Principle of Stats - Force System PDF

1 – Engineering mechanics is the science which 13 – A set of forces in equilibrium maybe added to considers the effects of forces on rigid bodies. any system of forces without changing the effect of the original syst...

1 – Engineering mechanics is the science which 13 – A set of forces in equilibrium maybe added to considers the effects of forces on rigid bodies. any system of forces without changing the effect of the original system. 2 – In statics we consider the effects and distribution of forces on rigid bodies which are and 14 – Action and reaction forces are equal but remain at rest. oppositely directed. 3 – In dynamics we consider the motion of rigid 15 – Free-body diagram is a sketch of the isolated bodies caused by the forces acting upon them. body which shows only the forces acting upon the body. 4 – Rigid body is a definite amount of matter the parts of which are fixed in position relative to each 16 – Applied forces are forces acting on the free other. body. 5 – Force is that which changes, or tends to 17 – Reaction forces are those exerted by the change the state of motion of a body. This free body upon other bodies. definition applies to the external effect of a force. 18 – Scalar quantities are quantities which 6 – The internal effect of a force is to produce possess magnitude only and can be added stress and deformation in the body on which the arithmetically. force acts. It is dependent on its point of application. 19 – A vector of a quantity can be represented geometrically. 7 – Principle of Transmissibility states that the 20 – Free vector is one which does not show the external effect of a force on a body is the same for point of application of the vector. all points of application along its line of action; i.e., it is independent of the point of application. 21. Triangle Law – If two forces are represented by their free vectors placed tip to tail, their 8 – The internal effect of a force is definitely resultant vector is the third side of the triangle, the dependent on its point of application. direction of the resultant being from the tail of the first vector to the tip of the last vector. 9 – Force system is any arrangement where two or more forces act on a body or on a group of 22 – If the angle between two forces becomes related bodies. zero or 180 o, the forces are collinear. 10 – Coplanar forces are when the lines of action 23. Mechanics – the science that considers the of all the forces in a force system lie in one plane; motion of bodies under the action of forces. otherwise, they are non-coplanar. 24 – Trigonometric Functions 11 – Concurrent forces are forces whose lines of action pass through a common point. Those in Angle 15o 30o 45o 60o 75o which the lines of action are parallel are called sin 0.259 0.500 0.707 0.866 0.966 parallel force systems. Those in which the lines of cos 0.966 0.866 0.707 0.500 0.259 action neither are parallel nor intersect in a tan 0.268 0.577 1.000 1.732 3.732 common point are known as non-concurrent force systems. 25. Statics – study of motionless system or 12 –Two forces are in equilibrium only when: systems that move with constant velocity. a) equal in magnitude b) opposite in 26. Equilibrium – a body at rest or moving with directions c) collinear in action constant velocity. 27. Vectors – quantities that add like forces. 31. The relationship between forces that act on 28. Kinematics – concerned with rates of change the body (e.g. wind and gravity) and the motion of of geometrical quantities in a moving system; it the body involves kinetics. does not involve the concept of force. 32. Particle – a body whose size does not 29. Kinetics – treats the causes and the nature of influence its response to the forces acting on it. motion that results from specified forces. 33. Scientific notation – the use of powers of 10 to display numbers. 30. The relationships among position, velocity, and acceleration of a moving body are defined by kinematics. (ex. A thrown ball) Classification of force system according to their line of action 1 – Coplanar – concurrent forces y F3 F1 y1 θ1 x1 x θ2 F2 2 – Coplanar – parallel forces P1 P2 P3 3 – Coplanar – non-concurrent forces P1 P2 P3 y θ x 1 – Coplanar – concurrent forces Sample Problems: 1 – From the given figure, find the components of each force and the magnitude of the resultant and its direction with respect to the x – axis. y F5 = 400N x1 F1 = 600N y1 θ5 = 60o x F2 = 100N θ4 = 45o F3 = 300N F4 = 250N 2 – Two horses on opposite banks of a canal pull a barge moving parallel to the banks by means of two horizontal ropes. The tensions in these ropes are 2000N and 2400N while the angle between them is 60o. Find the resultant pull on the barge and the angle between each of the ropes and the sides of the canal. Moment M – moment – (N.m) M = Fd F – applied force or weight – (N) d – lever arm or perpendicular distance – (m)