find the resultant of two forces acting on
body and having mognitude 10N each angle
between them is 60degree
Answers
Given :
- Magnitude of two vector forces, F₁ = F₂ = 10 N
- Angle between F₁ and F₂, θ = 60°
To find :
- Magnitude of Resultant Forces, R =?
- Direction of Resultant vector, α =?
Formula required :
- Formula to calculate Magnitude of resultant vector
R² = A² + B² + 2 A B cos θ
- Formula to calculate direction of resultant vector
tan α = ( B sin θ ) / ( A + B cos θ )
[ Where R is magnitude of resultant of two vectors with magnitudes A and B; and θ being the angle between vectors A and B ; α is the angle made by resultant vector with vector A ]
Solution :
Calculating Magnitude of resultant force
Using formula to calculate magnitude of resultant of two vectors
→ R² = F₁² + F₂² + 2 F₁ F₂ cos θ
→ R² = ( 10 )² + ( 10 )² + 2 ( 10 ) ( 10 ) cos 60°
→ R² = 100 + 100 + 200 cos 60°
putting value of cos 60° = 1/2
→ R² = 200 + 200 ( 1 / 2 )
→ R² = 200 + 100
→ R² = 300
→ R = √300
→ R = 10√3 N
Therefore,
- Magnitude of Resultant force is 10√3 Newton.
Calculating direction of resultant force
Using formula to calculate direction of resultant of two vectors
→ tan α = ( F₂ sin θ ) / ( F₁ + F₂ cos θ )
→ tan α = ( 10 sin 60° ) / ( 10 + 10 cos 60° )
→ tan α = ( 10 ( √3 / 2 ) ) / ( 10 + 10 ( 1 / 2 ) )
→ tan α = (5√3) / ( 10 + 5 )
→ tan α = (5√3) / 15
→ tan α = √3 / 3
→ tan α = 1 / √3
→ α = 30°
Therefore,
- Resultant force makes an angle 30° with the F₁ force.
Answer:
☃️Given :
Magnitude of two vector forces, F₁ = F₂ = 10 N
Angle between F₁ and F₂, θ = 60°
☃️To find :
Magnitude of Resultant Forces, R =?
Direction of Resultant vector, α =?
☃️Formula required :
Formula to calculate Magnitude of resultant vector
R² = A² + B² + 2 A B cos θ
Formula to calculate direction of resultant vector
tan α = ( B sin θ ) / ( A + B cos θ )
[ Where R is magnitude of resultant of two vectors with magnitudes A and B; and θ being the angle between vectors A and B ; α is the angle made by resultant vector with vector A ]
Solution :
Calculating Magnitude of resultant force
Using formula to calculate magnitude of resultant of two vectors
→ R² = F₁² + F₂² + 2 F₁ F₂ cos θ
→ R² = ( 10 )² + ( 10 )² + 2 ( 10 ) ( 10 ) cos 60°
→ R² = 100 + 100 + 200 cos 60°
putting value of cos 60° = 1/2
→ R² = 200 + 200 ( 1 / 2 )
→ R² = 200 + 100
→ R² = 300
→ R = √300
→ R = 10√3 N
Therefore,
Magnitude of Resultant force is 10√3 Newton.
Calculating direction of resultant force
Using formula to calculate direction of resultant of two vectors
→ tan α = ( F₂ sin θ ) / ( F₁ + F₂ cos θ )
→ tan α = ( 10 sin 60° ) / ( 10 + 10 cos 60° )
→ tan α = ( 10 ( √3 / 2 ) ) / ( 10 + 10 ( 1 / 2 ) )
→ tan α = (5√3) / ( 10 + 5 )
→ tan α = (5√3) / 15
→ tan α = √3 / 3
→ tan α = 1 / √3
→ α = 30°
☃️Therefore,
Resultant force makes an angle 30° with the F₁ force.