# Violating f=ma

1. Apr 23, 2006

### Mt. Nixion

I know that violating physics laws is impossible; this is just a question, so just answer it and don't say that can't happen. Anyways, if there is a light object and a heavy object, and forces of the same magnitude are exerted on the the objects, and despite the heavier mass, the heavier object accelerates at the same rate as the lighter object; is that a violation of Newton's second law (f=ma)?

2. Apr 23, 2006

### ZapperZ

Staff Emeritus
There's a problem here. Where do you get the idea that applying the same magnitude of force produces the same acceleration on the different objects?

I am guessing that you are trying to illustrate gravitational acceleration. But this is wrong. There is a difference between gravitational acceleration "g", and gravitational force or weight. g is identical for objects (close to earth's surface assuming no variation in with height). But weight isn't the same, since it is obvious that W=mg will be different for different m.

There are no violations here.

Zz.

3. Apr 23, 2006

### eljose

the answer is simple let be $$m(t)=at+b$$ then Newton equation becomes:

$$F=m\ddot{x}+a\dot{x}$$

4. Apr 23, 2006

### kudos213

Eljose, what does the equation of a line have to do with this topic? You need to be more clear if you are actually trying to answer this question.

To the original poster...First of all violating physics laws is NOT impossible, those laws are just numbers and equations men have come up with based on what they have observed in the real world. If, by experiment, we see that these equations do not hold we must revise them.

To answer your question regarding Newton's 2nd law...if two mass, one light one heavy both experience the same magnitude of force would they experience the same acceleration? No, look at the equation

F = m*a rewrite it solving for the acceleration...

a = F / m

Now if we have...

a_1 = F / m_1 & a_2 = F / m_2 (Since you've suggested the forces to be the same)

if m_2 > m_1 it is clear that a_2 would be less since the denominator is greater. This answer your question?

Ciao

5. Apr 23, 2006

### nrqed

well, to answer the question cold: yes, that would violate Newton's second law. Two objects with different masses feeling the same net force willl not have the same acceleration according to Newton's law.

Now, experimentally, this has never been observed (same force on two different masses give the same acceleration).

As ZapperZ, I have a hunch that you are thinking about free falling objects which have the same acceleration (if there is no air drag). Yes, objects of different masses have the same acceleration. But it is because they feel *different gravitational forces*. So no contradiction with Newton's law there!

6. Apr 24, 2006

### pmb_phy

In this case the force is greater on the heavier object buty since its mass is greater it won't accelerate faster than the lighter object.

Consider an object falling in a uniform gravitational field (neglecting air resistance). Then F = -mg where g = acceleration due to gravity = constant. m = mass of object. Then

F = ma = -mg ---> a = -g

See how the masses cancel out?

Pete -

ps - To be more precise one of the masses is inertial mass (that which defines momentum m = p/v) and the other is passive gravitational mass (that which is acted on by gravity). Since they are proportional to each other (as measured in a lab) they cancel out.

Last edited: Apr 24, 2006
7. Apr 24, 2006

### DaveC426913

Are you suggesting that I can push a dinky toy and an 18-wheeler with the same amount of force, and they will both accelerate at the same rate?

Your premise is incorrect.

8. Apr 24, 2006

### kuahji

I think others have summed it up pretty well.

Like another person has stated if you're trying to describe the gravitational effects on an object, you set up the equation as follows
Force=mass*accelerate

So if you have an object that's 5kg, to calculate the force you'd put in 5*9.8=49N

So the accelerate is always the same on Earth (it varries a little depending on your location). When you change the mass, you change the force. I'm not aware of any examples where this "law" has been broken.

9. Apr 24, 2006

### Hootenanny

Staff Emeritus
If what you say happens, then yes it would be a violation of Newton's law, but then again... it ain't gona happen.

~H