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If an object is pushed/pulled at a constant velocity and it doesn't accelerate, is there a net force still being applied to the object? A force is a push/pull so there must be a force, despite there being no acceleration, right?

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    $\begingroup$ You can also look at a force as being the negative of the spatial gradient of a potential. Thinking of pushes and pulls is more intuitive. $\endgroup$
    – Galen
    Commented Oct 28, 2022 at 3:51
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    $\begingroup$ If object goes at constant velocity, then no net force is applied. But it doesn't mean that no any force is applied. It can be quite contrary. For example, you keep an accelerator pedal steady for a car going at constant velocity. Engine chemical energy then is converted to wheels torque for compensating road induced dynamic friction force, i.e. $F_{net} = F_{engine} + F_{rolling-resistance} = 0$. Thus for a car you just need an engine force for keeping it inertial properties (same velocity), otherwise resistance will take it all. $\endgroup$ Commented Oct 28, 2022 at 8:46
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    $\begingroup$ Push or pull? That only depends on which way you look ;-). $\endgroup$ Commented Oct 28, 2022 at 11:10
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    $\begingroup$ @Galen A little pedantic comment: Force can only be viewed as a negative gradient of potential for conservative forces. $\endgroup$ Commented Oct 28, 2022 at 11:38
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    $\begingroup$ You may want to look at Newton's first law again. $\endgroup$ Commented Oct 29, 2022 at 3:13

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If you're pushing an object and it's not accelerating, you may confidently deduce that there is another force, acting on the object, of equal magnitude and opposite direction opposing your push.

This isn't Newtons 3rd law. The 3rd essentially says that the object itself pushes back as it accelerates. But if the object isn't accelerating, external forces on the object are in balance.

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    $\begingroup$ Should be Newton's 2nd law - in Newton's 3rd law the equal and opposite forces act on different objects. $\endgroup$
    – gandalf61
    Commented Oct 28, 2022 at 9:01
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    $\begingroup$ I don't think this answers the OP's question. You can deduce that even if the body is accelerating. $\endgroup$ Commented Oct 28, 2022 at 9:42
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    $\begingroup$ @preferred_anon Fixed the edit that falsely attributed this to Newton's 3rd. Thanks for the comment that alerted me to the damage. $\endgroup$
    – John Doty
    Commented Oct 28, 2022 at 12:08
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    $\begingroup$ @gandalf61 Thanks to you, too. $\endgroup$
    – John Doty
    Commented Oct 28, 2022 at 12:09
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    $\begingroup$ @JohnDoty Maybe someone confused this as talking about the 3rd law because of the idea of an equal and opposite force (even though you're not talking about a reaction force)? In fact the constant velocity does not really imply that there is any single force that is equal and opposite; it implies that there is one or more forces that together sum up to be equal and opposite to the pushing force. $\endgroup$
    – Ben
    Commented Oct 29, 2022 at 3:19
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If you push or pull an object to exert a force on it, and there are genuinely no other forces acting on it, then it is impossible for you to push/pull such that it moves at constant velocity. If there is a net force, there must be some acceleration; if there is no acceleration then there must be no net force.

You won't be able to test this because you don't have access to a frictionless void where there is no gravity (nor even to an environment that could approximate this, such as free fall in outer space). Your intuition about force and acceleration might be misleading you, because you have never in your life pushed or pulled on an object that wasn't also being affected by other forces.

In particular, the thing that often comes to mind is something like pushing a box across the floor. We are used to the obvious fact that you have to keep pushing to keep it moving, when physics tells us that if the box were pushed (with no other forces) it should accelerate, and then if we stop pushing it should keep moving at constant velocity. Obviously that's not what happens!

The main thing missing from this picture is that friction is a force that opposes motion. While the box is moving there is a friction force "pushing" it backwards, which will quickly decelerate it. So you have to keep pushing it with a force that balances out friction in order to have a net force on the box of zero, which will allow it to move at a constant velocity. Physics says that an object under absolutely no force at all behaves exactly the same as an object under lots of forces that all balance out to zero. So you pushing on it to oppose friction makes it behave like it being affected by no force; it does not behave like it is being affected by only your force.

It might help intuition if you consider pushing something on wheels, instead of a box. There are still forces opposing the motion, but they take much longer to decelerate it to zero. So you can see that a single push is enough to keep the wheeled object moving for quite a while after you stop pushing it. Hopefully that is enough to let you imagine the idealised case where there wasn't any other force like friction opposing the motion, and it would just coast forever. In that imaginary scenario if you were able to catch up with it and push it some more while it was travelling it would just accelerate (until it moved faster than you and you couldn't keep pushing it); there would be no way to "push it at a constant velocity".

You can only "push things at constant velocity" when something else is pushing back. Commonly the thing "pushing back" is friction, but if you're pushing something uphill gravity is also pulling down and you have to overcome that; in that case you can have a case where you need to keep pushing something just to hold it still! (In fact the "keep pushing to hold something still against gravity" scenario happens much more mundanely every time you hold something off the ground)

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Per Newton's 1st law an object at rest or moving at constant speed in a straight line remains at rest or moving at constant speed in a straight line unless acted upon by a net force.

Per Newton's 2nd law, the acceleration $a$ of an object is

$$a=\frac{F}{m}$$

where $F$ is the net force acting on the object.

It follows then from both laws that the net force on an object moving at constant speed in a straight line (zero acceleration) must be zero.

The above does not necessarily mean no force (push or pull) is acting on the object. It's just that there is an equal and opposite force (pull or push) somewhere also acting on the object.

Hope this helps.

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If the object has constant velocity, it isn't accelerating. Because $a$ = $\frac{F}{m}$, $\frac{F}{m}$ must be equal to zero. Multiplying both sides by $m$, we get that $F = 0$, so there is no net force. Each force causes a "phantom acceleration," and the real acceleration is the vector sum of these phantom accelerations. Similarly, the net force is the vector sum of forces, and considering the forces independently, they each provide a phantom acceleration in their direction, but there is no net force if and only if there is no "real" acceleration. It is possible to push or pull something at constant velocity if there are other forces acting on it, but if your force is the only force (which in reality could never happen due to gravity from everything in the universe), then the phantom acceleration caused by the force you apply is the only phantom acceleration, so it is the real acceleration, and since the force you apply is nonzero, the object changes velocity. It is possible to push or pull something with constant velocity, like pulling a tug-of-war rope or pushing a box across the ground, but that only happens because friction/air resistance/something else is acting against your force.

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Newton's 2nd law always holds true:

$$F_\text{net}=ma.$$

So, if you have constant velocity, meaning zero acceleration, then no net force is present, $F_\text{net}=0$.

But that doesn't mean that no forces are present. The net force is just the sum of all forces. Maybe you are pushing on the cart while a friction force is counteracting your push, so that their net force sums out to zero.

Whether you want to call a force push/pull is more of a subjective matter. Sure, you pushing the cart is obviously a pushing force, but what is a friction force? A pulling force? Ah well, this is just semantics and doesn't matter. As long as you are able to correctly identify the directions of forces that are involved, then this wording can stay ambiguous.

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Push / pull is the first intuitive notion of force to me. Later on, by using the elasticity property of materials, this notion can be quantified, and force is measured according to some displacement.

At a third stage, we note that for some controlled situations, a measured force is related to mass $\times$ acceleration. We now redefine force as something acting on a body, when it is accelerated. It has the advantage for example to help to calibrate springs and other devices that measures force by some displacement.

The side effect of that redefinition is that any object subject to a measured force, that doesn't accelerated as expected by the Newton's second law, must have by definition some other force, even if it can not be directly measured .

Examples:

An elevator moves with a constant velocity. The force on its cables can be measured by load cells. The force of gravity is postulated to explain the absence of acceleration. So, the net force is zero.

A heavy object is pushed horizontally, but doesn't move. The force acting on it can be also measured by a load cell. But the absence of acceleration obliges us to postulate a friction force, even if it can not be directly (that say by other way than merely by difference) measured. Again, the net force is zero.

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Newton's second law of motion is that force equals mass times acceleration (F=ma). This means that acceleration is a necessary part of force. No acceleration, no force. Velocity doesn't matter.

Newton's third law neatly explains your near epiphany here: for every action in nature there is an equal and opposite reaction. You lean on a wall, the wall "leans" back, and neither you nor the wall move. All the force you apply leaning can be traced through the timbers and into the earth, which you are standing on, so you're essentially leaning on yourself. This is the equal and opposite reaction. Without the timbers supporting the wall the opposite force works in your favor. The opposite force is still in your feet, but is met with Earth's mass, which gives way nearly nothing because of its size. You lean on the wall, it accelerates as long as you lean (a=F/m), then it continues moving before gravity takes it, another force, taking your applied force to zero.

In open space, when you push your friend who's equal to your mass, you and the friend accelerate equally away from each other during your push, but then no longer accelerate once you part, however you both now have equal velocity, but in opposite directions.

Back on Earth, "pulling at a constant velocity" is a perfectly sensible statement that intuitively has you thinking about a constant force to accomplish this. A truck pulls a trailer, keeping velocity, and is definitely applying force. But force is mass times acceleration, and the truck is not accelerating! Technically, it is. It is accelerating just enough so that the force equals the force of gravity and friction which are pulling the trailer in the opposite direction. We notice this opposite force when the truck stops pulling and the trailer decelerates. It's when the force applied overcomes friction and gravity is when the truck actually gains velocity, but regardless of practical gains or losses in velocity, acceleration is always present when force is applied.

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    $\begingroup$ As it’s currently written, your answer is unclear. Please edit to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers in the help center. $\endgroup$
    – Community Bot
    Commented Oct 28, 2022 at 7:16
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    $\begingroup$ If someone could explain the community bot comment above that might help. $\endgroup$
    – user21380
    Commented Oct 28, 2022 at 15:12
  • $\begingroup$ Acceleration is defined as a change in velocity. The truck does not accelerate when pulling the trailer. I feel that the best way to think about it is that each force provides a "phantom acceleration" and the real acceleration is the sum of all the "phantom accelerations." $\endgroup$
    – mathlander
    Commented Nov 24, 2022 at 16:29
  • $\begingroup$ Please edit your post to fix the physics and make it clear what is happening in the real world, not the world of these phantom accelerations. $\endgroup$
    – mathlander
    Commented Nov 24, 2022 at 16:36
  • $\begingroup$ @IsaacNewton I'm laboring under the belief that I am describing what happens in the real world. If you like calling it "phantoms", fine, but I'm believe there is no phantom. It is real. There is no "phantom acceleration" in the formula, just acceleration. $\endgroup$
    – user21380
    Commented Nov 24, 2022 at 18:28
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Consider two cars, A and B, that have bumpers mounted on springs for cushioning shocks. Now if car A with its engine on pushes car B (engine off and free-wheeling) along at a constant 70 mph then there is no net force between A and B because there is no acceleration. However, if we look at the springs on both cars, they are both compressed, indicating car A is exerting a a non zero pulling force on B and B is exerting an equal opposing push force on A (due to road and air friction retarding car B), but the forces cancel out.

If we now put car B behind car A and tie the bumpers together so that A tows car B at a constant 70 mph, again there must be a total net force of zero because there is no acceleration. When we check the bumper springs they are both stretched indicating that car A is pulling car B with a non zero force and car B is pulling car B with an equal opposing pulling force.

In summary, if there is no acceleration (motionless or constant velocity) then there is zero net force but there may be non zero component forces.

There is a clear distinction between pushing and pulling. When 2 objects are pulling each other, there is tension any connector between them and when they are pushing, there is compression in any connector between them. Also if the connector is removed in the pulling case, the two objects will progressively increasingly spatially separate if the forces remain constant, which won't happen in the pushing case.

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