Two forces acting in opposite direction have a resultant of 10 N. If they act at right angles to each other the resultant is 50 N , find the magnitude of each force.
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Answered by
4
let the 2 forces be p1 and p2.
given:
p1-p2=10.....(1)
p1^2 + p2^2=50^2.....(2)
2 equations 2 unknowns. hence they can be solved.
given:
p1-p2=10.....(1)
p1^2 + p2^2=50^2.....(2)
2 equations 2 unknowns. hence they can be solved.
Answered by
8
Resultant force when the forces are in opposite direction :
F₁ - F₂ = 10 N --- (1)
Resultant force Magnitude when the forces are at right angles:
F² = F₁² + F₂² + 2 F₁ F₂ Cos 90°
50² = F₁² + F₂² --- (2)
F₁² + ( F₁ - 10)² = 2500
F₁² - 10 F₁ - 1200 = 0
F₁ = [ 10 + - √4900 ] / 2 = 40 or -30 N
F₂ = 30 N or - 40 N
The magnitudes of the two forces are : 30 N and 40 N.
F₁ - F₂ = 10 N --- (1)
Resultant force Magnitude when the forces are at right angles:
F² = F₁² + F₂² + 2 F₁ F₂ Cos 90°
50² = F₁² + F₂² --- (2)
F₁² + ( F₁ - 10)² = 2500
F₁² - 10 F₁ - 1200 = 0
F₁ = [ 10 + - √4900 ] / 2 = 40 or -30 N
F₂ = 30 N or - 40 N
The magnitudes of the two forces are : 30 N and 40 N.
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