# (simple) Applying constant force - Newton's first Law

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1. May 26, 2015

### Starby

Another silly question...

Assuming a surface with no friction in space (you get the idea), I push/kick/give a 1kg block on this horizontal plane a force of 1N. It would start to accelerate in the direction i pushed it with at a rate of 1m/s² forever until another force acted upon it. So far so good I hope?

Now, is there any difference if I continuously apply 1N in the same direction to it while it travels along its path, would it accelerate any faster? Is "giving" an object a force of 1N in a direction in a single point of time the same as if I were applying 1N to it constantly during the eternity of time? I hope the question is clear enough. Also, could you say that in the first example that the force acting on the object is constant 1N?

Or does constant pushing of 1N add the forces together ? (1+1+1...etc?)

My hypothesis is that if "kicking" the object in the first example, it would travel at a constant speed, but not accelerate. However in the second example, I think it would accelerate. However I don't know WHY this would be if this is true..

Any good links to read up on this is appreciated, I'm finding the material I read about Newton's laws doesn't cover these types of questions really well, so I end up getting confused all the time.

Last edited: May 26, 2015
2. May 26, 2015

### theodoros.mihos

Please, recall your notes and books. You can see definitions for what is a force and what is the energy. Think about these thinks. Action-Reaction axiom have "light" like 1=1.

3. May 26, 2015

### Staff: Mentor

The first second you apply the 1N force, the mass accelerates. The second second with 1N force, it accelerates more. The third ... and so on.

Instead of "adding the forces together" we say "the time integral of force." But you have the basic idea right.

4. May 26, 2015

### Starby

Thanks, I think it's more clear now. I edited the post above, but you might not have had the chance to read it. So to make things clear, applying 1N in the first second would result in the object just moving along at a constant speed of (im guessing) 1m/s in the direction pushed. However the "time integral of force" would give it an acceleration of 1m/s², correct?

5. May 26, 2015

### Unified28

As long as you exert a force on an object it accelerates continuously due to that F=ma. If there is a force there is acceleration. Then if you exert a force for all eternity it would theoretically accelerate for all eternity. However near the speed of light the object would slowly converge to the speed of light due to that mass increases.

Why does it accelerate if there is a force? Perhaps because of mv=ft such that the object continuously gains momentum. It's not addition of force, but you can consider the multiplication as an addition, such that momentum is continuously added. Not as 1+1+1, but continuously. The acceleration is 1 m/s^2 if the mass of the object is 1 kg. Then in half a second it accelerates by 1/2 m/s.

6. May 26, 2015

### Starby

To clarify, the first object I push in my example will just go off at a constant velocity of 1m/s in pushed direction forever? As I'm not exerting force on it during its travel there will be no acceleration, hence there are no forces acting on it? The second object would accelerate constantly as I'm constantly giving it a force of 1N, and thus the acceleration will increase the speed or scalar of the velocity.

7. May 26, 2015

### rolotomassi

If you think about a friction-less surface and you apply a force of 1 N for 1 second to a 1 kg block you get an impulse F dt = m dv = 1 Ns. This causes the velocity to change from 0 m/s to 1 m/s in 1 second. After this there is no force. So it will carry on at 1 m/s. It will NOT accelerate for ever if you simply give an object an impulse.

If you push an object with a constant force, then it will continue to accelerate forever until something stops it as you say. For example something falling on earth, you may just as well (ONLY FOR THIS EXAMPLE) think of this as a force pushing the falling object from behind. Without drag and ignoring the negligible effect of 1/r^2 dependence, it will keep accelerating until it hits the floor. ( 9.81 + 9.81 +....) plus 9.81 m/s every second ... etc etc

8. May 26, 2015

### Bandersnatch

That's correct. Note that the 1 kg object will travel with the velocity specified (1 m/s) only if the force of 1 N was applied over time of 1 second. If you do the same setup, but apply the force for half the time, the object will reach 0.5m/s.

In general, the idea is that only forces cause changes in motion (where motion is the change in position over time = velocity). The change in motion is called acceleration. Without a force there is no acceleration (Newton's second law), so the object moves at whatever velocity it has (Newton's first law).

Keep in mind that all these quantities: position, velocity, acceleration and force are vectors (i.e., they have direction as well as magnitude).
Notice how there is a pattern here:
-velocity is the rate of change of position
-acceleration is the rate of change of velocity

9. May 26, 2015

### Starby

Thanks, my confusion came from trying to grasp WHY there will be no acceleration after the impulse. But I think I understand now, If F=ma it means the acceleration will be 1m/s², but this acceleration (change in velocity) is only for the brief duration of a second that this impulse lasts as I understand it. Because an acceleration requires exerting a force (and this is not true after the impulse), the object will thus just maintain its velocity as Newton's first law states.

Before I always thought that if gave an object this impulse it would continue to "have" a force, and thus an acceleration, I associated speed with "force". But constant speed has no force...

I hope I've got it right now..!

10. May 26, 2015

### Unified28

Since impulse is force over time, impulse and force is nearly the same thing. Also impulse represents the change of momentum.

If the impulse, Ft lasts only a second such that t=1, then yes. If the impulse lasts for more than a second such that t > 1, then it accelerates for longer as long as is the value of t.

It sounds to me like you got it right.

11. May 29, 2015

### Chandra Prayaga

All your questions are answered by Newton's 2nd law: Fnet = ma. Fnet means the total (vector) force. In your scenario, as long as you exert a force, there is acceleration. If you stop exerting a force, there is no acceleration. So, if you exert a force for a short time (such as a kick), there is acceleration for a short time. If you continue to exert the same force for a long time, then the object continues to accelerate for a long time.

There are conceptually unclear statements or questions in what you wrote: For example, "would it accelerate any faster?" What do you mean by accelerating faster? Once the force is given, and the mass is given, the acceleration is fixed by Newton's law. Also " Or does constant pushing of 1N add the forces together ? (1+1+1...etc?)". What forces? You are exerting one force of 1N.

There are several very good books which you can read, such as the one by Knight.

12. May 29, 2015

### Starby

Thanks, I have been given many good answers and understand pretty much how it works now. The reason for my unclear statements was my lack of understanding when I posted the thread. What I meant by "would it accelerate any faster" is if an object were to accelerate faster when exerting a force over a short amount of time
versus continuously. I somehow thought that if an object was kicked it would somehow maintain its force in the direction its going (and accelerate), but I know now it would accelerate to a certain point and maintain constant velocity, and that it maintains its velocity unless a force acts upon it (thus changing the acceleration). What I meant by adding forces has to do with my same misunderstanding, that force is somehow maintained after its been exerted..