Motion- Graphical Representative of Motion
* Motion can be represented using a line graph comparing dependent quantities and a common independent quantity.
* Time is always taken as the independent variable in graphical representation if motion.
* A distance – time graph represents the change in the position of an object with the time.
* A velocity – time graph represents the change in the velocity of an object with the time.
* The area under a velocity- time graph is equal to the magnitude of displacement of the body in a given time.
* The equations that define the relationship between velocity and acceleration of a body moving in a straight line are known as equations of motion.
* Velocity- time relation: v = u + at
* Position – time relation: s = ut + 1/2*at2
* Position – time relation: 2as = v2 – u 2
* When an object moves in a circular path with uniform speed, subtending equal angles at the centre of the circle in equal intervals, exhibits uniform circular motion.
Work and Energy- Work
* Work done by force acting on an object is equal to the magnitude of the force multiplied by the displacement of the object in the direction of the force.
Condition for work to be done:
* A net force should act on an object.
* The object must be displaced in the direction of the net force.
* Definition of work: work is said to be done when object is displaced on applying a certain force.
* Work done is the product of force and displacement: (W = F x s)
* Work is measured on joule in the SI system. One joule (j) is the work done when the net force of one newton acts on a body and displaces it in the direction of the force by one centimetre.
* The work done on the object is independent of the path traversed by the object.
* Work done is a scalar.
Work done can either positive or negative:
* Work done is positive if the force applied and the displacement, both are in the same direction.
* Work done is positive when the force acts in a direction opposite to the direction of displacement.
Work and Energy – Energy
* Energy id defined as the capacity to do work.
* The various forms of energy include kinetic energy, potential energy, thermal or heat energy, electrical energy and chemical energy.
* Energy stored in an object due to its position or place is known as potential energy.
* The gravitational potential energy of an object is the work done in raising it from the ground to a certain point against gravity. It is calculated using the expression PE = mgh.
* The energy possessed in a moving object is called kinetic energy. It is calculated by the formula:
EK = 1/2 mv 2
Where,
m is the mass of the object
v is the velocity of the object
* Energy can be converted from one form to another.
* Law of conservation of energy: Energy can neither be created nor destroyed, but can change its form.
* Power (P) is the rate of doing work. It is calculated using the expression:
P =W/t
Where,
W is the work done
t is the time taken
We express larger rates of energy transfer in kilowatts (kW).
Equilibrium of a Rigid Body
* If the net force acting on body is Zero, it moves with constant momentum. In such a case we say the body is in “transnational equilibrium”.
* If the vector sum of all the torques acting on a rigid body is equal to Zero, it is said to be in “rational equilibrium”.
* A rigid body is in mechanical equilibrium when the net external force and net external torque acting o it is zero.
* If a body in mechanical equilibrium is at rest, them the body is said to be in “static equilibrium”.
* Two parallel forces that are equal in magnitude and opposite in direction, acting on a rigid body with different lines of action forms “couple”.
* Moment of couple = r x F, Where ‘r’ is the perpendicular distance between the two forces.
* A couple is needed to make a rigid body rotate without translational motion.
* For a lever, effort x effort arm = load x load arm. This statement is known as “the principal of moments for a lever”.
* The mechanical advantage of a lever = effort arm / load arm.
Work Energy Theorem
* The dot product of two vectors is equal to the product of the magnitude of the two vectors and cosine of the angle between the vectors. The result of a dot product is always a scalar.
* Using the dot product, the work done is measured as the dot product of the force and displacement, which is equal to Fd cos θ.
* The work done can be positive, negative or Zero depending on the values of the angel between the force and the displacement, that is, θ.
* The work done by a force is positive when the angel between force and displacement is acute, that is, the angel is less than 90 degree.
* The work done by a force is negative when the angel between force and displacement is obtuse, that is, greater than 90 degrees and less than or equal to 180 degrees.
* The work done by a force is Zero is perpendicular to the displacement.
* The SI unit of work done is joule.
* The work- Energy Theorem states that the work done by a net force on an object is equal to the change in its kinetic energy.
Conservation of Mechanical Energy
* The Sum of kinetic energy (k) and potential energy (v) possessed a body is called the total mechanical energy of a body.
* The principal of Conservation of Mechanical Energy states that the total mechanical energy of a system is conserved if the forces doing the work on it are conservative.
* Work done by a conservative force will be path independent. It is equal to the difference between the potential energies between the initial and final position and is completely recoverable.
* Work done by a conservative force in a closed path is Zero.
