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Two forces of 595 newtons and 497 newtons act on a point. The resultant force is 1039 newtons. Find the angle between the two forces.

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Answer:

the angle between the forces is 36°

Step-by-step explanation:

if we assign the x axis to F1=595 N , thus F2=497 has an angle α respect with the x axis such that

F total x = F1 + F2 cos α

F total y = F2 sin α

and since

F total² = (F total x)² + (F total y)² = (F1 + F2 cos α)²+(F2 sin α)²

F total² = F1² + 2*F1*F2cos α + F2² cos² α + F2² sin² α

F total² = F1² + 2*F1*F2cos α + F2²

therefore

cos α = [F total² - (F1²+F2²)] /(2*F1*F2)

replacing values

cos α = [F total² - (F1²+F2²)] /(2*F1*F2) = [1039² - (595²+497²)]/(2*595*497)

cos α = 0.809

α = cos⁻¹ 0.809 = 36°

User Alex Sexton
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