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Applied Mechanics Back

Statics : It describes the concepts of calculating the components of a force and the moment of a force in addition with the concepts of a free body diagram.

Kinetics : The science which describes the relation of force to motion is called kinetics.

Displacement : Displacement of a particle is the vector change of position.

Simple Harmonic Motion : It is a rectilinear motion where the acceleration is directed towards a fixed point in the path and is proportional to the distance between that point and the moving point.
E.g: The motion of the projection on a diameter of a point moving with constant speed around a circle.

Displacement :      x = r cos (wt + e)
                           y = r sin ((wt + e)}

Velocity :             vx = -r w sin (wt + e) = -wy
                           vy = -r w cos (wt + e) = -wx

Acceleration :       ax = w2 cos (wt + w) = -w2x
                           ay = -r w2 sin (wt + e) = +w2y

Motion of a Projectile : The trajectory of path of a particle, is a parabola with coordinates x and y at any time t. The initial velocity of projection is v0, total of light is T, and downward acceleration is g. Then
                           x = (v0 cosq0) t
                           y = (v0 sinq0) t - gt2 / 2
                           v = (v02 - 2 gy)1/2
                           vx = v0 cosq0
                           vy = v0 sinq - gt
                           h = v02 / 2g sin 2q
                           y = v02 / 2g sin 2q, T = 2v0 / g sin w
If projection is horizontal, i.e., a bomb released from air plane is level flight.
                           q = 0, x = v0t; y = 1/2 gt2

Pendulum : For a simple pendulum, whose mass is concentrated at point L distance from the axis, the period of oscillation.
                           t = 2p (L / g)1/2

For a conical pendulum, h is the height of the cone of revolution.
                           t = 2p (L / g)1/2
and the angular velocity

For a compound pendulum, k is the radius of gyration about the axis and s is the distance between the axis and the centre of gravity, the length of the equivalent simple pendulum.
                           L = k2 / s

Rigid Body : A rigid body can be defined as a definite amount of matter the parts of which are fixed in position relative to one another.

Mass : It is the quantity of matter contained in it. The units of mass are kilogram, tonne, slug etc.

Momentum : The product of mass and velocity can be considered as Momentum.

Work : When the force acting on a body produces body movement the force is said to work. The work done by force is given by product of the magnitude of the force and distance acting on it. The work done by a variable force is equal to the average magnitude of the force multiplied by the distance through which it acts.

Moments and Couples : Moment of torque M of a force about a point or centre of moments is the product of the force magnitude and the arm or perpendicular distance S from the point to the action line of the force.
       M = F.S

Principles of Moments - Variations Theorem : The moment of the resultant of forces about a point in their plane or about a line is the algebraic sum of the moments of those forces about the point or line.

Couples : Two equal opposite and parallel forces acting on a body are known as a couple of which the arm is the perpendicular distance between the lines of action and the moment is the product of one of the force magnitude and the arm. The couple tends to produce rotation.

Resultant of a Couple : The resultant of any member of couple is another couple.

Representation of couple : A couple may be represented by a vector with length equal to the magnitude of the moment and direction perpendicular to the plane of the couple, pointed the way a right hand screw would advance if turned by the couple.

Centroid and Centre of Gravity : The centroid of a system of a parallel forces with a given points of application is the point through which their resultant will always pass however the forces may be turned while being kept parallel.

Friction : Friction may be defined as the contact resistant exerted by one body upon a second body when the second body moves or tends to move past the first body. Friction is a retarding force always acting opposite to the motion or the tendency to move.

Static and Kinetic Friction : When a block of weight W is subjected to force P to cause motion the corresponding frictional resistance F which increases linearly as long as a body does not move and the frictional force occurs. As the motion starts, does not remain at maximum value and kinetic friction ensures. The angle of static friction T is the angle with the horizontal plane at which sliding of one surface upon another will begin.
                           tanq = F / N

Hydrodynamic Friction : In case of a thick film of lubricant between the surfaces, the hydrodynamic friction can be represented as,
                           F = m VA / h
where m = coefficient of velocity
         h = film thickness of lubricant
         V = relative velocity
         A = area of contact
For a journal bearing with radius r, length L and clearance C, this equation becomes.
                           F = 4p2 m m L / c

Belt of Coil Friction : The friction opposite the slipping of belt line or brake band on a pulley or sheave. When power is transmitted, the tension T1, on the driving side of the belt is greater than the tension T2, on the driven side. If we neglect the centrifugal force, the tensions at incipient slipping are related by
                           T1 / T2 = etax
where a is the angle in over the entire arc of contact between belt and pulley. Power transmitted is
                           P = (T1 - T2)V
and maximum power is
                           Pmax = T2(efx - 1) = T1(1 - 1/efx) - V