Part One: Solving the Equilibrium Equations

- Find out the value of the right-side load.

Formula: Left Hand Force * Left Hand Distance = Left Hand Force * Left Hand Distance

- 10N*2M = XN*3M
- X= (10N*2M)/3M

= 6.6667N

- Find out the distance.

- 7N*XM = 8N*3M
- X= (8N*3M)/7N

= 18.6667M

- Taking moments at point marked R
_{1}, we can get the vector sum of clockwise and anticlockwise forces,

- 2M*10N = 4M*R
_{2} - R
_{2}= (2M*10N)/4M - R
_{2}= 5N

Now, taking moments at point marked R_{2}, we can get the vector sum of clockwise and anticlockwise forces,

- 4M*10N = 2M*R
_{1} - R
_{1}= (4M*10N)/2M - R
_{1}= 20N - 3M*15M = (3+X)M*5N
- 3+X= (3M*15N)/5N
- 3+X= 9

- Taking moments at point marked R, we can get the vector sum of clockwise and anticlockwise forces,

X= 9-3

X = 6M

Now, taking moments at the pivot, we can get the vector sum of clockwise and anticlockwise forces,

- 6M*5N = 3M*R
- R= (6M*5N)/3M

R= 10N

- Find out the distance.

- R= -3N

This comes from the principle of static equilibrium that the total sum of forces acting on a structure should be zero.

Part Two: Solving the Equilibrium Equations

**Theory of Structure**

1) The equilibrium requirement of the structure is that all particles in the structure must be at rest and that their total force must balance off at zero. This is only achieved when the vector sum of all forces acting on the object, as well as that of the moments about the point are zero. This is referred to as equilibrium. However, strength and stability refers to the ability of an object to maintain this status and resist changes due to external forces. Interaction coexistence denotes the ability of objects to maintain stability in spite of external forces.

2) Force of gravity means the amount of gravitational acceleration on an object multiplied by the mass of the object. According to Newton’s 2^{nd} Law, object acceleration is proportional to the amount of force applied. However, the acceleration stands in inverse proportion to the total mass of the same object.

Gravity is best explained in terms of the downward pull of materials towards the surface of the earth. It is basically a force that acts on objects in this manner. Mass, therefore, differs from weight in that weight is a force derived from mass. According to literature, mass is the total matter contained in an object, while weight is the total gravitational force exerted by the object towards the surface of the earth. In mathematical terms, weight is obtained from the product of gravitational force and mass of an object. Basically, mass is a scalar quantity while weight is a vector quantity that it has direction.

3) Generally, loads applied on structures cause them stress that eventually deforms or at least displaces them. Live loads encompass the kind of stress that is in motion and hence bears momentum and impact because these parameters only arise from dynamic structures. On the other hand, dead loads are merely placement of constant stress on an object over a long period of time without any motion.

Wind, which is a form of dynamic load, can change the direction of oscillations of large structures, when its momentum exceeds the magnitude of the dead load in the structure.

The oscillation of large structures is easily changed by wind because the wind has a large surface to act on, while the dead load of the structure is limited by its large size.

4) Load of existence would fit into the category of dead loads, while load of use would properly fit into the category of live loads.

5) The chair cannot push one up because it does not possess dynamic force or load. According to Newton’s Law of Reaction and Action, the opposite but equal push must be between two forces. In addition, he defines gravitational force as the pull towards the surface of the earth. This means that the floor has zero gravitational force and therefore cannot exert reaction force to the action force of the chair on it. This will not affect the principle of Newton’s Law which specifies the equality of opposite forces.

6) An object that is not in equilibrium is likely to fall and this is dangerous, especially for a moving vehicle.

The type of equilibrium that exists within a structure gives it strength while equilibrium in its environment gives it stability.

7) Materials undergo deformation and lose shape when external stress applied on them exceeds the force inside the object. It is basically a mismatch of internal and external forces. According to Robert Hooke, this offsets the actions of elasticity.

8) The different parts of static equilibrium are the momentum and the vector sum of the forces applied to a structure. The two parts can be used together to solve the two algebraic equations resulting from momentum and vector sum of external forces.

9) The ratio of distances equals the ratio of forces.

Part Three: Solving the Equilibrium Equations

- Stress is almost synonymous with pressure because it acts per unit area of a structure. This is different from force that is not measured per unit area that it acts upon. Instead, force acts per unit mass of a substance. Stress is applied on a structure.
- Stress is a push while strain is a pull.