The independance of horizontal and vertical motion

AI Thread Summary
The discussion centers on the independence of horizontal and vertical motion, particularly in the context of projectile motion, which follows a parabolic path. While empirical evidence supports this independence, participants express a desire for a convincing algebraic proof. One contributor mentions that treating gravity as a vector can help demonstrate this independence, referencing the concept of "gcos90" equating to zero. Others argue that the orthogonality of x and y unit vectors allows for separate treatment of these components, but emphasize that physical truths are ultimately proven through experimentation, not purely through algebraic means. The conversation highlights the intersection of theoretical physics and practical experimentation in understanding motion.
Cheman
Messages
235
Reaction score
1
The independance of horizontal and vertical motion...

Obviously it is possible to prove the independance of horizontal and vertical motion empirically - we only need look at projectile motion following a parabolic path. However, I have never found a convincing algebraic proof the for the independence of these 2 types of motion.

I have asked my physics teacher and he says that it can apparetly be proved by treating Gravity as a Vector, and then assessing the overall motion of a body - apparently things like "gcos90" appears, which obviously equal "0", and this can be used to show the independance of horizontal and vertical motion.

If anyone could supply me with a convincing algebriac proof i would be really greatful! :-p

Thanks in advance. :smile:
 
Physics news on Phys.org
Cheman said:
Obviously it is possible to prove the independance of horizontal and vertical motion empirically - we only need look at projectile motion following a parabolic path. However, I have never found a convincing algebraic proof the for the independence of these 2 types of motion.

I have asked my physics teacher and he says that it can apparetly be proved by treating Gravity as a Vector, and then assessing the overall motion of a body - apparently things like "gcos90" appears, which obviously equal "0", and this can be used to show the independance of horizontal and vertical motion.

If anyone could supply me with a convincing algebriac proof i would be really greatful! :-p

Thanks in advance. :smile:

What do you mean by "algebraic proof"? If you accept the mathematical concept of a vector, then if you have the vector oriented along the x-axis, can you find the component of the vector along the y-axis?

Zz.
 
The x and y unit vectors are orthogonal, thus the x and y components can be treated seperately. A ZapperZ pointed out, there really is no algebraic proof to consider.

Claude.
 
You also need to define how vectors multiply before you can say that\hat{x} and \hat{y} are orthagonal. A metric such as

ds^2 = dx^2 + dy^2

is one way of giving the necessary defintion of the vector product \hat{x} \cdot \hat{y}, and a diagonal metric such as the specific example above is necessary and sufficient to make these two vectors orthagonal.
 
You can't prove a physical fact mathematically! They can only be proven by experiment (what you called "empirically").

(If you assume that physical velocity can be represented by mathematical vectors, then you can use the properties of vectors. Of course, you would have to base that "assumption" on experiment.)
 

Thread '1:1 versus 2:1 Mechanical Advantage debate'

The rope is tied into the person (the load of 200 pounds) and the rope goes up from the person to a fixed pulley and back down to his hands. He hauls the rope to suspend himself in the air. What is the mechanical advantage of the system? The person will indeed only have to lift half of his body weight (roughly 100 pounds) because he now lessened the load by that same amount. This APPEARS to be a 2:1 because he can hold himself with half the force, but my question is: is that mechanical...
View full post »

Thread 'Newton's first law?'

Some physics textbook writer told me that Newton's first law applies only on bodies that feel no interactions at all. He said that if a body is on rest or moves in constant velocity, there is no external force acting on it. But I have heard another form of the law that says the net force acting on a body must be zero. This means there is interactions involved after all. So which one is correct?
View full post »
Thread 'Beam on an inclined plane'

Thread 'Beam on an inclined plane'

Hello! I have a question regarding a beam on an inclined plane. I was considering a beam resting on two supports attached to an inclined plane. I was almost sure that the lower support must be more loaded. My imagination about this problem is shown in the picture below. Here is how I wrote the condition of equilibrium forces: $$ \begin{cases} F_{g\parallel}=F_{t1}+F_{t2}, \\ F_{g\perp}=F_{r1}+F_{r2} \end{cases}. $$ On the other hand...
View full post »

Similar threads

Projectile motion problems with No horizontal acceleration
Replies
17
Views
18K
Horizontal motion and vertical motion are effectively independant
Replies
5
Views
2K
Is R=0 enough for circular motion?
Replies
8
Views
2K
Questions in [ motion in two dimensions ]
Replies
2
Views
2K
Horizontal and vertical independance
Replies
2
Views
2K
Studying Skipping Chapters in Stewart’s Calculus? (Pearson's Edexcel IAL Background)
Replies
2
Views
130
Objective questions regarding projectile motion - 2 dimension .
Replies
28
Views
6K
Projectile Motion: Given Horizontal Distance Travelled and Time Taken
Replies
1
Views
3K
Is there a simpler way to understand the Lorentz factor?
Replies
2
Views
3K
Lagrangian problem (rigid body+particle)
Replies
16
Views
4K

Hot Threads

Recent Insights

Back
Top