# Newtonian Mechanics

1. Jul 17, 2007

### lLovePhysics

Okay, I'm sort of confused about forces and acceleration here. Does any force cause an acceleration? What if the force is constant? So does it depend on the situation of the applied force to see if the object accelerates? For example, if you apply a constant force on an object at rest, then the object will accelerate at first and then move with a constant velocity right? Someone please explain this to me. Thanks. :yuck:

2. Jul 17, 2007

### CompuChip

Basically, yes, a net force causes an acceleration. This is Newton's second law, (it it's best known form, $$F = m a$$), which you've probably heard about. Suppose I push against a block of 1kg with a force of 3N. Then the block will accelerate at 3 m/s^2 (Newton's law). It will keep on doing this, as long as I push. That is: the velocity of the block, after a time t, will be v = 3t. As soon as I stop pushing, the force stops - the left hand side F vanishes. Therefore, also the acceleration stops, and the block will continue to slide eternally, with speed v = 3t0, where t0 is the time I stopped pushing.

Now let's add in friction. When I push with a force of 3N, but there is friction, the net force will be smaller than 3N (if I gradually turn up the force, instead of just switch it on, the net force will in fact be 0 until I push hard enough to overcome the static friction; in this case of an object at rest). Similarly, when I stop pushing the moving block, the net force will not be zero: there will still be a contribution from the friction. This net force is now in the opposite direction though (it works against the direction of movement) so, mathematically, the force is negative. Then so is the acceleration, in other words: the block decelerates. Finally, it will come to a stop (the frictional force decreases with the velocity, luckily - if it we're constant, the block would slow to a stop and then continue to accelerate in the other direction ).

So note the word net in the first line. You can also see it by considering gravity. If I drop an object in free fall, it accelerates with g (which is about 10 m/s^2). Earth exerts a force of m g on the object. By hanging the object from a force meter, you could actually measure the force and determine g from it. Of course, if the object lies on a table, gravity also acts. But now the table also exerts a force (the normal force), which is exactly equal and opposite, hence the net force is zero and there is no acceleration. If you put the object on a slope, the normal force also acts, but (as the name suggests) it acts normal to the surface. Therefore, not the entire force, but just a component of it, cancels the gravitational force -- hence the object will accelerate downwards (of course, the horizontal component will cause it to accelerate sidewards as well -- in other words: the object will slide down the slope).

3. Jul 17, 2007

### sftrabbit

The thing I don't get is Newton's third law.. I've just come to accept what it says whether I think it makes any sense or not.

If every force has an equal and opposite reaction, then surely absolutely nothing in the universe would move, and as a whole, the net force of the entire universe would be 0. Surely this law cancels out every force? As with your block example, if you push it at 3N, and it pushes back with 3N, then why does it move?

4. Jul 17, 2007

### Cthugha

Newton's third law does not state, that all forces cancel each other out.
Those two forces you mention act on different bodies.
So in the block example, you push the block with 3N and it pushes you with 3 N. So the block moves away from you and you move away from the block as well.

Just try to push away a wall while standing on slippery ground (laminate for example) and you will agree, that there is a force, which acts on you.

5. Jul 17, 2007

### sftrabbit

My feet would only slip because I'm putting a force on the floor using my legs. Surely that's not the wall doing that. I have a Rubik's cube in front of my right now. If I push it, it moves. I don't move. It doesn't push me back just has forcefully... :S

6. Jul 17, 2007

### Cthugha

No. That's wrong. Slipping is due to the wall pushing you away.

Anyway, an even simpler example is walking. You do not move because the earth moves away due to your feet pushing it away, but due to the earth pushing you away. Push-up workouts work the same way.

Concerning the cube: the mass of the cube and your mass are very different. So you will not be affected by a large acceleration.

Last edited: Jul 17, 2007
7. Jul 17, 2007

### xez

Well the law says that for every force there's an equal
and opposite reaction in the sense that to apply a force
on something, that something also applies an oppositely
directed force on you.

You can't 'push' without the object you're 'pushing'
'pushing back' on you. Don't read more into it than
that. It's not saying that the force must produce
any other reaction than that.

If I stand on the ground, the earth
produces a downward force on my body, but the
ground produces an upward force on my body which
I perceive as my weight, and I don't fall (accellerate).

If there were no counterbalancing force due to me standing
on the ground, the earth's gravity force still would
produce a force on my mass, but since the force would be
unbalanced, I'd accellerate in free fall directed to the
center of the earth.

However those aren't the key principles of balanced vs.
unbalanced forces in the action/reaction law, the
equal and opposite reaction would be that gravity
produces a force = G * my_mass * earth_mass / r^2
on my_mass, but in exactly the same way
my_mass produces a force on the earth_mass in the
opposite direction.

The force will be approximately 9.81N/kg of my_mass
but of course the resultant accelleration of my_mass
and earth_mass will be very different!

Thus in the strict sense, the earth doesn't orbit the sun
any more than the sun orbits the earth, they orbit
each-other i.e. they orbit the center-of-mass of the
earth+sun system, but because of very disproportionate
masses the sun just wiggles a tiny bit and the earth
swings around an orbit of ~ 93 million miles radius.

In another example, the tension in a rope under static
conditions is everywhere the same. So if the
rope pulls up on a pail, the pail pulls down on the rope
the same amount. If the rope is held up by a pulley,
the pail pulls down on the pulley through the rope, and
for the pulley not to fall, it must pull up with equal force
on the pail through the rope.

8. Jul 17, 2007

### sftrabbit

Ahhh. So it's due to F=ma. Although the same force is being applied to both, a larger acceleration is only gained if the mass is smaller?

I think I get it now. Thanks..

9. Jul 17, 2007

### alvaros

the same force is the key point.

We were trained to resolve problems about forces, accelerations ..
And, in other problems we were asked: where is the reaction force ?

Forces have always two sides: they push away two bodies ( or body -field ) or they join two bodies. So its the same force ( not two: action-reaction )

What would happen whith this approach ?
Is there anyting erroneous ?

10. Jul 17, 2007

### ice109

the third law is a direct consequence of the conservation of momentum so yes all forces do cancel out in the long run.

11. Jul 18, 2007

### alvaros

From ice109:
"the third law is a direct consequence of the conservation of momentum " ( A )

You also could say:
the conservation of momentum is a direct consequence of the third law. ( B )

Both are true and A implies B and B implies A. This means A = B.

You can choose any of them as "fundamental" and infer the other.

From ice109:
"so yes all forces do cancel out in the long run."
No, they dont.

Action and reaction always happen: at the same time, at the same point, whith the same intensity ( newtons ) but in opposite directions.

More:
books always draw a force like -----> or <-------

This is imposible, such forces does not exist. Something must pull or push.

The real forces are <-----> or >---------<

I know this is nothing new, its another way of teaching, easier, I think.