Question

A particle is acted upon by three forces equal to 50 N, 100 N and 130 N, along the three sides of an equilateral triangle, taken in order. Find the magnitude, direction and position of the resultant force.

Answer 1

Given : A particle is acted upon by three forces equal to 50 N, 100 N and 130 N, along the three sides of an equilateral triangle, taken in order.

To Find : the magnitude, direction

Solution:

Lets Take    50  N along  x axis

Then 100 N  

Then 130N

50N  - along x axis = 50 N   along y axis  = 0 N

100N  along x axis  =100 Cos120°  along y axis = 100 Sin120°

    => along x axis  = = -50N    along y axis = 50√3N

130N  along x axis  =130 Cos240°  along y axis = 130 Sin240°

    => along x axis  = = -65N    along y axis = -65√3N

Total along x axis = 50 N -  50N - -65N = -65N

Total along y axis = 0 N +50√3N - 65√3N = -15√3N

Net force =   √ ( -65)² + ( -15√3)²  =  70N  

Direction =  201.8°  to the x axis

magnitude, = 70 N

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