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Question

A particle is acted upon by four forces simultaneously, 30N due east 20N due north 15N due west 40N due south find the resultant force of the particle?


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Solution

Step 1: Given data

Four forces act on a particle as shown in the figure.

Step 2: To find

The resultant force on the particle.

Step 3: Calculation for magnitude of resultant force

We know, resultant of the forces acting in opposite direction can be found by taking their difference.

Here, force in the north-south direction,

FNS=40-20=20N towards south.

Force in the east-west direction,

FEW=30-15=15N towards east.

Resultant force,

F=FNS2+FEW2+2FNSFEWcosθF=202+152+2×20×15×cos90°θ=90°theforcesarerF=400+225+600×0F=625F=25N

Step 4: Calculation for angle made by the resultant force

tan(θ)=2015tan(θ)=530

Hence, the resultant force of the particle is 25N and it will make 53°with the west.


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