Vectors Flashcards
What are the two main characteristics of a force?
Magnitude and direction
How can a force be represented graphically in two dimensions?
As a vector
What does the length of a force vector represent?
Magnitude
What does the angle of a force vector indicate?
Direction
How can a force vector be split?
Into vertical and horizontal components
What is the formula for the vertical component of a force vector?
F_vertical = sin(θ)
What is the formula for the horizontal component of a force vector?
F_horizontal = cos(θ)
What is the resultant magnitude of a force vector?
|F| = Resultant magnitude
What does equilibrium mean in the context of forces?
Overall resultant force of zero
What are the conditions for static equilibrium?
- The sum of the forces in the horizontal direction is zero
- The sum of the forces in the vertical direction is zero
- The sum of all moments is zero
What is the definition of an equilibrant force?
The force needed to bring the system into equilibrium
How is equilibrium achieved with two forces?
F1 + F2 = 0, i.e. F1 = -F2
What is the mathematical representation of net forces in equilibrium?
ƩF_V = 0, ƩF_H = 0, ƩM = 0
What is a concurrent coplanar force system?
All lines of action pass through the same point
What is a non-concurrent coplanar force system?
Forces do not pass through the same point, leading to rotation
What theorem may be needed to calculate the magnitude of forces?
Pythagoras’ theorem
What is the formula for Pythagoras’ theorem?
a² + b² = c²
How can angles between force vectors be calculated?
Using trigonometry, tan(θ) = Opposite/Adjacent
What is the resultant force in a system with three forces?
F1 + F2 + F3 = 0, i.e. F1 = -(F2 + F3)
What is the resultant force when two forces are acting?
R = √(R1² + R2²)
What is the significance of the angle in force calculations?
It determines the direction of the force
What is the formula to find the angle that a resultant force makes with the horizontal?
θ = tan⁻¹(Opposite/Adjacent)
What is meant by coplanar forces?
Forces that act within a two-dimensional plane
What is the resultant force when calculating the equilibrium of multiple forces?
Sum of horizontal and vertical components
