Enter the magnitude of one force and the angles opposite to the other two forces into the calculator to determine the magnitudes of the other two forces using Lami’s Theorem. This calculator assumes that the forces are in equilibrium.
Lami’s Theorem Formula
The following formula is used to calculate the magnitudes of the forces based on Lami’s Theorem.
A / sin(α) = B / sin(β) = C / sin(γ)
Variables:
- A, B, C are the magnitudes of the three forces in equilibrium (N)
- α, β, γ are the angles opposite to the forces A, B, C respectively (degrees)
To calculate the magnitudes of forces B and C using Lami’s Theorem, you can rearrange the formula to solve for B and C given A and the angles β and γ:
B = A * (sin(β) / sin(γ))
C = A * (sin(180 - β - γ) / sin(γ))
What is Lami’s Theorem?
Lami’s Theorem is a law of statics that describes the equilibrium of three coplanar, concurrent and non-collinear forces. It states that for a body to be in equilibrium under the action of three forces, each force must be proportional to the sine of the angle between the other two forces. This theorem is widely used in engineering and physics to solve problems involving force systems in equilibrium.
How to Calculate Forces using Lami’s Theorem?
The following steps outline how to calculate the magnitudes of forces using Lami’s Theorem.
- First, determine the magnitude of one of the forces (A) in Newtons (N).
- Next, determine the angles opposite to the other two forces (β and γ) in degrees.
- Use the formulas B = A * (sin(β) / sin(γ)) and C = A * (sin(180 – β – γ) / sin(γ)) to calculate the magnitudes of forces B and C.
- Finally, calculate the magnitudes of forces B and C in Newtons (N).
- After inserting the variables and calculating the results, check your answers with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Magnitude of force A = 50 N
Angle opposite to force B (β) = 60 degrees
Angle opposite to force C (γ) = 45 degrees
