ to make contact with the other side of the rocket (since both the ends of the chamber will have moved the same distance). So setting those equal:

$$d_b = d_r + l$$

Replacing $d_b$ and $d_r$ with the formulas and solving for $l$:

$$(v_0 t) = (v_0 t - \frac{1}{2} a_r t^2) + l$$
$$(v_0 t) - (v_0 t - \frac{1}{2} a_r t^2)= l$$

Collecting terms and simplifying:

$$(v_0 - v_0) t + \frac{1}{2} a_r t^2= l$$
$$(0) t + \frac{1}{2} a_r t^2= l$$
$$\frac{1}{2} a_r t^2= l$$

Solving for $t$:

$$t= \sqrt{\frac{2 l}{a_r}}$$.

Note that this doesn't depend on either the mass of the object or the velocity that it and the rocket are traveling at when the acceleration changes.

 

[Drakkith]

I don't see how that will prevent the lighter object reaching the other side of the ship more quickly.
The ship would have to accelerate at the same velocity for both which it won't becuase it's more massive with one object on board than the other.

No, the engines are only exerting a force on the ship, not the ball. The ship is not more massive because the ball is there. Only once the ball reaches the other side of the ship will it's mass have to be taken into account in regards to the acceleration.

Imagine you are in a ship floating in space with a ball in the center of a room just floating there. You fire your thrusters at a constant rate until the ball hits the side of the room. The rate of acceleration is independent of the mass of the ball because the ball is NOT having any work done upon it until it hits the wall. If I were an observer floating next to you looking in the window I would NOT see the ball move at all while the ship moved around it until it touched the wall.

This is exactly the same as when we stop firing the thrusters and begin to decelerate. As soon as the thrusters stop firing, neither the ship nor the ball are accelerating any longer. They are in the same situation as the above example, except with the ball floating at one edge of the room instead of the center. When I begin to fire my thrusters and decelerate the ship, I am NOT doing anything to the ball until it reaches the other side of the room, at which point it will touch the wall and we will have to expend energy to accelerate it as well, at which point it's mass comes into play.

 

[Buckleymanor]

No, the engine is accelerating the ship, but is not doing any work on the ball until it hits the edge. The ship and its contents are more massive, but it's what the engine is doing work on or accelerating that matters, and it isn't doing either to the ball initially. And aren't we starting to get into the basics of General Relativity here?

Of course it is, from the moment the craft leaves from wherever it takes off from it is doing work on every part of the ship including every thing on board.

 

[Buckleymanor]

No, the engines are only exerting a force on the ship, not the ball. The ship is not more massive because the ball is there. Only once the ball reaches the other side of the ship will it's mass have to be taken into account in regards to the acceleration.

From the moment the ship takes off it will expend more fuel and accelerate less if a heavy object is on board if this was not the case you could take a mountain on board and use no more fuel than if a marble was there.
What is mass if it is not the resistance to a force applied.

 

[Drakkith]

From the moment the ship takes off it will expend more fuel and accelerate less if a heavy object is on board if this was not the case you could take a mountain on board and use no more fuel than if a marble was there.
What is mass if it is not the resistance to a force applied.

Ignore the ship taking off. Focus on the deceleration part. That is where your confusion lies. If the ball is NOT in contact with the ship then the ship cannot exert a force upon it, meaning that it takes no extra energy to decelerate the ship while the ball is not in contact with the ship.

 

[Buckleymanor]

Ignore the ship taking off. Focus on the deceleration part. That is where your confusion lies. If the ball is NOT in contact with the ship then the ship cannot exert a force upon it, meaning that it takes no extra energy to decelerate the ship while the ball is not in contact with the ship.

I agree it won't exert a force on the ball if it is not in contact with it but it will still have to use more energy to decelerate a faster moveing ship, and that depends on which ball was on board when it was first accelerating.

 

[Drakkith]

I agree it won't exert a force on the ball if it is not in contact with it but it will still have to use more energy to decelerate a faster moveing ship, and that depends on which ball was on board when it was first accelerating.

We are not decelerating to a stop, we are only decelerating until the ball hits the opposite wall. The ship will not take more time to decelerate for either one.

 

[TurtleMeister]

I agree it won't exert a force on the ball if it is not in contact with it but it will still have to use more energy to decelerate a faster moveing ship, and that depends on which ball was on board when it was first accelerating.

It appears that your misconception is that the speed relative to the point of take off is relavent to this time interval. Well, it is not. The time interval in question remains the same regardless of what speed the spacecraft has attained relative to the start point and regardless of how much energy it took to achieve that speed.

 

[Jasso]

I agree it won't exert a force on the ball if it is not in contact with it but it will still have to use more energy to decelerate a faster moveing ship, and that depends on which ball was on board when it was first accelerating.

$$F = ma$$
The accelration only depends on the total force applied and on the mass that is being accelerated. Since there is no force on the ball when not in contact, it will not be accelerated, so the only thing being accelerated is the ship. Since the only thing being accelerated is the ship and the thrusters have the same force in both cases, it will have the same acceleration in both cases until the ball hits the other side.

 

[Buckleymanor]

It appears that your misconception is that the speed relative to the point of take off is relavent to this time interval. Well, it is not. The time interval in question remains the same regardless of what speed the spacecraft has attained relative to the start point and regardless of how much energy it took to achieve that speed.

So for a spaceship traveling at allmost lightspeed the time intervall will be the same as craft traveling at 1000Kph.

 

[Whovian]

So for a spaceship traveling at allmost lightspeed the time intervall will be the same as craft traveling at 1000Kph.

I think we're talking in the reference frame of the ship(?), in which case it won't matter what velocity it is traveling at relative to the takeoff point. The ship observes the takeoff point as time dilated and length contracted, the takeoff point observes the ship as time dilated and length contracted.

 

[TurtleMeister]

So for a spaceship traveling at allmost lightspeed the time intervall will be the same as craft traveling at 1000Kph.

Yes, that is correct (in the reference frame of the spacecraft ).