Introduction to Statics (Engineering Mechanics), Assignments of Physics

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TUGAS MEKANIKA TEKNIK 1

Oleh :

FAIZUR -----------------

NRP 42----------------

Dosen : Irfan Syarif Arief, S.T, MT. INSTITUT TEKNOLOGI SEPULUH NOVEMBER

Engineering Mechanics

Chapter 1. Introduction to Statics

Mechanics

Mechanics is the physical science, which deals with the effects of forces on objects. As the oldest of the physical sciences, mechanics is logically divided into two parts : Statics, which concerns the equilibrium of bodies under the action of forces, dynamics, which concerns the motion of bodies.

Basic Concepts

Space , is the geometric region occupied by bodies, whose positions are described by linear and angular measurements relative to a coordinate system. Time , is the measure of the succession of events and is a basic quantity in dynamics. Time is not diretly involved in statics problems. Force , is the action of one body on another. As a vector, force have a direction of its action. The action of force is characterized by its magnitude. A particle is a body of negligible dimensions. In the mathematical sense, a particle is a body, whose dimensions are considered to be near zero, so we may analyze it as a mass concentrated at a point. Rigid body. A body considered rigid, when the change in distance between any two of its points is negligible for the purpose at hand.

Scalars and Vectors

Scalar quantities are those with which only a magnitude is associated. Vector quantities posseses both magnitude and direction. Vectors can be classified into : A free vector , is one whose action is not confined to or associated with a unique line in space. This vector describes equally well the direction and magnitude of the displacement of every point in the body. A sliding vector has a unique line of action in space but not a unique point of application. A fixed vector is one for which 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.

When expressed in rectangular components, the direction of the vector with respect to, say, the x -axis is clearly specified by the angle Ө , where tan Ө = Vy Vx A Vector may be expressed mathematically by multiplying its magnitude by a vector n , whose direction follows vector V. The vector n is called a unit vector. V = Vn In three dimensional vector, it is convenient to express the rectangular components of V, in terms of unit vectors i , j , k , which are vectors in the x- , y- , and z- directions. V = V (^) x i + V (^) y j + V (^) z k The direction cosines l , m , and n of V , defined by l =cos Өx m =cos Өy n =cos Өz So the magnitudes of the components of V can be written as Vx = lV Vy = mV Vz = nV where, from the Pythagorean Theorem, V 2 = Vx 2

• Vy 2
• Vz 2 Note that this relation implies that (^) l^2 + m^2 + n^2 = 1

Newton’s Laws

Law I. A particle remains at rest or continues to move with uniform velocity (in a straight line with a constant speed) if there is no unbalanced force acting on it. Law II. The acceleration of a particle is proportional to the vector sum of forces acting on it, and is in the direction of this vector sum. Law III. The forces of action and reaction between interacting bodies are equal in magnitude, opposite in direction, and collinear (they lie on the same line) Newton’s second law forms the basis for most of the analysis in dynamics. As applied to a particle of mass m , it may be stated as F = ma where F is the vector sum of forces acting on the particle and a is the resulting acceleration. Newton’s first law contains the principle of the equilibrium of forces. This law is actually a consequence of the second law, since there is no acceleration when the force is zero. The third law states that forces always occur in pairs of equal and opposite forces.

Units

In mechanic we use four fundamental quantities called dimensions. QUANTITY DIMENSIONAL SYMBOL SI UNITS U.S. CUSTOMARY UNITS UNIT SYMBOL UNIT SYMBOL Mass M kilogram kg slug - Length L meter m foot ft Time T second s second sec Force F newton N pound lb SI Units The International System of Units, abbreviated SI (from the French, Systeme International d’Unites ), is accepted in the US and throughout the world, and is a modern version of the metric system. By international agreement, SI units will in time replace other systems. U.S. Customary Units The U.S customary, or British system of units, also called the foot- pund-second (FPS) system, has been the common system in business and industry in English-speaking countries.

On the surface of the earth the only gravitational force of appreciable magnitude is the force due to the attraction of the earth. For a body of mass m near the surface of the earth, the magnitude of weight, or gravitational force W can be expressed as W = mg The weight W will be in newtons (N) when the mass m is in kilograms (kg) and the acceleration of gravity g is in meters per second squared (m/s^2 ). In U.S. customary units , the weight W will be in punds (lb) when m is in slugs and g is in feet per second squared. The standard values for g of 9.81 m/s^2 and 32.2 ft/sec^2 will be sufficiently accurate for our calculatons in statics.

Exercise

1. Three forces applied on an object as the image and data below : F1 = 10 N Ө 1 = 60o F2 = 15 N Ө 2 = 45o F3 = 20 N Ө 3 = 30o Find ∑F with its angle towards the x -axis and then draw a simple diagram showing your results. Answers : Fx =cos θ 1 × F 1 +cos θ 2 × F 2 −cos θ 3 × F 3 =cos 60 o × 10 N +cos 45 o × 15 N −cos 30 o × 20 N = 5 N +10,61 N − 17 Fy =sin θ 1 × F 1 −sin θ 2 × F 2 + sin θ 3 × F 3 =sin 60 o × 10 N −sin 45 o × 15 N +sin 30 o × 20 N =8,66 N −10,61 N + 1 ∑ F = 2

√ Fx

2

• F (^) y 2 = 2

2 +8, 2 = 2

2

√ 67,72=8.23 N

θ =tan − 1 Fy Fx =tan

− 1 8,05^ N

−1,71 N

=tan − 1 −4.71=− 78 o Picture for number 2

2. Find the mutual force of attraction between two objects! (Both length is 60 m and both objects is symetrical) G = 6,673 * 10-11^ m^3 /kg s^2 Answers :