# Multiheaded monster Force, acceleration and the speed of light.

• s_shrum

#### s_shrum

Multiheaded monster...Force, acceleration and the speed of light.

Me and my long time friend have been fighting over this for too long and can never seem to get together to head over to the College to get a prof. to settle this.

I am looking for:

2) Practical ways of explaining them

There are two problems (plus one more that I will add in for the theorists in the crowd) so I will throw them out 1 at a time and list my and my friends conclusions. Please tell me if one of us is right (or if we are both wrong) and if you can, please provide your reasoning.

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Question 1:
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GIVEN:
An object or thing (like a child on roller skates) is producing a force that moves that object 10 mph

GIVEN:
a small propulsion device (like a roman candle) that produces a force that moves it 2 mph

TEST CASE:
Strap the roman candle to the moving child ;-) not for real this is all hypothetical.

QUERY:
If an obect (the child) has a force greater then the propulsion (the roman candle), does the force of the propulsion:

a) do nothing to the total force; neither decrease or increase

My reasoning: Because force, regardless of its multiple sources, is additive when acting as propulsion (or subtract from it if acting against an object as resistance).

His reasoning: Because the propulsion force is less then the objects force, there will be no effect

QUESTION 2:
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Disregarding fuel weight, gravity of large planets, black holes, etc, let's set up a hypothetical scenario...in the empty void of space...

GIVEN:
A rocket ship is standing in space at 0mph (P0). It then produces a propulsive blast (B1) that causes the speed of the rocket to begin traveling from a dead stop (speed = 0) to a speed of 10mph.

GIVEN:
A week later, a 2nd *equal* blast (B2) is produced (I'll call this point in space P1).

What will the speed of the rocket be after the second blast in relation to P0:

a) 10mph
b) greater then 10mph

My answer: B - Greater then 10mph
My reasoning: The effects of the second blast provides a force which (based on my answer to the previous question) is additive. I conceed that the final speed may not be 20mph but will still add some additional speed to the rocket.

My freind's answer: A - 10
His reasoning: Becuase the blast is equal, the force output will be equal to the speed that the rocket is moving at and therefore will have no effect.

THEORY QUESTION 1:
===============

Is it possible to travel faster then the speed of light

a) no
b) yes

My answer: YES but... :-) My answer is based on my inital V-zero starting point (say Earth). I say that it is possible to obtain and pass the speed of light *c* based on the speed I am traveling away from my *original* V-zero starting point. As I pass the speed of light, those persons left behind at the V-zero starting point (Earth), will only see my traveling away UP TO the speed of light, even though my ship (and me in it) are traveling faster then light in relation to them (based on Einstein's law of addition). I conceed that I, in my ship, will never go faster then the speed of light as the speed of light is constant BASED ON MY RELATION TO THE LIGHT.

My Friend's answer is NO...just because nothing can go faster then the speed of light.

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I know this is kinda lengthy but I need to put an end to this mess...my friend is easily frustrated and it is driving me nuts that I can't get him to comprehend the difference between acceleration and speed.

TIA

Sean Shrum

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A head on collision does more damage than if you were to rear end a car that was going at the same speed but going the same direction. So that answers both 1 and 2. As for going faster than the speed of light that's a million dollar question.

Offf ! This is not going to be easy !

Question 1:
I don't quite understand this question.
First of all you cannot say that a force makes a speed.
A (resultant) force acting on an object will cause it to accelerate.
An acceleration of an object for a certain amount of time will give it a certain speed.
So your question needs to be rephrased, and make clear wether the time of effect of the force is the same on both objects.

Question 2:
Let me just make sure i got the question right first.
There is a certain rocket.
The rocket is at the middle of space, away from planets or other objects.
The rockets makes a moving blast.
The rocket moves at a certain speed after the blast is over (assumed to be 10 mph).
(that means that a force because of the blast made a certain acceleration on the rocket, which stayed for a certain time, therefore giving the speed of 10 mph for the rocket)
Now after some time ...
(you must know that at this point (And even before the second blast) the speed of the rocket will STILL be 10 mph, according to the first law of Newton).
Another blast is made by the rocket (of the same type, for the same time)

Well, the speed of the rocket after the second blast will be more than 10 mph (typically 20 mph). (assuming that the rocket did not 'rotate' in anyway, actually it needs a third blast to rotate)
This can be explained in more than a single way.
The first way :
The blast is a certain acceleration, and we said that the blast time is the same in both cases, and a certain acceleration acting for a certain amount of time means the same change in speed.
In other words ...
If the acceleration of the rocket was 10mile/(hour^2), and stayed for the time of 1 hour, it will give a change of speed of 10 mph.
At the first blast, the speed of the rocket before the blast was 0 mph. so a change of 10 mph will make the speed of the rocket to 10 mph.
In the second blast the speed of the rocket initially was 10 mph, and a change of 10mph will make the speed of the rocket into 20 mph.
The second way .
Since both of the blasts are identical, it means that both took the same amount of energy.
That energy (originally in the fuel) would have changed into other forms of energy (thermal, kinetic (which makes the movement), and at the same ratios.
So the same blast will make the same change of kinetic energy.
Kinetic energy (KE) is taken to equal :
[del]KE=0.5*m*[del]v^2.
Where m is the mass of the object, and v is the velocity of it.
Because the mass of the rocket did not change from the first blast to the other (you said we would forget about the fuel change), therefore the change in velocity ([da]v) was the same in both cases Question 3:
No, you cannot pass the speed of light.
You have some kind of an idea, the speed of light measured by different people will not be the same, but it will always be less than ( c ).
It is quite complicated to explain how this is true, cause it does not agree with our everyday observations.

Hope i helped .

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As STAii has already pointed out, both you and your friend appear to have some misconceptions about the connection between force and speed(or velocity).

When a force is applied to an object, it will accelerate until the force ceases. (it will continue to increase speed until the force stops) The greater the force, or the smaller the mass of the object, the greater the acceleration. Once the force is removed, the object will continue at a constant speed until a new force is applied.

I think what is confusing you is that this is not what appears to happen normally in everyday life.

This is because there are more forces involved then the one pushing the object. There are also forces due to friction (with the air, ground etc.) these forces act in opposition to the force pushing the object, and act to slow it down and stop it. An object will maintain a constant speed only when the forces balance. If the pushing force exceeds the friction forces, the object will speed up according to the difference. If the friction forces exceed the pushing force, trhe object will slow to a stop, (or if not moving to begin with, won't move at all.

In space, as with your rocket question, Friction forces are, for all practical purposes, zero, so you don't have to take them into account. The rocket will accelerate each time a force is applied to it.

Hi,

For
Q-1. Not sure. The propulsion device exerts force continuously but the object/child seems to exert in a burst. I'm not sure the populsion device could enhance the child's ability to exert more force.

Q-2 Yes. under the setup the individual burst of the rocket add to the velocity. examples satellite boosters being activated to adjust the position in its orbit.

Theory Q1 : No. If we assume that u r able to reach the velocity of light for argument then ur time dilation is infinity and the distance u have to travel contracts to zero. question of further acceleration does not arise at all. in no time u could be anywhere. remember that velocity of light c is constant in vacuum in any frame of reference including ur fast moving frame of reference. faster than light travel is not possible..!

To be more succinct:

Question 1: Newton's first law says an object at rest tends to stay at rest and and object in motion tends to stay in motion unless acted upon by an outside force. Therefore there is no inherrent force associated with a kid on roller skates. Adding a force increases (or decreases) the velocity according to f=ma (force = mass times acceleration).

Question 2: See question 1. If the first blast got the rocket going at 10mph, the second will add 10mph, bringing the total to 20.

Note, these are simplistic examples. Please, no one bring up friction and relativity. This doesn't need to be that complicated.

Theoretical question 1 (oops, I guess we do have to consider relativity). If you COULD travel faster than the speed of light, a person on Earth shining a flashlight on you would see you accelerate away from him, then suddenly disappear. But due to relativity, you can't accelerate to the speed of light and no observer would measure your speed to be faster than light.

WOW! Thanks for all the replies...let me explain Q1 a little bit more, bounce a reply question to A2 and then ponder with you more about my theory question.

I understand that various sources of FORCE are additive...let's say like a 4-engine jet plane. I understand that if each of these 4 engines are producing a force of X that the total force exerted on the aircraft will be

4 * X

Following this logic, let's say that 2 of the 4 engines are operating at half the power (and therefore producing half the force) of the remaining 2. My logic says that the resultant total force will be:

2 * X + 2 ( X / 2 )

Which means that the force applied to the aircraft will be less than 4 times but greater than 2 times. This, based on F=ma or a=F/m means that you will have a faster acceleration and therefore, over an equal time period will have traveled farther than if you were using only 2 engines.

My conclusion to this is that regardless of the amount of force that the engines are producing, they all help to push the aircraft forward. This means that 1) the aircraft will accelerate faster and 2) it's top speed will be greater than if it was using only 2 engines.

However, my friends conclusion is that because the force exerted by these 2 "half-power" engines is less then the 2 full power ones, no additional force will be exerted by the 2 half-power engines which would give the following:

2 * X + 0 ( x / 2 )

Therefore, does nothing to enhance the aircraft's acceleration and top speed.

I'm pretty sure that I am correct but I haven't been able to think of a practical example that would demonstrate this to him...granted I used the plane example with him and he still didn't get it.

As for the answers to Q2: Would it be correct to say that at each time the rocket produces a blast, the velocity at that time *in relation to the ship in space is always to be considered as zero...or do you always treat it as a moving vector (speed and direction)...hmmm after saying that I think it's *moving vector*. Anyways, my thoughts on this are that the second blast would make the rockets speed faster, but I was unsure if the second blast would produce a equal amount of speed gain...instead of 20, maybe it would be 18, and so on and so on with each successive blast.

As for my theory question, so far everyone has stated (pretty much) that the 2nd blast in Q2 will produce additional velocity. Based on this, if you have a *never ending power source* that could do these short practical 10mph bursts for a total of 30 million times:

10+10+10+10+10+...

Could you not attain the speed of light of 299,792,458 m/s (and pass it) *in relation you starting point*?

See my logic ;-)

Your input will be greatly apprechiated...

TIA

Sean Shrum

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1. Add to it. Obviously depending on the direction of the force vector. (of course, as explained, force does not produce velocity but acceleration)
2.You are correct. If the blast goes off, there is no resultant force on the ship. Hence it undergoes motion at a constant velocity. The second blast gives an momentary second resultant force, and if sustained for the same amount of time, would cause the same change in velocity. At such low velocities and without a resistance force proportional to velocity, the current velocity of the ship is of almost no consequence.

T1. By speed of light, you mean c right? Then no, by conventional methods (things like quantum entanglement (teleportation) and wormholes may offer a possibility)
The way you described does not work. Time dilation in relation to the Earth time frame (ie. the coordinate you are measuring realtive to) would occur to you as well as to earth. Though you will feel time is progressing normally, your velocity will reduce and power required will increase towards infinity.

now... for the latest post...

I understand that various sources of FORCE are additive...let's say like a 4-engine jet plane. I understand that if each of these 4 engines are producing a force of X that the total force exerted on the aircraft will be
4 * X
Following this logic, let's say that 2 of the 4 engines are operating at half the power (and therefore producing half the force) of the remaining 2. My logic says that the resultant total force will be:
2 * X + 2 ( X / 2 )
That is correct. (ok, turbulence and stuff may occur, but don't worry about that)
However, my friends conclusion is that because the force exerted by these 2 "half-power" engines is less then the 2 full power ones, no additional force will be exerted by the 2 half-power engines which would give the following:
2 * X + 0 ( x / 2 )
This is deeply, deeply wrong. It is very easy to prove by counterexample. Lift a pen. When you lift a pen, you exert a force on it that is greater than the force of gravity. By this hypothesis, the pen no longer has a weight. So what keeps it from flying into outerspace? What is the "weight" you feel in your hands? Another example is to push a door. At one scale, your hand is applying a force to the door. But you can consider it at each individual cell on your skin applying a small individual force on the handle (this also brings in the concept of pressure. Pressure is the force applied per unit area) Now, do we get the sum of the forces of the individual cells, or does just one count? I don't exactly think human cells are built to handle that sort of reaction force. Hmm... you edited it.
Ok... continued...
As for my theory question, so far everyone has stated (pretty much) that the 2nd blast in Q2 will produce additional velocity. Based on this, if you have a *never ending power source* that could do these short practical 10mph bursts for a total of 30 million times:
10+10+10+10+10+...
Could you not attain the speed of light of 299,792,458 m/s (and pass it) *in relation you starting point*?
According to classical mechanics, you can. But as we get into higher velocities, relativistic effects begin to be more and more apparent. As the object increases velocity, it experiences more time dilation relative to whatever it's velocity is approaching c with respect to. So, you will get closer and closer, but without infinite energy and hence force, never get there.
Consider a scenario. We have two spaceships heading away from earth. 1 is some way ahead of the other and is traveling at 0.5 c away from the earth. The other is chasing it and traveling at 0.9 c relative to the earth. As the 2nd captain looks back at earth, it would seem that his acceleration apparently has little effect on his velocity. He keeps pumping more and more power to the engines, but time dilation simply increases to compensate. If he looks forwards at the first ship, his acceleration seems to be much closer to what is expected, because the speed of 1 relative to 2 is less that that of 2 relative to the earth. This is expressed in the equation:

t = t0/[squ]( 1- v^2/c^2)

t = time from observer (eg from man on ship to earth)
t0 = time as seen in the same time frame as observer

Originally posted by FZ+
the 2nd captain looks back at earth, it would seem that his acceleration apparently has little effect on his velocity. He keeps pumping more and more power to the engines, but time dilation simply increases to compensate.
This is incorrect.

As a captain aboard a relativistic spaceship, you will measure no boundary to your maximum velocity. You can accelerate forever, and you will measure your velocity with respect to the stars are getting larger forever. On the helm of your spacecraft , nothing weird ever happens. You continue to fire your rockets at a constant force, and you continue to measure yourself accelerating -- forever.

You have confused time dilation -- time dilation does NOT mean that the captain on the rocketship measures his own acceleration as diminishing. (This would violate Galilean equivalence, by the way -- you can't measure uniform motion unless you look outside.) Instead, time dilation means that an outside observer would measure the rocket's acceleration as diminishing.

It takes light roughly 4 years to travel between Alpha Centauri and Earth. If you were on a rocket, you could travel between the two in one year -- or two minutes -- or one femptosecond -- according to your own watch. An observer in a frame stationary wrt the stars would measure that the quickest possible journey would be four years, however.

In the limit as the rocket approaches c, the captain would say that it took him zero time to travel between Earth and Alpha Centauri, while an Earthling would say it took him roughly four years.

- Warren

You're probably right. I get confused at times...

Originally posted by s_shrum

2 * X + 2 ( X / 2 )

Which means that the force applied to the aircraft will be less than 4 times but greater than 2 times. This, based on F=ma or a=F/m means that you will have a faster acceleration and therefore, over an equal time period will have traveled farther than if you were using only 2 engines.
It seems you have a little flow of logic in there.
You said that the force applied will be less, this is right.
Then you say that the acceleration will be more, and this is wrong.
You have made a right equation, i don't see why you made this wrong conclusion !
F=ma
Therefore:
a=F/m
so as F gets smaller, a must get smaller too, and not bigger .

Maybe at the beginning you were comparing the force to the case of the 4 engines, and then you compared the acceleration with the case of the two engines (which will be right then).

As for the answers to Q2: Would it be correct to say that at each time the rocket produces a blast, the velocity at that time *in relation to the ship in space is always to be considered as zero...or do you always treat it as a moving vector (speed and direction)...hmmm after saying that I think it's *moving vector*. Anyways, my thoughts on this are that the second blast would make the rockets speed faster, but I was unsure if the second blast would produce a equal amount of speed gain...instead of 20, maybe it would be 18, and so on and so on with each successive blast.

As for my theory question, so far everyone has stated (pretty much) that the 2nd blast in Q2 will produce additional velocity. Based on this, if you have a *never ending power source* that could do these short practical 10mph bursts for a total of 30 million times:

10+10+10+10+10+...

Could you not attain the speed of light of 299,792,458 m/s (and pass it) *in relation you starting point*?
No, you would not attend the speed of light.
Most people use the Newtonian laws to solve questions with speeds far from the speed of light.
Using the Newtonian laws, you will get the conclusion that we all got, which is that the blast will increase the speed of the rocket by the same amount each time.
This can be taken to be 'true', although there will be a little difference that no one will ever see.
But when you get nearer and nearer to the speed of light, Newtonian laws get wronger and wronger, and you will have to use relativity.
If you use relativity, you will see that each blast will get a slightly smaller speed than the blast before it.

Hope i helped.

Note that I said that your acceleration would be faster than *2 engines*...not faster then 4.