# B F=ma -- True or an Illusion...

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1. Dec 20, 2017

### Pranav

Imagine, There's a ball in deep space traveling with a constant velocity of 25m/s and is having mass 25kg.
Now as I said, ball is traveling with a constant velocity that simply means acceleration=0 and now if we calculate the force with F=ma we will end up with 0. But if that ball collide with a Space Shuttle it will produce a change in velocity of shuttle, which can be only be done by force. So, how the hell can we say that Force is equal to zero in this case.

If you are weak in imagination try considering this as an example:-
One day, I am driving my 1814.369kg or simply 4000 pounds car on a straight road which is applying no friction to my car's with a constant velocity of 35m/s and suddenly Mr.Einstein comes in front of my car(even I don't know how) I thought of Newton's formula F=ma according to which Mr.Einstein will not die but will start traveling with me(As their is no friction being applied by the road) but when I actually hit the Mr.Einstein, he died.
If you don't believe ask your friend to hit you with a car with a constant velocity of 30km/hr and If you don't die=>
Congrats!!!

Next Time I am going to use speech to text for writing long questions.

2. Dec 20, 2017

### jbriggs444

The fact that a ball has no acceleration now says nothing about the force and acceleration it will undergo when it collides with a space shuttle or the hood of your car.

3. Dec 20, 2017

### Pranav

Sir, Do you want to say that Force is somewhere related to velocity....?

4. Dec 20, 2017

### jbriggs444

No. If I'd wanted to say that, I'd have mentioned that acceleration is the first derivative of velocity.

The point is that F=ma relates acceleration (a) at a particular time to force (F) at that same time. It does not relate acceleration now to force later or force now to acceleration later.

5. Dec 20, 2017

### Pranav

But Sir my a is zero during my whole journey.

6. Dec 20, 2017

### jbriggs444

Not if you collide with a space shuttle, it's not.

7. Dec 20, 2017

### Pranav

But if i collide with a space shuttle the my acceleration will be changed to retardation.

8. Dec 20, 2017

### jbriggs444

Any change in velocity over time is an "acceleration", regardless of whether the object speeds up, slows down or changes direction.

9. Dec 20, 2017

### Pranav

What if acceleration is negative, will Force also be negative??

10. Dec 20, 2017

### Staff: Mentor

The force is zero while it is not accelerating (free space) and non zero while it is accelerating (collision). The question is why you would think that the force should be the same in the two cases. Based on your own personal experience surely you can appreciate the fact that the force during a collision is different from the force during a non-collision.
If he starts traveling with you then what is his acceleration?

11. Dec 20, 2017

### jbriggs444

Yes. Force and acceleration are both vector quantities. They have both magnitude and direction. If the net force is in a particular direction then the associated acceleration will be in that same direction.

12. Dec 20, 2017

### Pranav

It is arising another question in my mind:- How will negative Force affect on a body??

13. Dec 20, 2017

### Pranav

Thank You very much Sir you explained it to me in a very simple manner.
Once Again, Thanks!!

14. Dec 20, 2017

### jbriggs444

A "negative" force is nothing more than a force in the opposite direction. For instance, staggering into the wall on the right and then staggering into the wall on the left.

Which direction you choose to call positive and which negative is purely up to you.

15. Dec 20, 2017

### Staff: Mentor

I'm not sure if You're figured it out by now, but something not said explicitly:

You're making the mistake of trying to apply f=ma as one single condition, over the entire life of an object. "a" (and its integrals and derivatives) has a time component, so the inputs and outputs can change over time.

Or more succinctly: your fist post says "in this case", when clearly it contains TWO separate cases where f=ma produces a different answer (both of which are correct).

16. Dec 20, 2017

### TurtleMeister

17. Dec 20, 2017

### jbriggs444

That sounds close. One might [mistakenly] reason thus:

"There is a concept of the "force of a collision". The impacting object imparts this force on the target. In order to impart such a force, the impacting object must have possessed the force prior to impact. How much force did the impacting object possess? One applies the formula F=ma to see. If an object was on an unaccelerated straight line path then the force is zero. But wait, this makes no sense."​

The problem is that "force" is not an attribute possessed by an object. Instead it is a number that describes one aspect of an interaction between two objects -- how hard are they pushing or pulling on one another at a particular moment. Force is also not a conserved quantity. It does not have to be carried into and out of an interaction. It can change during an interaction. [And the "force of a collision" is more a meaningless generality than a specific measurable thing].

By contrast, energy and momentum are conserved quantities. At all times before, during and after an interaction the total momentum is the same. At all times before, during and after an interaction the total energy is the same.

Last edited: Dec 20, 2017
18. Dec 20, 2017

### sophiecentaur

Of course. The acceleration is negative because the force was in the direction against the original velocity.
Look up the strict definitions of all the quantities that have been touched on in this thread. The system is self consistent and won't give you any paradoxes.

19. Dec 26, 2017

### albertrichardf

One thing to add: F = ma is a formula that is applicable at any point in time.

What I mean by that is that F = ma only tells you about the force at the instant you apply it. Say you apply the formula at t = 0. The force is F = ma, with a being the acceleration at t = 0. This tells you nothing about the force at t = 1. You'd need to apply F = ma, again, but this time a is the acceleration at t = 1.
F = ma gives you the instantaneous force, and the force at a given instant tells you nothing about the force at the next. So even if F = ma = 0 for the first leg of the journey, it doesn't mean that in the second leg, F = 0.

There are formulations of physics that aren't instantaneous, but rather, give you information about the whole path. One such formulation is the principle of least action, where you actually work out a property that holds for a given path. In classical mechanics, for instance, the principle tells you that the path taken will be the one that always has the lowest (or highest, it doesn't really matter. The point is that it is an extremum) value for ∫(K - U)dt for the given time of travel, where K is the kinetic energy and U the potential energy. This is descriptive of the path: you could make up any number of paths where this integral is not an extremum, but the principle of least action tells you that the real path is the one that always satisfies this condition. This is in contrast to the force approach, which tells you nothing about the path taken, and instead tells you the force at any given time.

20. Dec 26, 2017

### ChocolateScrub

Before the object hits the space shuttle, F=ma=0, since there is no acceleration.
When it hits the space shuttle, the object experiences a negative acceleration, giving rise to a negative force. Newton's Third Law says that this force must be part of an action-reaction pair, so the space shuttle experiences an equal positive force.
This is why Mr Einstein dies, because his body experiences a force from the collision. The car loses momentum and kinetic energy while Einstein gains momentum and kinetic energy. These are the two quantities that are "exchanged" during a collision. Force can change at any instant, and isn't conserved.