Mechanics Flashcards
Branch of mechanics that deals with forces and their effects on bodies at rest
Statics
Branch of mechanics that deals with forces and their effects on bodies in motion
Dynamics
Branch of dynamics that deals with bodies in motion due to the application of forces
Kinetics
Branch of dynamics that deals with bodies in motion without taking into account the forces that cause such motion
Kinematics
An agent which produces or tends to produce, destroy, or tends to destroy the motions of a body
Force
A force acting on a body may…
Change the motion of a body, retard the motion of a body, balance the forces already acting on a body, and give rise to the internal stresses in a body
To determine the effects of a force acting on a body, we must know the following characteristics of a force:
Magnitude of the force, line of action of the force, nature of the force (push and pull), and the point at which the force is acting
Magnitude of force is expressed in which units…
Newtons in SI units, kilogram force (kgf) in MKS units
Single force which produces the same effect as produced by all the forces acting on a body
Resultant force
If two forces, acting simultaneously on a particle, are represented in magnitude and direction as two adjacent sides of a (BLANK), then their resultant may be represented in magnitude and direction by the diagonal of that (BLANK). Which law does this refer to?
Parallelogram law of forces
If the resultant of a number of forces is zero, then the particle will be in…
Equilibrium
When two of more forces act on a body, they are said to form a…
System of forces
Forces whose lines of action lie on the same plane
Coplanar forces
Forces which meet at one point
Concurrent forces
Forces that meet at one point and their lines of action also lie on the same plane
Coplanar concurrent forces
If three forces acting on a body are in equilibrium, then each forces is proportional to (WHAT) between the two other forces
The sine of the angle
Turning effect produced by a force, on the body, on which it acts
Moment
What is equal to the product of the force and perpendicular distance to the body on which it acts?
Moment
SI unit of the moment of a force
Newton*meter
If a number of coplanar forces acting on a particle are in equilibrium, then the algebraic sum of their (BLANK) about any point is equal to the (BLANK) of their resultant force about the same point
Moment
Forces whose lines of action are parallel to each other
Parallel forces
Parallel forces that act in the same direction
Like parallel forces
Parallel forces that act in the opposite direction from one another
Unlike parallel forces
Two equal and opposite forces whose lines of action are different (at a normal distance from one another)
Couple
Perpendicular distance (x) between the lines of action of two equal and opposite forces
Arm of a couple
Magnitude of a couple
Product of one of the forces and the arm of the couple
A (BLANK) produces rotational motion for the body on which it acts
Couple
The point through which the whole mass of the body acts, irrespective of the position of the body
Center of gravity
COG of a uniform rod
Middle point
COG of a rectangle
Point at which its diagonals intersect
Moment of the moment, i.e. the second moment of mass or area of a body. Usually denoted with I.
Moment of inertia
Distance from a given reference where the whole mass or area of the body is assumed to be concentrated to give the same value of I
Radius of gyration (k)
Units for mass moment
kg-m2
Units for moment of inertia
m4 or mm4
If the moment of inertia about an axis passing through its center is known, then the moment of inertia about any other parallel axis is given by…
Parallel axis theorem
A force acting in the opposite direction to the motion of a body
Friction
Friction experienced by a body when at rest
Static friction
Friction experienced by a body in motion
Dynamic friction
Maximum value of frictional force that comes into play when a body just begins to slide over the surface of the other body
Limiting friction
Laws of static friction…
Opposite direction to body, magnitude is equal to the force that tends to move the body, magnitude of limiting friction bears a constant ratio to the normal reaction, force is independent to the area of contact, force depends on the roughness
Laws of dynamic friction
Opposite direction, magnitude bears a constant ratio to the normal reaction, slight decrease with increase in speed
Ratio of limiting friction (F) to the normal reaction (Rn) between the two bodies
Coefficient of friction (mu)
Device that enables us to lift a heavy load, W, by a comparatively small effort, P
Lifting machine
Ratio of load lifted (W) to the effort applied (P)
Mechanical advantage
Ratio of the distance moved by the effort to the distance moved by the load
Velocity ratio
Work done on the machine, equal to the product of effort and the distance through which it moves
Input of the machine
Work done by the machine, equal to the product of load lifted and distance through which it has been lifted
Output of the machine
Ratio of output to input of the machine
Efficiency of the machine
Structure, made up of several bars, riveted or welded together
Truss or frame
Composed of members just sufficient to keep it in equilibrium, when loaded, without any change in its shape. “n = 2j-3”
Perfect frame
Rate of change of displacement with respect to its surrounding. Scalar quantity
Speed
Rate of change of displacement with respect to its surrounding, in a particular direction. Vector quantity.
Velocity
Rate of change of velocity in a body. Positive when velocity increases with time, negative when velocity decreases with time.
Acceleration
In the case of vertical motion, acceleration (a) can be substituted for…
g = 9.81 m/s2
When a body falls from a height, its velocity is equal to…
v = sqrt(2gh)
Every body continues in a state of rest or uniform motion unless acted upon, the rate of change of momentum is directly proportional to the impressed force and takes place in the same direction in which the force acts, and for every action there is an equal and opposite reaction
Newton’s Laws of Motion
Matter contained in a body
Mass
Force by which a body is attracted towards the center of the earth
Weight
Total motion possessed by a body
Momentum (mass x velocity)
Force equal in magnitude but opposite and collinear with the applied force producing the acceleration
Inertia force
The force, while acting upon a body of mass 1 kg, that produces an acceleration of 1 m/s2 in the direction of which it acts
Newton = 1 kg*m/s2
The path traced by a projectile in space
Trajectory
Total time taken by a projectile to reach maximum height and return to the ground
Time of flight
Distance between the point of projection and the point where the projectile strikes the ground
Range
Angle described by a particle from one point to another, with respect to time. Vector quantity.
Angular displacement
Rate of change of angular displacement of a body. Usually expressed in revolutions per minute (rpm) or radians per second (rad/s). Denoted by omega.
Angular velocity
Angular velocity equation:
omega = (2piN)/60 rad/s, given N [rpm]
Rate of change of angular velocity
Angular acceleration
The normal component of linear acceleration along a circular path
Centripetal acceleration
When the body moves along a circular path with uniform velocity, then it will only have…
Centripetal acceleration
When a body moves along a straight path, then it will have only…
Tangential acceleration
A body is said to vibrate with simple harmonic oscillation, if it satisfies two conditions:
Acceleration directed towards center, acceleration proportional to distance from center
Maximum displacement of a body from its mean position
Amplitude
Time taken for one complete revolution of a particle in harmonic oscillation
Periodic time
Number of cycles per second and reciprocal of time period
Frequency
Heavy bob suspended at the end of a light inextensible and flexible string
Simple pendulum
Bodies which rebound after impact are called…
Elastic bodies
Bodies which do not rebound after impact are called…
Inelastic bodies
Whenever a force acts on a body and the body undergoes a displacement in the direction of force, then (BLANK) is said to be done
Work
Mathematically, work done is defined as…
Work done = force * displacement
The unit for work done
N*m
Rate of doing work per unit time
Mechanical power
Unit for mechanical power
Watt (N*m/s)
Product of force on an object and the object’s velocity
Power
Capacity for doing work. Mathematically, equal to the work done on a body in altering either its position or its velocity.
Mechanical energy
Energy possessed by a body for doing work, by virtue of its position
Potential energy
Potential energy stored by an elastic body when deformed
Strain energy
Energy possessed by a body, for doing work
Kinetic energy
