# Ok so my teacher has recently covered this chapter, but one of the

1. Jul 16, 2012

### Celluhh

Ok so my teacher has recently covered this chapter, but one of the concepts that has been bugging me for ages. Fr an object to experience zero acceleration, the forces acting on it have to be balanced. That means tha applied force has to equal the frictional force so that the resultant force will be zero. But why, if the forces are balanced, won't they cancel out each other, and leave no force to actually cause the object to more at constant speed?yes I know that according to newtons second law, no net force equal zero acceleration, but where Does the object get its energy to do work? Ie remain at constant velo.i just can't seem to understand how, and my teacher doesnt want to answer my stupid question, so all help is greatly appreciated! Oh by the way, when there is a resultant force acting on a object, will the applied force still be acting on the same object? No right ?

2. Jul 16, 2012

### Mark M

Think of an object in empty space, first. If I give it a push, it will continue to move in the direction I applied the force until someone or something else stops it. Until then, it will remain at that constant velocity. In order to stop the object, you will need make it's acceleration negative (slowing it down), which via Newton's second law, requires a net force that is pushing against it's motion. If the applied force is equal to the frictional force, then no acceleration is occurring, and the object will be moving with a constant velocity.

EDIT: Oh, and to add. It gets it's ability to do work from the fact that you needed to accelerate it to get it to that constant velocity. This requires you to put a force on it, which will then be transferred by that object to whatever it does work on.

3. Jul 16, 2012

### nasu

Re: Dynamics

When the object moves with constant speed there is no net work done by or on the object. Its kinetic energy is constant.

In order to have some work involved the object must be either slowed down or accelerated.
In both these cases the net force is not zero. To slow down, the applied force must be decreased, to accelerate it must be increased.

I don't know what you mean in the the last two sentences.

4. Jul 16, 2012

### AlephZero

Re: Dynamics

If that is true, then why does my car engine have to keep burning fuel when I'm driving at constant speed on a level road?

Answering the OP's question, you seem to be thinking that the only sort of energy involved here is mechanical energy. If you are pushing an object at constant speed against a friction force, the applied force (equal and opposite to the friction force) is doing work (= force x distance), and that work is mostly converted into heat. (Of course you can think of heat energy as the amount of kinetic energy stored in the vibratiion the atoms making up the material, but that is usually "too much information" for solving dynamics problems!)

5. Jul 16, 2012

### harrylin

Re: Dynamics

The others have already explained it rather well, but I'll add to that.

- I hope that it's clear now that no work is needed to remain at constant speed if there is no friction. Think of falling on ice, how far you can glide thanks to little friction.

- The subtle thing with friction is that work must be done to overcome the friction. And that work results in heat (think of the brakes of your car).

So, to sum it all up (literally), and perhaps answering your last question:

The force Fapp that you apply on the object remains on the object, and it is countered by the friction force and the force* due to inertia that counters acceleration Facc = -ma. The friction force Ffriction increases with increasing speed (for simplicity, let's neglect the force that is needed to get the object "unstick" from the floor). Thus the object accelerates until the friction force is equal (but opposite) to your applied force on the object. Schematically, from the moment of getting in motion on a smooth floor until reaching top speed:

Fapp + Facc + Ffriction = 0

1. Fapp ≈ -Facc = ma (if Ffriction is small at low speed)
2. Fapp + Facc + Ffriction = 0 (the acceleration decreases because the friction force increases)
3. Fapp + Ffriction = 0 (acceleration zero, your applied force is balanced by friction force)

All forces are in dynamic equilibrium all the time (third law of Newton: "Whatever draws or presses another is as much drawn or pressed by that other").

Does that help?

*Note: confusingly, the term "inertial force" has been hijacked for something completely different; here we only discuss real forces.

Last edited: Jul 16, 2012
6. Jul 16, 2012

### Mark M

Friction. The friction between the road and your car resists it's motion. So, to overcome it, you must burn fuel to apply a force on your car to move it forward.

7. Jul 17, 2012

### Celluhh

I think u understand what I mean , but the object will not do work on anything else in it's path right ? It itself is doing work ?

8. Jul 17, 2012

### Celluhh

What do you mean by this ?

9. Jul 17, 2012

### AlephZero

Re: Dynamics

Oh well. If you ask a rhetorical question on a forum, there's always somebody ready to answer it

10. Jul 17, 2012

### harrylin

Re: Dynamics

I'm not sure what you mean with "resultant force", nor what you mean with "work together"...

I did explain to you how the applied force minus the friction force results in acceleration of the object, and that this acceleration is controlled by the object's inertia. Perhaps it's useful to phrase it again differently: The object's inertia delivers the missing counter force by means of its acceleration.

Thus in my earlier answer I tried to clarify the dynamic force balance that I thought you were after to understand by giving you an example of what happens, and why, as function of the time. Thus you can understand how dynamic force equilibrium results in a top speed - which is the point where your discussion with your teacher started off.

If you can understand why and how that point was reached, then all following questions disappear. For example, "Fr an object to experience zero acceleration, the forces acting on it have to be balanced" is inaccurate: the sum of all forces is always balanced according to Newton's 3d law, as I explained. For the object of your example to experience zero acceleration, the friction force has to be equal and contrary to the applied force.
What exactly is still not clear?
That footnote was for some people who could misinterpret my referral to inertial effects as referral to a fictitious force, despite my careful phrasing. If you are not into such things, then you can safely ignore it.

Last edited: Jul 17, 2012
11. Jul 17, 2012

### Celluhh

What do you mean ?

Oh and mark m, the applied force on the car already balances the frictional force, since ye car moves at constant speed. So how can there be extra frictional force acting on the car ?

12. Jul 17, 2012

### Celluhh

In this case do you refer to inertial force as effects of mass ?
I understand what you are trying to say , you are actually clear in yor explanations. It's just that I have a weird mindset I guess, and I havent found the actual answer I am looking for , but if I was learning this chapter for the first time and having difficulty grasping concepts, your post would be very helpful. Except , like I said , I don't like to accept things easily especially when I can't seem to visualise them. So yup. Thanks a lot though !!

13. Jul 17, 2012

### Mark M

They don't work very well on the Internet. :smile

What exactly do you mean?

Let me give another explanation - constant velocity doesn't require any force, nor does it do any work. So, if the applied force and frictional force cancel out, you'll get zero acceleration. The velocity of the object is irrelevant, long as it's constant. Remember that Newton's second law is F = ma. If the friction and applied force are balanced then there isn't any acceleration. Notice, however, that it doesn't discriminate between different constant velocities (called inertial frames of reference). You could be moving over one million meters per hour, but as long as the friction is equal to the applied force, you won't change speed.

14. Jul 17, 2012

### harrylin

Re: Dynamics

Yes, certainly (except that I did not refer to "inertial force" but to "the force due to inertia", for the reason that I explained): http://dictionary.reference.com/browse/inertial?s=t
You're welcome!

15. Jul 18, 2012

### Celluhh

Is this your explanation to why an object moving at constant velocity doesn't require a force ?

16. Jul 18, 2012

### Mark M

I was referring to the fact that if this object, say, slammed into another, it would exert a force on it. I thought your original question regarded how the object got the energy to do this, which is what I explained.

17. Jul 18, 2012

### Celluhh

Re: Dynamics

When a 200N force is applied to an object on a frictionless surface, object remains at constant velo. But when a force is applied to an object on a surface with friction, and the net force is 200N the object accelerates. So this means that the applied force is still acting on the object on the surface with friction right ?

18. Jul 18, 2012

### Mark M

Well, let's break it down case by case.

If we exert a force on an object on a frictionless surface, it will accelerate to a certain speed (given by F = ma), and then proceed at a constant velocity. And because of Newton's first law (an object in motion stays in motion until acted on by another force), it will continue at this constant velocity.

Rather than applying the force once, let's say we continue to apply to force. Say, by strapping a rocket to the object. Now, the acceleration given by F = ma will stay constant (consent force means constant velocity), and the object will get faster and faster. As in the previous example, if we then stop applying the force (I.e., Turn off the rocket), the object will continue at whatever velocity it achieved and stop accelerating.

Now, let's try a surface with friction. Friction is a constant force that pushes against your motion. Remember, constant force means constant acceleration. In the case of friction, this means constant deceleration. So, if we give it a one time force, such as a push (as in our first example), it will accelerate to some constant speed. But, in the first, example, the object continued at this speed because there was no outside force. But now there is, friction. Remember that I said that friction leads to a constant deceleration (until you hit 0 velocity, then friction stops, obviously). So, the object will decelerate down to 0 velocity.

Next, let's say we apply a constant force again, but on a surface with friction. Firstly, the object accelerates to a certain speed (F = ma), but then the friction resists. In the last example, the force from friction decelerated the object. So, the force from friction is negative. If we respond with an equal but opposite constant force with our rocket, the two will cancel to zero. So, since F = ma, the object has no acceleration. So, whatever original constant velocity we got it to, it will stay at. Compare this to the case of constant force without friction, where, rather than having a constant velocity, the object had a constant acceleration.

How's that?

19. Jul 20, 2012

### Celluhh

Re: Dynamics

Yup I get you , but the constant force u mentioned in the last para is the applied force right ? But isnt the applied force only a one time force ?

20. Jul 20, 2012

### harrylin

Re: Dynamics

You can apply a force as long as you wish.