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
what is thermal conductivity ?

Q What is Seebeck effect? Seebeck revealed that in a circuit consisting of two dissimilar metals like iron and copper an emf is developed when the junctions are maintained at

What are "Overtones" and "Harmonics" ? How are they build in an open pipe? Derive the mathematical equations for the frequencies of the harmonics produced in an open pipe.

The size of nucleus is measured in: (1)amu (2)Angstrom (3)Fermi (4)cm Ans: (3)Fermi

Describe with the help of a labelled diagram the underlying principle and working of a step-up transformer. Why cannot such a device be used to step-up D.C. voltage? Or Dr

Before manufacturing of transformers we must know the important parts of transformer which need to be manufactured. Following are the main parts of transformers. (a)          Fo

why the least distance of distinct vision is 25 %

What is the shortest possible time in which a bacterium could travel a distance of 8.4 cm across a Petri dish at a constant speed of 3.5 mm/s?

Ampere; A (after A.M. Ampere, 1775-1836) The basic SI unit of electric current, described as the current that, while going through two infinitely-long parallel conductors of ne

a. A certain radioactive material emits gamma rays with energy 1 MeV. Another sample of radioactive material emits gamma rays with energy 10 keV. If both of these emit the same amo