Calculation of % component of resultant force

[soundproof]

Hi everyone,
This appears to be a trivial question but I'm uncertain to the correct answer.

If I have forces of 3N, 4N and 5N in the x,y and z directions respectively. The resultant force will be the square root of these components squared ≈ 7N. If I want to describe any of the components as a % of the resultant force, how is this done?

I have seen in a journal paper that from my example the z-component of the force is calculated as 71.4% (5/7*100) of the resultant force, while the y-component was 57% of the resultant force. The addition of these percentages is greater than 100% so this cannot be true.

If I calculate the z-component as a % of the resultant force by dividing the squares of each number (5^2/7^2*100), then the addition of each % component sums up to be 100% (x - 18%, y - 32%,z - 51%). Is this method correct and if so can someone explain to me why it is necessary to square both vectors.

Thank you

 

[tiny-tim]

welcome to pf!

hi soundproof! welcome to pf!

If I want to describe any of the components as a % of the resultant force, how is this done?

this seems a pretty crazy idea to me

what would be the point? ​

anyway … you have |F| ~ 7, F.i = 3, F.j = 4, F.k = 5

3² + 4² + 5² ~ 7²,

so of course (3/7)² + (4/7)² + (5/7)² ~ 1

 

[HallsofIvy]

Hi everyone,
This appears to be a trivial question but I'm uncertain to the correct answer.

If I have forces of 3N, 4N and 5N in the x,y and z directions respectively. The resultant force will be the square root of

the sum of

these components squared ≈ 7N. If I want to describe any of the components as a % of the resultant force, how is this done?

The magnitude of the resultant force will be \sqrt{9+ 16+ 25}= \sqrt{50}= 5\sqrt{2} which is, yes, about 7.
So the x component is about 3/7= 0.429... or about 43% of the whole, the y component is about 4/7= 0.571... or about 57% of the whole, and the z component is about 5/7= 0.714 or about 71% of the whole.

I have seen in a journal paper that from my example the z-component of the force is calculated as 71.4% (5/7*100) of the resultant force, while the y-component was 57% of the resultant force. The addition of these percentages is greater than 100% so this cannot be true.

You are reading a journal paper and cannot do basic arithmetic?? Of course, the percentages do not add to 100%, they are not numbers, they are vector components:
\sqrt{(.42)^2+(.57)^2+(.71)^2}= 1 instead.

If I calculate the z-component as a % of the resultant force by dividing the squares of each number (5^2/7^2*100), then the addition of each % component sums up to be 100% (x - 18%, y - 32%,z - 51%). Is this method correct and if so can someone explain to me why it is necessary to square both vectors.

Thank you

You cannot find a "percentage" of a vector because a vector is not a number. What you are doing is finding percentages of lengths of vectors. And the length of a vector is, by definition, the square root of the squares of the components.

 

[soundproof]

Thank you for your replies.

Just to clarify regarding this statement -

You cannot find a "percentage" of a vector because a vector is not a number.

So, it is not correct/possible to describe a vector in terms of % contributions of x, y and z components? And this is because I am trying to relate a length/scalar to a vector?

 

[tiny-tim]

So, it is not correct/possible to describe a vector in terms of % contributions of x, y and z components?

you can describe anything you like, but if you want the percentages to add to 100, it's difficult to see how it could be of any practical applicaton

(we can define the efficiency of a force …

if we want something to move horizontally, but we pull on it with a rope at an angle, then the efficiency would be the horizontal component divided by the whole force)​