Laws of conservation of mechanical energy: It state that the total mechanical energy of a system remain constant if only conservative forces are acting on the system of particles and the work done by all other forces is zero. The initial potential and kinetic energy of the system are Ui and Ki respectively. The final […]
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Potential energy of spring: When a spring is compressed or elongated by a force F and the elongation or compression is x, then F x. Or, F = kx [where k is the force constant of spring]Â ——-(i) If Fe is the elastic force or restoring force applied by spring, then Fe = – kx
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Conservative and non-conservative field: A force is said to be conservative if the work done by or against the force in moving a body depends only on the initial and final position of the body not the nature of the path. Gravitational force, electrostatic force between two stationary charges, spring force etc. are conservative force.
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Work energy theorem: Work done by all forces like conservative, non-conservative, external, internal acting on a particle is equal to the change in kinetic energy of it. Therefore, according to work energy theorem we can say that the work done by the resultant force acting on the particle (which is equal to the sum of
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Work done by static friction: When static friction is acting between body and the surface, then there is no relative displacement between body and surface. Therefore static friction doesn’t perform any work. If a body is placed on a rough surface and force is applied on the body and we have to calculate the work
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Work done by a variable force: If either the magnitude or direction or both the magnitude and direction of the applied force change, then we can say the force is variable. To calculate the work done by the variable force we have to consider the work done for an infinitesimal displacement i.e. dw = . .
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Work: Work is said to be done when a force is applied on a body and the body is displaced through a certain distance in the direction of the applied force. If F is the force is applied on a body at an angle θ with displacement S, then work done on the body is
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Vector product or cross product: The vector product of two vectors and is defined as the product of the magnitudes of and and the sine of the angle between them. If and creates angle θ then = AB. Where is the unit vector perpendicular to the plane of and . Properties of cross product:  =
Scalar product or dot product: The scalar product of two vectors and  is defined as the product of the magnitudes of and  and the cosine of the angle between them. If A and B creates angle θ then, . = AB . Properties of dot product: (i) . = BA  = AB  = . (ii)
Representation of a vector by coordinates: Let us consider OX, OY and OZ are three perpendicular axes, where O is the origin. Let P is a point with coordinates (x, y, z) and  =  is the position vector of P. , and are the unit vectors along + ve X, Y and Z axis. Let
