Untitled Quiz

Study Notes

F_R is the resultant force, the sum of all forces acting on an object
Forces are defined as vectors, represented in 3D space by the following equation: Force = (x) i + (y) j + (z) k
F₁, F₂, F₃ are forces acting on an object, calculated by adding or subtracting the corresponding values of x, y, and z.
In the first example, F₃ is calculated by subtracting F₁ and F₂ from F_R.
The direction of the force defines whether the corresponding value is positive or negative.
For example, F₂= 300 lb, with the force acting in the z-direction and the arrow pointing upwards
- x = 300 cos 65 cos 40
- y = 300 sin 30
- z = 300 sin 40
F_exy, F_exz, F_zy, are forces acting on an object, calculated using trigonometry and other forces.
In the example on Page 2, F_exz, F_zy are calculated by applying trigonometry to F_exy
The first example on Page 2 demonstrates how F₁ can be calculated by multiplying F₁ by a constant.

The particle is in equilibrium when the sum of the horizontal forces (∑F_x) and the sum of the vertical forces (∑F_y) are equal to zero.
This means the net force acting on the particle is zero and the particle is at rest.
The sum of the forces acting on a particle is calculated by adding the corresponding components of the force vectors along the x-axis and the y-axis.
Example on Page 4:
- The equilibrium condition is represented by the equations ∑F_x= 0 and ∑F_y= 0, where F_x is the horizontal force and F_y is the vertical force.
Equilibrium is important in understanding how objects behave under the influence of forces and it's a fundamental concept in statics and mechanics.

A, B, C, D are points in 3D space, their position can be defined as:
- A= (x_A) i + (y_A) j + (z_A) k
Example on Page 3:
- C= -3 i + 4 j + 0 K, therefore, C has coordinates (-3, 4, 0).
The distance between two points can be calculated by applying the distance formula.
AB, BD, BD| are vectors that indicate the direction and magnitude of the distance between the points.
U_AB is the unit vector, a vector with a magnitude of 1, and it indicates the direction of the line segment AB.

Mg represents the weight of the object attached to the spring
F_g, F_s are the forces acting on the object, where F_g is the force of gravity and F_s is the force exerted by the spring.
K is the spring constant or stiffness of the spring, it can be utilized to calculate F_s.
F_s = K * x, where x is the displacement from the equilibrium position.
For example, if the spring is stretched or compressed, the force exerted by the spring will be proportional to the amount of deformation.

The information about the forces on a body helps to understand how to calculate forces in different directions, along with the resultant force.
The information about equilibrium helps to understand how to analyze the forces acting on a body and determine if it's at rest or in motion.
The information about the spring helps to understand how to analyse and calculate the forces acting on a body connected to a spring.
The information about the spring helps us understand how to calculate how much force a spring exerts based on its stiffness and how far the spring is compressed or stretched.