[Momentus (OP)]

In Newton?s drawing he applies a single,  but large impulse at right angles to the line AB
 In my diagram I apply a force at right angles to the line AC.
Newton deflects to line BC. In his drawing, AB & BC are the same length indicating that the speed is unchanged.
In my drawing there is a deflection to the line CD. AC a & CD are the same length indication that the speed is unchanged.

Newton makes it quite clear that even with repeated impulses applied at right angles to the direction, the speed remains unchanged. Thus he shows that his centripetal force causes a body to orbit at constant speed.

The blue ball does not increase its speed to 5 units. The large impulse does not change the speed. It does not do it in Newton?s drawing, it does not do it in my drawing.

So once again I will point out that you got the right answer but for some reason you refuse to accept your own answer!  Your attitude is really strange.

My answer is now and always has been, from the start that the blue ball does not change speed. It moves at 4 units before and after the collision. My drawing shows that AC a & CD are the same length and represent the same speed.
In Newton?s drawing, AB & BC are the same length representing the same speed.
 When the blue ball is subjected to repeated collisions, orbits at constant speed. Just  like Newton?s drawing

Newton Centripetal 3.png (24.51 kB . 296x272 - viewed 129 times)

[Bored chemist]

It is not a simple vector sum.

Why not?

[Momentus (OP)]

If I drive my car in a straight line

If I drive for 4 miles turn 48 Degrees and drive for 4 miles will have traced the path of the blue ball. It would have no bearing on the discussion.
You cannot accelerate( increase speed) a mass by applying force at right angles to its line of action. You can only accelerate a mass by applying a force along its line of action.

[Momentus (OP)]

Why not?

Ask sir Issac. Read his book. Study centripetal force. Look at the drawing. You cannot accelerate a mass by pushing at right angles to its motion. therefore you cannot accelerate the blue ball from 4 to 5. It is not a vector sum

[paul cotter]

If one applies a force at 90 degrees to an object in motion the velocity component in the original direction will not change but acceleration will undoubtedly occur in the direction of the applied force.

[Bored chemist]

You cannot accelerate a mass by pushing at right angles to its motion.

You can.
That's what the tension does if you swing something round on a string.

[Origin]

You cannot accelerate a mass by applying force at right angles to its line of action.

That is not true according to physics or even according to you!
You showed that before the collision the blue balls movement in the y direction was zero and after the collision the blue balls speed was 3 m/s in the y direction.  That obviously means the blue ball accelerated from 0 to 3 m/s.

You continue to argue with yourself!  This is really weird.  Are you by chance using dark logic?

[Origin]

My answer is now and always has been, from the start that the blue ball does not change speed. It moves at 4 units before and after the collision.

Wrong, you said this:

the blue mass moves on the line of CD an unchanged speed of 4 units and also along the line of BC at  speed of 3 units.

That means the blue ball is moving 4 units in the x direction and 3 units in the y direction which means the ball is moving at 5 units along a line that is 36.9 degrees from the CD line (x-axis).

So it seems the source of your confusion is that you do not realize that before the collision the blue ball is moving at 4 units along the line of travel and after the collision the blue ball is moving at 5 units along the new line of travel, even though the math clearly shows that.

Think about it for a second before you say no.

[Momentus (OP)]

Perpendicular force.
Changes the velocity of a moving mass
By changing the direction of the mass.

It is also known as centripetal force.

The earth is subjected to a centripetal force as its velocity constantly changes in orbit around the sun.

Mass subjected to a perpendicular force, be it the large impulse that Newton refers to, or the continuos force of gravity keeping the earth in orbit, does not increase the speed of the mass.

The only force acting on the moving blue mass is a perpendicular force.
The only force acting on the blue mass cannot increase its speed.
The speed of the blue mass remains as constant as any other mass subjected to a perpendicular force.

To claim that

collision the blue ball is moving at 5 units along the new line of travel,

is an expression of your belief, it has no basis in science

[Origin]

is an expression of your belief, it has no basis in science

No it is a straight forward use of physic and math.

You stated that after the collision the blue ball was moving at 4 units along the x-axis and 3 units along the y-axis.
Based on this please answer this simple question:  What is the speed of the blue ball along its direction of travel?

After you answer the first question could you also answer this question?  If the red ball was initially moving at 20 units so the final speed of the blue ball 4 units along the x-axis and 20 unit along the y-axis what would the balls speed be along the direction of travel?

One final question.  This does not have anything to do with a collision.  A green ball is moving with a speed of 5 m/s along the x-axis and 5 m/s along the y-axis.  What is the speed of the ball along its direction of travel?

Thanks

[Origin]

Perpendicular force.
Changes the velocity of a moving mass
By changing the direction of the mass.
It is also known as centripetal force.

Nope.  Your collision scenario is not an example of centripetal force.

The only force acting on the blue mass cannot increase its speed.
The speed of the blue mass remains as constant as any other mass subjected to a perpendicular force.

This is just something that you made up.  Please supply any sources that support your claim that a collision that occurs between 2 balls at a right angle will not increase the speed of one of the balls (except for the trivial example where the balls have the same mass and speed).

[Momentus (OP)]

What is the speed of the blue ball along its direction of travel?

I assume that you have not read any of the posts where I state. The speed of the blue ball does not change.

[Momentus (OP)]

Please supply any sources that support your claim

Sir Issac  Newton The principia.

[Origin]

the posts where I state. The speed of the blue ball does not change

I am afraid we are at an impasse here because you do not understand the basics of motion and basic math.
You believe that a point located at x=4 units and y=3 units is 4 units from the origin.  This is just plain wrong and is something you should have learned in highschool.  The worst part is you refuse to learn.  Oh well...

[Momentus (OP)]

In increasingly vain hope that anyone with an understanding of Newtonian dynamics gives a damn

The blue mass is moving at a speed of 4 units in the direction AC as shown in the diagram.

A perpendicular force is applied to the mass by an interaction with a red mass, bringing the red mass to rest. The red mass has a speed of 3 units, bringing the mass to rest imparts a momentum of 3m to the blue ball.

This changes the momentum of the blue mass by 3m. Equal and opposite exchange of momentum, opposed force.

Momentum is a vector quantity of mass and velocity. When the mass is not changed any change in momentum is brought about by a change in velocity.

Velocity can be changed by Altering speed and by altering direction. Either separately or in combination.

To change the speed of a moving mass a force must be applied along the line of motion of the mass.

To change the direction of a moving mass, a force must be applied perpendicular to the mass.

Applying these rules to the blue mass will alter the direction on the mass so that it is moving at a speed of 3 units along the line of action of the force, that is perpendicular to its original direction of travel. This is an equal and opposite exchange of momentum with the red mass.

This is achieved by opposing forces, the force to accelerate the red mass to a halt is opposed by the force required to accelerate the blue mass into a new direction.

Note there is no force left over to act along the line of motion of the blue mass. It has all been used up. There is no momentum left over from the collision, it has all been accounted for.

As there is no force to act along the line of action the speed of the blue ball is not changed.

The blue mass is now moving at a speed of 3 units in the direction perpendicular to the original line of motion. Accounting for all of the momentum given up by the red mass, All of it. 
It is also moving at a speed of 4 units in an as yet undetermined direction.

The direction that the blue mass is now moving can be determined by simple geometry. It is moving along the hypotenuse of a right-angled triangle at 4 units and along the perpendicular side of the triangle at 3 units. Just as drawn in the original diagram.

That is Dark Motion.

[Bored chemist]

You are saying that everything you predict is simple Newtonian stuff.
But Newtonian physics doesn't seem to explain the observed behaviour of matter in space.
The only way it works is if you add "dark matter" etc.

So, your idea is either "Newtonian", in which case it doesn't remove the need for dark matter or it's something new, in which case you shouldn't say things like

That is Dark Motion.

There's nothing "dark" about it.

Essentially, your ideas are wrong, or they are irrelevant.
Which i sit?

[Momentus (OP)]

your ideas are wrong

Which bit is wrong? I have worked an example from first principles.

[paul cotter]

You don't understand basic mechanics. Applying any force to a body will result in +/- acceleration, regardless of the angle with respect to the body's previous movement.  Centripetal forces are involved with rotations and have no application in the present scenario.

[Origin]

It is also moving at a speed of 4 units in an as yet undetermined direction.

I'm sorry that you can't work out this problem.  But since you don't know how to do the math it doesn't make much sense for you to claim you can guess the answer.
If you do the math you will find that the speed of the blue ball is 5 units and at an angle that is 36.9 degrees from the x-axis.

[Bored chemist]

Which bit is wrong?

Answering that is your job, not mine.
I just pointed out that your post is either wrong or irrelevant.