Q. 95.0( 1 Vote )
100 coplanar forces each equal to 10N act on a body. Each force makes an angle π/50 with the preceding force. What is the resultant of the forces?
Now the total angle covered by the 100 coplanar forces of 10 N each is given by:
Total Angle Covered =
The head of the last force vector joins the tail of the first vector. Thus this makes a regular polygon of 100 sides. For a regular polygon (that is a polygon having all sides equal) we will always have an equal and opposite pair of force.
For Example, consider a square as shown below:
This is a regular polygon of 4 sides having same force magnitude. Thus they would cancel each other.
Now, consider a regular hexagon as shown below.
This is a regular polygon with six sides.
All forces have one force that is equal and opposite of it. Hence,
Similarly, our regular polygon of 100 sides also has .
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Motion in two dimensions, in a plane can be studied by expressing position, velocity and acceleration as vectors in Cartesian co-ordinates A = Axî + Ayĵ where î and ĵ are unit vector along x and y directions, respectively and Ax and Ay are corresponding components of (Fig. 4.9). Motion can also be studied by expressing vectors in circular polar co-ordinates as A = Ar + Aɵ where = = cosθ î + sin θ ĵ and = − sin θ î +cos θ ĵ are unit vectors along direction in which ‘r’ and ‘θ ’ are increasing.
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(e) Find velocity and acceleration in polar vector representation for particle moving along spiral described in (d) above.
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