Objectives
(1) A branch of the physical sciences that is concerned with the state of rest or motion of bodies that are subjected to the action of forces
(2) Rigid Body Mechanics & deformable-body mechanics(solid mechanics) & fluid mechanics
A. Rigid body Mechanics
a. statics : deals with the equilibrium of bodies that are either at rest or move with a constanct velocity)
b. dynamics : concerned with the accelerated motion of bodies
(1) Basic quantities
A. length : locate the position of a point in space and theerby describe the size of a physical system
B. time : a succession of events, important in dynamics
C. mass : a measure of a quentity of matter used to compare the action of one body with that of another.
manifests itself as a gravitational attration between two bodies
a measure of the resistance of matter to a change in velocity
D. Force : a push or pull exerted by one body on another
occur when there is direct contact between the bodies
completely characterized by its magnitude, direction, and point of application.
(2) Idealizations
A. particle : has a mass, but a size that can be neglected.
B. rigid body : a combination of a large number of particles in which all the particles remain at a fixed distance from one another, both before and after applying a load.
C. concentrated force : the effect of loading which is assumed to act at a point on a body
(3) Newton's Law of Motion
A. 1st Law : A particle originally at rest, or moving in a straight line with constant velocity, tends to remain in this state provided the particle is not subjected to an unbalanced force.
B. 2nd Law : A particle acted upon by an unbalanced force F experiences an acceleration a that has the same direction as the force and a magnitude that is directly proportional to the force.
\[F = ma\]
C. 3rd Law : The mutual forces of action and reaction between two particles are equal, opposite, and collinear.
(4) Newton's Law of Gravitational Attration
\[F=G\frac{m_1 m_2}{r^2}\]
where
F = force of gravitation between the two particles
G = universal constant of gravitation; according to experimental evidence, \(G = 66.73(10^-12) m^3/(kg· s^2)\)
\(m_1, m_2\) = mass of each the two particles r = distance between the two particles
(5) Weight : Any two particles or bodies have a mutual attractive (gravitational) force acting between them. However, the only gravitational force having any sizable magnitude is that between the earth and the particle.
\[W = G \frac{m M_e}{r^2} = mg\]
(1) SI Units : length (m), time (s), mass (kg), force \(N = \frac{kg \times m}{s^2}\)
(1) prefixes : G, M, k, m, \(μ\)) , n
(1) Dimensional homogeneity : eath term must be expressed in the same units
(2) Significant Figures : Show significant figures by using notation not 23400 but \(23.4(10^3)\)
(3) Rounding Off Numbers :
(4) Calculations : Do not round off calculations until expressing the final graph.
Read the problem carefully and try to correlate the actual physical situation with the theory studied.
Tabulate the problem data and draw to a larger scale any necessary diagrams
Apply the relevant principles, generally in mathematical form. When writing any equations, be sure they are dimensionally homogeneious.
Solve the necessary equations, and report the answwer with no more than 3 significant figures
Study the answer with technical judgement and common sense to determine wheter or not it seems reasonable.