Resolution of forces by calculation, Physics

Resolution of Forces by Calculation:

One vector was resolved into two mutually perpendicular components.

2489_solution by calculation.png

So if there are several vectors each can be resolved into two components.

e.g.    F1   in directionθ1,   gives   F1 sinθ1,  and  F1 cosθ1

          F2   in directionθ2,   gives   F2 sinθ2,  and  F2 cosθ2

          F3   in directionθ3,   gives   F3 sinθ3,  and  F3 cosθ3

          etc.
Once the components have been resolved, they can be added to give a total force in the Datum direction, and a total force perpendicular to the Datum.

1019_solution by calculation1.png

2458_solution by calculation2.png

These additions can be done laborio


usly 'by hand' but the modern scientific calculator renders this unnecessary.

Each vector should be entered and multiplied by the cosine of its direction and added consecutively to arrive at a total, F cosθ.

This procedure should be repeated, by multiplying each vector by the sine of its direction, and added consecutively to give F sinθ.

To calculate the Magnitude of the resultant,

          Add  (F sinθ )2  +  (F cosθ)2    (= F2)

And find the square root of the addition  (=F)

To calculate the Direction of the resultant,

          Divide  (F sinθ )  by  (F cosθ)   (= Tanθ)

and find the Angle (direction) that has that resultant,

923_solution by calculation3.png

Note that the values of sine and cosine take both positive and negative values, depending on the direction.

The calculator automatically takes account of this during the procedure.

The only occasion when ambiguity can arise is when finding the angle of the direction (there may be an error of 180º).  This can be resolved by inspection. Note the following:

675_solution by calculation4.png

With reference to the ambiguity of direction,

note that  1949_solution by calculation5.png =  (A)  gives the same angle (direction) as   Fsinθ/-FCosθ =  (B).  Thus, F sinθ  and F cosθ  have to be inspected to see which is negative.  Solution (A) or (B) can then be selected.

Similarly,   Fsinθ/FCosθ gives the same result as  -Fsinθ/-FCosθ                    . 

Again, inspect the values of F sin q and F cosθ to see whether both are positive or negative.

Posted Date: 9/14/2012 7:43:13 AM | Location : United States







Related Discussions:- Resolution of forces by calculation, Assignment Help, Ask Question on Resolution of forces by calculation, Get Answer, Expert's Help, Resolution of forces by calculation Discussions

Write discussion on Resolution of forces by calculation
Your posts are moderated
Related Questions
State and illustrate Lenz's law with examples Derive a mathematical expression for a force between two parallel conductors carrying a current.

The potential difference across the terminals of a cell when it is not supplying any current is known as it's emf.

A 2.5 kg rock is located on the Earth''s surface. If the mass of the moon is 7.4 E 22 kg, and the separation distance between the center of the rock and the center of the moon is 3

What is the specific resistance of material of a conductor. What do you mean by thermoelectric refrigerators?

The microwave (rotational) spectrum of 12 C 16 O having  a series of lines spaced by 115.3 GHz. Suppose that the rotational  energy levels of this molecule can be approximated by

Q. State any three properties of the nuclear forces. (i) A Nuclear force is charge independent. (ii) A Nuclear force is the strongest recognized force in nature. (iii) Nucl

What are the electron microscopy application areas? Electron microscopy application areas are as follows: a. Biology and life sciences b. Semiconductor and data storage

Cosmic background radiation; primal glow The background of radiation typically in the frequency range 3 x 10 11 to 3 x 10 8 Hz discovered in space in the year of 1965. It is

The lead alloy: Most of the soldering in the electronic industry is carried out using tin lead alloy. Pure lead metals at 327 0 C, whereas tin melts at 232 0 C and the mixture of

The simple equation E = mc² is not usually applicable to all these types of mass and energy, except in the special case that the total additive momentum is zero for the system unde