1 - Introduction to Statics, Vectors, Newton's Laws, Forces, and Moments

Question 1

What are dimensionally homogeneous values?

Answer 1

Dimensional homogeneity is the concept where the dimensions of variables on both sides of an equation are the same.

Question 2

What is a rigid body?

Answer 2

A body is rigid when the change in distance between any two of its points is negligible for the purpose at hand.

Question 3

What are the six basic concepts?

Answer 3

1. Space
2. Time
3. Mass
4. Force
5. Particles
6. Rigid Body

Question 4

What is a free vector?

Answer 4

A vector whose action is not confined to or associated with a unique line in space.

For example, if a body moves without rotation, then the movement or displacement of any point in the body may be taken as a vector.

Question 5

What is a sliding vector?

Answer 5

A vector is a unique line of action in space but not a unique point of application.

For example, when an external force acts on a rigid body, the force can be applied at any point along its line of action without changing its effect on the body as a whole, and thus it is a sliding vector.

Question 6

What is a fixed vector?

Answer 6

A vector where a unique point of application is specified.

The action of a force on a deformable or nonrigid body must be specified by a fixed vector at the point of application of the force.

Question 7

What is the parallelogram law of combination?

Answer 7

The law states that two vectors V1 and V2 treated as free vectors, may be replaced by their equivalent vector V, which is the diagonal of the parallelogram formed by V1 and V2 as its two sides. This combination is called the vector sum and is represented by the vector equation:

V = V1 + V2

Question 8

What is the triangle law?

Answer 8

The Triangle law of vector addition states that when two vectors are represented as two sides of the triangle with the order of magnitude and direction, then the third side of the triangle represents the magnitude and direction of the resultant vector.

Question 9

How can you express the magnitude and direction of a vector using rectangular components?

Answer 9

V = Vxi + Vyj + Vz*k

Question 10

What are the direction cosines of a vector?

Answer 10

l = cos (theta_x)
m = cos(theta_y)
n = cos(theta_z)

Question 11

How can you express the magnitudes of the components of a vector V?

Answer 11

Vx = l*V = V*cos(theta_x)
Vy = m*V = V*cos(theta_y)
Vz = n*V = V*cos(theta_z)

Question 12

Using Pythagorean Theorem, express the vector components as a combined vector?

Answer 12

V^2 = Vx^2 + Vy^2 + Vz^2

Question 13

What are Newton’s Laws of Motion?

Answer 13

1. A particle in a state of rest or motion will remain in that state until an external force is acted upon it.
2. Force equals mass times acceleration:

F = ma

3. Every action has an equal and opposite reaction.

Question 14

What is the principle of the equilibrium of forces?

Answer 14

If the size and direction of the forces acting on an object are exactly balanced, then there is no net force acting on the object and the object is said to be in equilibrium.

Question 15

What are the four fundamental dimensions used in Engineering?

Answer 15

1. Length
2. Mass
3. Force
4. Time

Question 16

What is the law of gravitation?

Answer 16

F = G * ( m1 * m2)/r^2

Question 17

What is the formula for weight?

Answer 17

W = m * g

Newtons (N) are the units.

Question 18

What must the complete specification of the action of a force contain?

Answer 18

Magnitude, direction, and a point of application

Question 19

What is the difference between external and internal forces?

Answer 19

External forces are forces caused by an external agent outside of the system. Forces external to a body can be either applied forces or reactive forces.

Internal forces are forces exchanged by the objects in the system. The relation between internal forces and internal deformations depends on the material properties of the body.

Question 20

What are reactive and applied forces?

Answer 20

Newton’s third law of motion tells us that for every action force there is an opposed and equal reaction force. In any interaction between two objects, the first object exerts a force on the second, and the second object exerts a force back on the first object that is equal in magnitude and opposite in direction.

The second force is the reactive force while the first force is the applied force. For example, pulling on a rope attached to a fixed point the applied force is the pull action while the reactive force is the tensile force in the rope.

Question 21

What is the Principle of Transmissibility?

Answer 21

The principle states that a force may be applied at any point on its given line of action without altering the resultant effects of the force external to the rigid body on which it acts.

Question 22

What are force classifications?

Answer 22

There are two types:

1. Contact force. A contact force is produced by direct physical contact. E.g. a force exerted on a body by a supporting surface.
2. Body force. A body force is generated by virtue of the position of a body within a force field such as a gravitational, electric, or magnetic field. E.g. a weight force.

Question 23

What are concentrated and distributed forces?

Answer 23

Every contact force is actually applied over a finite area and is therefore really a distributed force. Force can be distributed over an area, as in the case of mechanical contact, over a volume when a body force such as weight is acting, or over a line, as in the case of the weight of a suspended cable.

As all forces are technically distributed forces, concentrated forces don’t exist in the real world beyond the imaginary. The weight of a body is the force of gravitational attraction distributed over its volume and may be taken as a concentrated force acting through the centre of gravity.

Question 24

What are concurrent forces?

Answer 24

Two or more forces are said to be concurrent at a point if their lines of action intersect at that point. This can often be interpreted in the form of a parallelogram or triangle.

Question 25

What is a moment?

Answer 25

Just as a force has the tendency to move a body in the direction of its application, a force can also tend to rotate a body about an axis. The axis may be any line which neither intersects nor is parallel to the line of action of the force. This rotational tendency is known as the moment M of the force. The moment is also referred to as torque.

Question 26

What is the magnitude of the moment?

Answer 26

M = F * d

Where F is the applied force and d is the distance from the applied force to the object.

The moment is a vector M perpendicular to the plane of the body. The sense of M depends on the direction in which F tends to rotate the body.

Question 27

What are the units of moments in SI units?

Answer 27

Newton-meters (N.m)

Question 28

What is Varignon’s Theorem?

Answer 28

The principle states that the moment of a force about any point is equal to the sum of the moments of the components of the force about the same point.