Four forces are acting on a particle. one force of magnitude $$3$$ N is directed upward, another is directed $$37o$$ East of North having magnitude $$5$$ N, third is directed in $$south-west$$ direction is of magnitude $$42N$$ and fourth force is $$5nN$$. If the particle is in equilibrium. The value on n is $$_______$$.

Question

Four forces are acting on a particle. one force of magnitude $$3$$ N is directed upward, another is directed $$37o$$ East of North having magnitude $$5$$ N, third is directed in $$south-west$$ direction is of magnitude $$42N$$ and fourth force is $$5nN$$. If the particle is in equilibrium. The value on n is $$_______$$.

Infinity Learn · Accepted Answer

Here, F→$$1=3k^F$$→$$2=5cos$$⁡$$37$$∘$$+5sin$$⁡$$37$$∘$$i^=4i^+3j^$$ and F→$$3=$$−$$42cos$$⁡$$45$$∘$$i^$$−$$42sin$$⁡$$45$$∘$$j^$$ $$=$$−$$4i^$$−$$4j^For$$ equilibrium of the particle    F→$$1+F$$→$$2+F$$→$$3+F$$→$$4=0$$ or     $$3k^+3j^+4i^$$−$$4i^$$−$$4j^+F$$→$$4=0$$∴    F→$$4=j^$$−$$3k^$$∴    F→$$4=1+9=10$$∴    $$n=2$$

Scalars and Vectors

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Scalars and Vectors

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Four forces are acting on a particle. one force of magnitude 3 N is directed upward, another is directed 37o East of North having magnitude 5 N, third is directed in south-west direction is of magnitude 42N and fourth force is 5nN. If the particle is in equilibrium. The value on n is _______.

Here, F→1=3k^F→2=5cos⁡37∘+5sin⁡37∘i^=4i^+3j^ and F→3=−42cos⁡45∘i^−42sin⁡45∘j^ =−4i^−4j^For equilibrium of the particle F→1+F→2+F→3+F→4=0 or 3k^+3j^+4i^−4i^−4j^+F→4=0∴ F→4=j^−3k^∴ F→4=1+9=10∴ n=2

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