Need Basic Physics Help

[Space05us]

When an object is in equilibrium the vector sum of forces equals zero (ΣF=0).

This makes perfect sense to me for an object at rest, or in static equilibrium. When it comes to an object in motion, dynamic equilibrium, I am baffled. I understand the concept that the object is not accelerating. What I can't understand is how an object continues to move if the two forces acting upon it cancel each other out, or how it moves in the first place.

One example given by my textbook: "When the push on the crate is as great as the force of friction between the crate and the floor, the net force on the crate is zero and it slides at an unchanging speed."

If the force of the push is equal to the force of friction the object would not move, right? Apparently I am wrong but I don't understand how.

Another example it gives is an airplane flying at a constant speed. Assuming drag is the only force acting upon the airplane it still has to overcome that force in order to move, just like friction in the first example, right?


I'm under the impression that I shouldn't need to imagine any extraordinary circumstances to understand this. Ultimately I get it, it's just another way of stating Newton's First Law of Motion. I think it's just the examples provided in the textbook that are confusing me.



Let me make up my own example. A potato is flying through space at 1m/s, simply because that's what it has always done. Along come two gremlins, one decides the potato should go the opposite way it is currently going, and the other thinks it should continue on it's current course. So they both ram into the potato at the same time with the same exact force and continue to push on it for all of eternity. The potato continues to go along at the same speed and direction because the gremlins cancel each other out. The potato is in dynamic equilibrium because before the two forces were applied it was moving. Had it been at rest it would now be in static equilibrium.

Right?

What is a real world example of this? Surely not the crate example?

[aneeshm]

The example works for massless gremlins capable of exerting force in a vacuum (rocket packs?).

A simpler way to understand the crate example would be to ponder the answer to this question: when you're pushing a heavy crate so that it moves with a fixed speed, you still have to keep pushing it in order for it to move at that fixed speed, don't you?

[Wiglaf]

With regards to physics, that is not true if it is on a conveyor belt.

[Space05us]

The example works for massless gremlins capable of exerting force in a vacuum (rocket packs?).

I was being fantastic. The problem I seem to be having is understanding dynamic equilibrium in ordinary circumstances.

A simpler way to understand the crate example would be to ponder the answer to this question: when you're pushing a crate so that it moves with a fixed speed, you still have to keep pushing it in order for it to move at that fixed speed, don't you?

But in order to set the crate in motion you have to overcome any opposing forces, how can those opposing forces be equal if the object is in motion?

If the opposing forces, your push and friction, are not equal then the crate is not in equilibrium.

If the forces are equal then the crate won't move.

[snoopy369]

The crate example is fine... just map the crate to the gremlins example. One gremlin is you; the other is friction. Assume the crate is moving along at 1m/s, due to your initial acceleration of it; then friction pushes it back at (say) 5m/s^2 acceleration. You push forward with 5m/s^2 acceleration. The crate continues forward at 1m/s as if nothing were pushing it.

Separate your initial push from your continued push. The initial push to get it up to 1m/s velocity is the same as, in your example, whatever got the potato to move 1m/s in space. Something must've accelerated it in the first place. Your initial push does that. Now, once it's going 1m/s, you must apply a force identical to friction to keep it going at that rate. Two separate force vectors, even if they seem to be together. You don't have to push as hard once it's going as you do to get it going, after all.

[Dr Strangelove]

Just remember Fugg's law: "If you push anything hard enough it will fall over."

[Space05us]

The crate example is fine... just map the crate to the gremlins example. One gremlin is you; the other is friction. Assume the crate is moving along at 1m/s, due to your initial acceleration of it; then friction pushes it back at (say) 5m/s^2 acceleration. You push forward with 5m/s^2 acceleration. The crate continues forward at 1m/s as if nothing were pushing it.

Separate your initial push from your continued push. The initial push to get it up to 1m/s velocity is the same as, in your example, whatever got the potato to move 1m/s in space. Something must've accelerated it in the first place. Your initial push does that. Now, once it's going 1m/s, you must apply a force identical to friction to keep it going at that rate. Two separate force vectors, even if they seem to be together. You don't have to push as hard once it's going as you do to get it going, after all.

Thank you snoopy! Not sure why that didn't come to me to begin with, but eh, hindsight.

[Space05us]

Separate your initial push from your continued push. The initial push to get it up to 1m/s velocity is the same as, in your example, whatever got the potato to move 1m/s in space. Something must've accelerated it in the first place. Your initial push does that. Now, once it's going 1m/s, you must apply a force identical to friction to keep it going at that rate. Two separate force vectors, even if they seem to be together. You don't have to push as hard once it's going as you do to get it going, after all.

I've been thinking again.

The initial push gets the crate into motion, at which point you can push it just enough to put it in dynamic equilibrium.

What if you push the crate at a constant speed of 100km/h? It takes an increase in force to cause the acceleration, but is an increase in force required to maintain the new speed?

[DaShi]

No, the crate doesn't move at all when you push it because it applies an equal but opposie force while insulting your mother.

[Heraclitus]

Separate your initial push from your continued push. The initial push to get it up to 1m/s velocity is the same as, in your example, whatever got the potato to move 1m/s in space. Something must've accelerated it in the first place. Your initial push does that. Now, once it's going 1m/s, you must apply a force identical to friction to keep it going at that rate. Two separate force vectors, even if they seem to be together. You don't have to push as hard once it's going as you do to get it going, after all.

I've been thinking again.

The initial push gets the crate into motion, at which point you can push it just enough to put it in dynamic equilibrium.

What if you push the crate at a constant speed of 100km/h? It takes an increase in force to cause the acceleration, but is an increase in force required to maintain the new speed?

Imagine a long train traveling at 100 km/h hitting a rail cart and you'll get it quickly.

[Kuciwalker]

You can't push (exert force on) something with a speed (distance/time), you can only push it with a force (mass*distance/time^2).

[Heraclitus]

You can't push (exert force on) something with a speed (distance/time), you can only push it with a force (mass*distance/time^2).

This is of course true but I think he knows that, I understood his question differently.

What if you push the crate at a constant speed of 100km/h? ?

I asumed it was informal speak for:

-you hit the crate with a velocity of 100km/h
-dv/dt = 0 , your speed is constant



(that is why I gave the example of the train whose mass far exceeds the mass of the rail cart to give him an intuitive idea of what happens).

[snoopy369]

Separate your initial push from your continued push. The initial push to get it up to 1m/s velocity is the same as, in your example, whatever got the potato to move 1m/s in space. Something must've accelerated it in the first place. Your initial push does that. Now, once it's going 1m/s, you must apply a force identical to friction to keep it going at that rate. Two separate force vectors, even if they seem to be together. You don't have to push as hard once it's going as you do to get it going, after all.

I've been thinking again.

The initial push gets the crate into motion, at which point you can push it just enough to put it in dynamic equilibrium.

What if you push the crate at a constant speed of 100km/h? It takes an increase in force to cause the acceleration, but is an increase in force required to maintain the new speed?

So you have a cart going one speed, with you applying a constant force, and then you increase that force? It will increase in speed until it achieves the new equilibrium, which is when friction negates your now increased constant force [extreme simplification: friction increases with speed]. There is some speed S whereby the force applied by the round to the cart's wheels is equal to your applied force; it will increase in speed until that force is achieved, at which point it will again be in equilibrium.

[snoopy369]

Draw the force diagram.

---->|-|<-- 0m/s
That's the cart, with your initial push on the left, and friction on the right.
---->|-|<---- 1m/s
Now it's in dynamic equilibrium, where friction cancels your push.
--------------->|-|<---- 1m/s
Now you push harder.
--------------->|-|<-------- 10m/s
Still accelerating.
--------------->|-|<------------- 50m/s
Still accelerating.
--------------->|-|<--------------- 100m/s
Now you're in dynamic equilibrium again, because friction at 100m/s is equal to your push.

[KrazyHorse]

To a first approximation frictional force is independent of the velocity (as long as the velocity is greater than 0). This is vastly different than drag forces caused by moving something through a fluid, of course.