Engineering Mechanics Flashcards
Mechanics ?
continuum?
Rigid body ?
Deformable body ?
Mechanics is the physical science which deals with the effects of forces on objects.
A hypothetical continuous distribution of matter is called continuum.
Rigid body:
A body is rigid when the changes in distance between any two of its points is negligible for the purpose at end.
Deformable body:
A body is deformable when the changes in distance between any two of its points is not negligible.
Laws of mechanics –
Ist law , 2nd law , 3rd law
which laws valid only in inertial frame of reference.
Inertial frame of reference ?
Gravitational law ? Parallelogram law ? Triangle law
Euler’s law ?
Laws of mechanics –
Ist law - A body at rest or in motion will so untill an external force is applied on it.
2nd law - The change of motion is proportional to the natural force impressed and is made in a direction of the straight line in which the force is impressed.
3rd law - For every action there is an equal and opposite reaction.
The first two laws of Newton are valid only in inertial frame of reference. An inertial frame of reference has a constant velocity.
Gravitational law -
Parallelogram law, Triangle law
Euler’s law -
The rate of change of angular momentum of a body about an origin O equals the moment impressed upon it about the origin.
Principle of transmissibility ? valid for rigid or deformable or both ?
Moment
Varignon’s Theorem:
Couple ?
When the body is in complete equilibrium ?
Wrench ?
Principle of transmissibility -
The state of rest or of motion of a rigid body is unaltered if a force acting on the body is replaced by another force of the same magnitude and direction but acting anywhere on the body along the line of action of the applied forces.
principle of transmissibility is valid for rigid body only.
Moment -
The moment of a force about a point O is the cross product of r and F, where r is the position vector of any point on the line of action of force with respect to O.
just as force has a tendency to translate the body, moment has a tendency to rotate the body about the point.
Varignon’s Theorem:
Moment of a force about any point is equal to the sum of the moments of the components of that force about the same point.
The moment produced by two equal, opposite and non-collinear forces is called a couple.
Any system of forces may be replaced by its resultant force R and the resultant couple M.
The magnitude and direction of M depend on the particular point O (point of concurrency) selected. The magnitude and direction of R , however, are the same no matter which point is selected.
In dynamics we usually select the mass center as the reference point.
The change in the linear motion of the body is determined by the resultant force, and the change in the angular motion of the body is determined by the resultant couple.
In statics, the body is in complete equilibrium when the resultant force R is zero and the resultant couple M is also zero.
When the resultant couple vector M is parallel to the resultant forces R, the resultant is called a wrench.
A particle is in equilibrium when ?
When a body is in equilibrium, R? and M?
Different type of force systems.
Three force theorem:
A system of three forces in equilibrium ?
Lami’s theorem?
Reactions?
The virtual work done ?
A particle is in equilibrium if it is stationary or it moves uniformly relative to an inertial frame of reference.
When a body is in equilibrium, the resultant of all forces acting on it is zero. Thus that resultant force R and the resultant couple MR are both zero.
Different type of force systems.
- Collinear forces:
In this system, line of action of all the forces act along the same line.
Tug of war - Coplanar parallel force:
In this system, all forces are parallel to each other and lie in a single plane.
See-saw - Coplanar concurrent point:
In this system, line of action of all forces pass through a single point and forces lie in the same plane.
Weight suspended by two inclined strings. - Coplanar non-concurrent forces:
All forces do not meet at a point, but lie in a single plane. - Non coplanar parallel forces:
In this case, all the forces are parallel to each other, but not in the same plane.
Book on table. - Non-coplanar concurrent forces:
In this system, all forces do not lie in the same plane, but their line of action passes through a single point.
Tarazuu.
7.All forces do not lie in the same plane and their lines of action do not pass through a single point.This is the most general case.
Three force theorem:
A system of three forces in equilibrium must be coplanar and either be concurrent or be parallel.
Lami’s theorem:
If three forces coplanar and concurrent forces acting on a particle keep it in equilibrium, then each force is proportional to the sine of the angle between the other two.
Reactions:-
These are self-adjusting forces developed by the other bodies, which come in contact with body under consideration. When two bodies come in contact, both apply equal and opposite force on each other. If the contact surface is smooth, the force will be in the normal direction of surface of contact. This is not true, if friction is present.
The virtual work done by external active forces on an ideal mechanical system in equilibrium is zero for any and all virtual displacements consistent with the constraints .
Trusses ? Applications? solved
Trusses
A framework composed of members joined at their ends to form a structure is called a truss.
Two force member, forces either in compression on tension.
Truss is used for supporting moving or stationary load e.g Bridges, roof supports.
Method of joints
Method of sections
Frame ? Guidelines for analysis of frame?
Frame
A structure is called a frame if at least one of its individual members is a multiforce member.
A multiforce member is defined as one with three or more forces acting on it, or one with two or more forces and one or more couples acting on it.
Frames are structures which are designed to support applied loads and are usually fixed in position.
Frames:
- Support loads.
- Usually stationary.
- Fully constrained.
In a member of truss, forces are directed along the member only.
Following are the guidelines for the analysis of frame structure:
Dismember the frame/machine. Draw Free Body Diagram of each member. Apply physical laws(Equilibrium equations) to each member.
Load: Effort : Mechanical advantage: Velocity Ratio: Input : Output: Efficiency :
Wheel and Axle Pulley System Gears : Rack & Pinion: Cam Crank and Rod Chains and Belts Ratchet
Ratchet and pawl mechanism :
Inclined plane
Lever: KInds?
Law of machine :
Reversible or self locking? what and when?
Frames and machines consist of multiple parts assembled together in a number of possible ways. For example, the parts could be pin-connected or welded together. The primary difference between frames and machines is that there are moving parts in machines and not in frames.
Load: This is the resistance to be overcome by the machine. (W)
Effort : This is the force required to overcome the resistance to get the work done by the machine. (P)
Mechanical advantage: This is the ratio of load lifted to effort applied. W/P
Velocity Ratio: This is the ratio of the distance moved by the effort to the distance moved by the load in the same interval of time. D/d
Input : The work done by the effort is known as input. PD
Output: It is defined as useful work got out of the machine, i.e. the work done by the load. Wd
Efficiency : This is defined as the ratio of output to the input.
Efficiency of an ideal machine is 1. In that case, Wd =PD, which gives W/P= D/d. Thus, for an ideal machine, mechanical advantage is equal to velocity ratio.
Wheel and Axle
Pulley System
Gears : Gears can be used to amplify/reduce the torque/speed
Rack & Pinion: Rotary to linear motion.
Cam A cam is a wheel with shaped profile on it.
Crank and Rod Rotary to reciprocating.
Chains and Belts chain or belt connects two separated wheels
Ratchet A ratchet is a device that allows a wheel to turn in only one direction.
Ratchet and pawl mechanism : allows rotation in one direction.
Inclined plane An inclined plane can be used to alter the effort and distance involved in doing work, such as lifting loads. The trade-off is that an object must be moved a longer distance than if it was lifted straight up, but less force is needed.
Lever: A straight rod or board that pivots on a point known as a fulcrum.
There are three classes(kinds) of levers.
class -1 lever has its fulcrum located somewhere between the effort and the load. The direction of force is changed with this type of lever.
eg scissors, and pilers.
class -2 lever, the fulcrum is at one end, the effort is at the other end and the load is in the middle. With this kind of lever, the direction of effort is not changed.
wheelbarrow (single wheel cart by nagar nigam), nut cracker
class-3 lever. The fulcrum is at one end and the effort is applied between the fulcrum and the load. With this kind of lever, the direction effort is not changed.
ice tongs, tweezers, fishing rod
Law of machine : The relationship between the load lifted and the effort required in a machine is called the law of machine. This is generally a straight line which does not pass through the origin.
If the removal of effort while lifting results in lowering of the load, the machine is said to be reversible. The machine is said to be self-locking if the load is not lowered on removal of the effort.
A lifting machine is reversible if its efficiency is greater than 50 percent and self locking if its efficiency is less than 50 percent.
