Frictional resistance to the relative motion of two solid objects is usually proportional to the force which presses the surfaces together as well as the roughness of the surfaces. Since…
Category: B.Tech./1Sem/Mechanical Engg
Lami’s Theorem
If three concurrent forces acting on a body keep it in equilibrium, then each force is proportional to the sine of angle between the other two forces. If three concurrent…
Equilibrium for Coplanar Forces | Condition of Equilibrium Coplanar Forces
Equilibrium for Coplanar Forces | Condition of Equilibrium Coplanar Forces: Forces in equilibrium mean that they are balanced. Coplanar forces act in the same plane. Two balanced forces are equal…
Vectors Representation
Vectors can be graphically represented by directed line segments. The length is chosen, according to some scale, to represent the magnitude of the vector, and the direction of the directed…
The Moment of a Force
The Moment of a force is a measure of its tendency to cause a body to rotate about a specific point or axis. This is different from the tendency for…
Parallelogram Law of Vector Resolution
According to the parallelogram law of vector addition: “If two vector quantities are represented by two adjacent sides or a parallelogram then the diagonal of parallelogram will be equal to the…
Composition of Forces
If two or more forces are acting simultaneously at apoint, the same effect can be produced by a single forceof the proper size and direction. This single force,which is equivalent to the action of two or more forces,is called the resultant. Putting component forcestogether to find the resultant force is called compositionof forces. (See fig. 2-2.) The vectors representing theforces must be added to find the resultant. Because avector represents both magnitude and direction, themethod for adding vectors differs from the procedureused for scalar quantities (quantities having onlymagnitude and no direction). To find the resultant force when a force of 5 pounds and a force of 10 pounds are applied at a right angle to point A, refer to figure 2.The resultant force may be found as follows:Represent the given forces by vectors AB and ACdrawn to a suitable scale. At points B and C drawdashed lines perpendicular to AB and AC, respectively.From point A, draw a line to the point of intersection X,of the dashed lines. Vector AX represents the resultantofthetwoforces.Thus,whentwomutuallyperpendicular forces act on a point, the vectorrepresenting the resultant force is the diagonal of arectangle. The length of AX, if measured on the samescale as that for the two original forces, is the resultantforce; in this case approximately 11.2 pounds. Theangle gives the direction of the resultant force withrespect to the horizontal.Mathematically,theresultantforceofperpendicular forces can be found by using thePythagorean theorem which deals with the solution ofright triangles. The formula is C2 = a2 + b2. This statesthat the hypotenuse, side “C” (our unknown resultantforce) squared is equal to the sum of side “a” (one of ourknown forces) squared and side “b” (another of ourknown forces) squared.
Unit, Free, Forced and Fixed Vector
UNIT VECTOR :A unit vector is defined as a vector in any specified direction whose magnitude is unity i.e. 1. A unit vector only specifies the direction of a given vector.…
Vector Quantities
Vector quantities, however, refer to both the direction of the medium’s movement as well as the measurement of the scalar quantity. Increase/Decrease in Temperature – The measurement of the medium’s…
Scalar Quantities
Scalar quantities, as stated above, are the measurements that strictly refer to the magnitude of the medium. There are absolutely no directional components in a scalar quantity – only the…