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mccoy1 said:Hi folks, can someone please point out how Atkin got the following relative velocity A-B equation: see attached file. It's in atkin pchem 9e page 834.
Thank you all.
tiny-tim said:hi mccoy1!
vrel A-B is the component of vrel in the AB direction, ie vrelcosθ
by Pythagoras, cosθ = adj/hyp = √(d2 - a2)/d
mccoy1 said:… then you get
Vrel,A-B =vrel/cos(theta) = vrel[d2/(d2-a2)]1/2 , which is not the equation in the attached file or am I doing something wrong?
mccoy1 said:As an aside, in 8e of the same book …sorry, i don't have the book (i was going on your picture)
tiny-tim said:mccoy1 said:As an aside, in 8e of the same book …sorry, i don't have the book (i was going on your picture)
Yes I know. I copied that image from Atkin 9e. I've also attached an image and a text copied from 8e.
Cheers.
mccoy1 said:… the authors have multiplication instead of a division between cos(θ) and vrel (which I think is impossible!) …
tiny-tim said:no, i can't see what I'm supposed to be looking at
btw, it should be multiplication …vrel is the whole vector, and vrelcosθ is the component
mccoy1 said:Ok there's a section (almost 1/2 way down the page) where it says "Justification 22: The collision cross-section"
The only trouble I've with that is vrel,A-Bcos(θ) is supposed to be scalar component of vrel,A-B along vrel. To me , it seems like vrelcos (θ ) is a scalar component of vrel along 'a' in the diagram.
I'm lost!
Edit: okay i think I'm wrong on the last bit. vrelcos (θ) is a scalar component of vrel on vrel,A-B, but the equation vrel,A-B suggests that it's a vector .
The relative velocity equation is a formula used to calculate the velocity of an object in relation to another object. It takes into account both the velocities and directions of the two objects.
The relative velocity equation is derived from the concept of vector addition. It takes the individual velocities of the two objects and combines them to find the resulting relative velocity.
The variables in the relative velocity equation are the velocities of the two objects and the angle between their directions of motion. The equation is typically written as Vrel = V1 + V2 - 2V1V2cosθ.
The relative velocity equation is commonly used in physics and engineering, particularly in scenarios where two objects are moving in different directions or at different speeds. It can also be applied in navigation and transportation, such as calculating the speed and direction of a boat relative to the current of a river.
One limitation of the relative velocity equation is that it assumes the two objects are moving in a straight line and do not accelerate or decelerate. Additionally, it does not take into account external forces such as friction or air resistance. It is best used in idealized situations and may not accurately represent real-world scenarios.