Homework Help: Force changing direction of velocity vector-like this?

1. Nov 14, 2005

boris16

hi

I know force only can change direction of velocity vector when it is perpendicular to it.

So if original horizontal velocity V(h) is perpendicular to force:

-force changes a bit the direction of original velocity vector V(h)
-Original Velocity vector is no longer perpendicular to force
-Force now also adds vertical velocity component to the object

-Net velocity keeps getting bigger and constantly changes direction ( object has parabolic path )

-V(h) has still the same magnitude and is no longer horizontal, but now it has horizontal component and this component is perpendicular to force and again force changes the direction of V(h)'s horizontal component...

Are the above stages correct?

thank you

2. Nov 14, 2005

Staff: Mentor

Not sure what you are doing here. The initial velocity is purely horizontal. But, since gravity acts down, a vertical component of velocity is added, changing the direction of the total velocity vector. The horizontal component remains unchanged.

3. Nov 14, 2005

dx

No, it can change the direction of the velocity vector in all directions except when it is parallel to it.

4. Nov 14, 2005

boris16

I assumed since perpendicular force can only change the direction of horizontal velocity vector but not its magnitude that it first must change direction of original velocity vector V(h) by just a little so that it is no longer perpendicular to velocity vector.Then it can add vertical component and in
that way it changes the direction of net velocity vector.
Since force changed the direction of original horizontal velocity vector V(h) ( just a little bit), V(h) now has horizontal component ( V(h1) ) that is perpendicular to force. So I assumed force now changes the direction
of V(h1) ...

Where is my reasoning wrong?

You mean a perpendicular ( to velocity )component of force can change the direction(by that I don't mean changing the direction of net velocity by adding another component to velocity, but actually changing the direction of a vector) ?

5. Nov 14, 2005

dx

If you want the direction of the velocity to change without the magnitude changing, then the force has to be perpendicural to the velocity. Other wise, the direction of the velocity can be changed by any force which has a perpendicular component.

6. Nov 14, 2005

boris16

So is what I said in my previous post correct or not,and if not where i was wrong?

7. Nov 14, 2005

Staff: Mentor

For a force to only change the direction, but not the magnitude, of the velocity it must remain perpendicular to the velocity. This is not the case with gravity and an initial horizontal velocity. The force is only perpendicular to the velocity for an instant. Compare this to a ball being whirled on a string: here the tension in the string is continuously perpendicular to the velocity, so the direction can change without the speed changing.
The change in velocity is downward, thus the new direction is no longer horizontal. Only if the force were changing direction at the same rate as the velocity changed direction (thus keeping perpendicular to the velocity) would the speed remain the same. This doesn't happen with gravity; the direction of the force is fixed.
Not sure what you mean here, since the direction of the "net" velocity is the direction.

8. Nov 14, 2005

boris16

And in that instant it changes direction of original velocity V(h) for just a bit, and after that it adds vertical component to velocity vector. Right?

And if it changed V(h)'s direction for a bit,then since V(h)'s direction is no longer horizontal, V(h) now has a horizontal component V(h1), and since V(h1) is perpendicular to force the story repeats itself ( note that at all time this is happening there is also a vertical component that constantly gets bigger ).
So in fact horizontal velocity keeps getting smaller since force constantly changes its direction

component of net velocity.
That component is always perpendicular to force and I assumed force besides increasing vertical velocity component, also changes direction of horizontal component V(h).

9. Nov 14, 2005

Staff: Mentor

Wrong. As soon as you say "just a bit" you have moved beyond the instant where the velocity is perpendicular to the force.

How can a vertical force affect the horizontal component of velocity?
I have no idea why you think this.
How can "horizontal" change direction?

Note that the statement "If the force remains perpendicular to the velocity, the direction will change but not the speed", only holds if "velocity" means actual velocity, not merely a component. A related, but different, statement is: "A force can only change the velocity parallel to its direction". Thus if the force is only vertical, only the vertical component of velocity changes; the horizontal component remains fixed.

10. Nov 14, 2005

boris16

I don't understand what you're trying to say.
If force can't add vertical component if it is perpendicular to original velocity vector, then it must change the direction of original velocity vector before it can add vertical velocity component

It's only a name for a original velocity vector. Obviously the moment it changes direction it is no longer horizontal. But I still call it horizontal vector V(h) so when I reference it you know what I'm talking about. But we could call it Bob the moment it is no longer perpendicular, and call Bob1
Bob's horizontal component after it too has direction changed by force perpendicular to Bob1. But of course once we call Bob1 Bob's horizontal component,it is no longer horizontal. At that moment, Bob2 is horizontal component( actually it is not yet called Bob2 since it still is horizontal)
See what I mean?

11. Nov 14, 2005

Staff: Mentor

Who says that the force can't add a vertical component of velocity? Of course it can. In fact, that's all it can do.

It's simpler than you think. A net force on an object produces an acceleration in the direction of the force. In this example, that acceleration is downward, thus the only change in velocity is downward.

Now if you can arrange that the force keeps itself perpendicular to the changing velocity, then the direction will change but not the speed. That's not the case here.

12. Nov 14, 2005

boris16

darn it. I thought I knew this stuff and then you tell me that is not the case

It made prefect sense to me that if force keeps itself perpendicular to
changing velocity, it will only change direction because it will always stay perpendicular and when perpendicular it can'y add vertical component.

If that is not the case, could you explain it to me as simple as possible why force doesn't change magnitude of velocity if it stays perpendicular to it?

13. Nov 14, 2005

Staff: Mentor

This is true. But that's not what happens in simple projectile motion. For the force to stay perpendicular to the the changing velocity, that force would have to continually change direction. It doesn't.
Better to say: When perpendicular it can't add a parallel component.

14. Nov 14, 2005

boris16

I'm asking now for perpendicular forces in general.

This is confusing.If:

A-force doesn't change its direction and is at first perpendicular to velocity,then it only changes net velocity vector by adding vertical component.But direction of original velocity vector stays the same

B-if force is always perpendicular to original velocity vector, then it is able to change its direction,but not by adding vertical component (in case A it didn't change direction of original velocity vector, but it did change net velocity)

Why in case A it doesn't change the direction of original velocity, but in case B it does?

what is going on? This is totally confusing

Last edited: Nov 14, 2005
15. Nov 14, 2005

Staff: Mentor

I have no idea what you mean by "original velocity vector", except the initial velocity of the projectile. At any given time there is only one velocity, made up of its components. This velocity changes (speed and direction) with time. In this case, the "original velocity vector" (at time t = 0) is a vector with a nonzero horizontal component and a zero vertical component. As time goes on, the horizontal component stays the same, but the vertical component changes (due to the constant vertical force). But a statement such as "the direction of the original velocity vector stays the same" doesn't make any sense to me.

If the force is always perpendicular to the velocity, then it's not helpful to talk about "horizontal" and "vertical" components, since they change. Instead, talk about perpendicular (to the velocity) and parallel (tangential). Then a true statement becomes: If the force is always perpendicular to the velocity, then only the direction of the velocity changes. (A key word is always.) Note that it means: perpendicular to the velocity vector at all times, not just perpendicular to the "original" velocity vector. Being perpendicular to the "original" velocity vector for an instant does nothing.

16. Nov 14, 2005

Staff: Mentor

In both cases, the direction of the velocity vector changes! In case B, only the direction changes because the force stays perpendicular to the velocity.

17. Nov 14, 2005

boris16

True,but you keep missing the point of what I'm trying to ask. In case A direction and size is changed by adding vertical component to velocity, but original velocity vector component stays the same.

In case B the direction of original velocity vector ITSELF is changed. WHY does that happen if force stays perpendicular to velocity?

Does force say "ups, whenever I try to add vertical component to velocity something changes my direction, and so since I can't add vertical component I will just change the direction of velocity vector" ?
You see now what I want to know?

18. Nov 16, 2005

boris16

please this is important to me!Could someone try to provide some explanation for questions I gave in my previous post?

19. Nov 16, 2005

dx

Imagine it this way. Take a spring and fix one end of it. To the other end, tie a string. Now, if you pull the string and keep your pull always perpendicular to the spring, then the spring will only rotate. But if you pull at a greater angle, it will rotate and also stretch.

20. Nov 16, 2005

boris16

Good analogy. Can you also provide some reasoning similar to one I had ( perpendicular force can't add vertical velocity component to horizontal velocity while it is perpendicular to velocity, so it first has to change a bit the direction of horizontal velocity bla bla bla bla) before DOC_AL shattered that theory of mine ( and my piece of mind ) into little pieces? I'm asking since my mind understands best that way