Kinetics PDF

KINETICS PROF. VIBHA K. PHYSICS K. J. SOMAIYA POLYTECHNIC , VIDYAVIHAR MUMBAI  COURSE CONTENTS NEWTON’S LAWS OF MOTION MOMENTUM IMPULSE, IMPULSIVE FORCE APPLICATIONS OF LAWS OF MOTION RECOIL OF GUN WORK , POWER, ENERGY ENERGY: POTENTIAL ENERGY,...

KINETICS PROF. VIBHA K. PHYSICS K. J. SOMAIYA POLYTECHNIC , VIDYAVIHAR MUMBAI  COURSE CONTENTS NEWTON’S LAWS OF MOTION MOMENTUM IMPULSE, IMPULSIVE FORCE APPLICATIONS OF LAWS OF MOTION RECOIL OF GUN WORK , POWER, ENERGY ENERGY: POTENTIAL ENERGY, KINETIC ENERGY NUMERICALS : MOMENTUM, IMPULSE, WORK, POWER, ENERGY  Scalars and Vectors ⚫ A scalar is a physical quantity with magnitude only. ⚫ Ex. – Temperature, mass, length ⚫ A vector is a physical quantity with both a magnitude and direction. ⚫ Ex. – Force, Velocity, Displacement  Distance and Displacement ⚫ Distance - the total length of the path travelled by an object. ⚫ It is a scalar quantity, involves magnitude. ⚫ It can never be negative. ⚫ Displacement- the change in position of an object from its initial position to its final position. measures the shortest path between start and end points. ⚫ It is a vector quantity, involves both magnitude and direction. ⚫ Displacement can be positive, negative, or zero, depending on the direction of movement. ⚫ Thus, distance is a scalar, and displacement is a vector. ⚫ If we return to the start, displacement is zero, but distance is not  Speed and Velocity ⚫ Speed - refers to how quickly an object is moving. ⚫ It is a scalar quantity, which means it only has magnitude. ⚫ Velocity- not only describes how fast an object is moving but also includes the direction of its motion. ⚫ It is a vector quantity, which means it has both magnitude and direction.  Acceleration and Retardation ⚫ Acceleration - rate at which an object’s velocity changes over time.. Mathematically, acceleration is calculated by ⚫ Retardation - is also known as deceleration or negative acceleration. It refers to the rate at which an object’s velocity decreases over time. It is actually the opposite of acceleration  NEWTON’S LAWS OF MOTION ⚫ 1 Law – An object at rest will stay at rest, st and an object in motion will stay in motion at constant velocity, unless acted upon by an unbalanced force. ⚫ 2nd Law – Force equals mass times acceleration. ⚫ 3 Law – For every action there is an equal rd and opposite reaction. Newton’s First Law of Motion (Inertia) ⚫ An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line unless acted on by an unbalanced force.  Newton’s Second Law of Motion (Momentum Law) ⚫The acceleration of an object depends on the mass of the object and the amount of force applied. where, ⚫F is the net force applied to the object, ⚫m is the mass of the object ⚫a is the acceleration.  Newton’s Third Law of Motion (Action & Reaction) ⚫ For every action there is an equal and opposite reaction. ⚫ Whenever one object exerts a force on another object, the second object exerts an equal and opposite force on the first. F12 = - F21  Momentum ⚫ Momentum is defined as the mass in motion. ⚫ The momentum is the product of the mass of the particle and its velocity. It is denoted by (p). ⚫ It is a vector quantity i.e. it has magnitude and direction. ⚫ Unit – SI system: Kg.m/sec CGS system: g.cm /sec  Sample problems ⚫ Question : A bicycle of 45 kg at a 20 km velocity is on the highway, what will be its momentum? Solution: ⚫ Given: m = mass of bicycle = 45kg v = velocity (speed) of bicycle = 20 m/s Thus by using formula for momentum, p=m×v p = 45 × 20 p = 900 kg.m/s  FORCE ⚫ A Push or Pull on one object by other is called Force ⚫ Since it has both direction and magnitude Force is a vector quantity. ⚫ When a force is applied on body ❖ It may change its state of rest. ❖ It may change its direction of motion. ❖ It my change its shape. Force  The rate of change of momentum is called Force. Where, F is Force, dp is Change in Momentum dt is Change in Time ⚫ Unit – SI system: Kg.m/sec2 or newton CGS system: g.cm/sec2 or dyne 1 newton = 105 dyne  Impulse and Impulsive Force ⚫ Impulse is defined as the force acting on the body for a very shorter period of time. ⚫ Impulse is a vector quantity and the formula for impulse is given, Impulse = F × Δt = change in momentum = mv - mu ⚫ where, Δt is the time interval F is the force. ⚫ V= final velocity ⚫ U = initial velocity ⚫ SI Unit= N.sec ⚫ CGS Unit = dyne.sec  Sample problems ⚫ Problem. Calculate the impulse if a force of 200 N is exerted on an object for 5 s. Solution: We have, F = 200 N Δt = 5 s Using the formula we get, Impulse = FΔt = 200 x 5 = 1000 Ns  Conservation of momentum ⚫ For an isolated system the initial momentum of the system is equal to the final momentum of the system Final momentum (Pf ) = Initial momentum (Pi ) m1 u1 + m 2 u2 = m 1 v 1 + m 2 v 2 ⚫ Total momentum before collision = Total momentum after collision  Applications law of conservation of momentum 1. Recoil of gun 2. Rocket propulsion  Weight ⚫ Mass is the measure of the amount of matter in a body. Mass is denoted using m or M. ⚫ Mass is measured in Kilogram or gram ⚫ Weight is the measure of the amount of force acting on a mass due to the acceleration due to gravity. Weight usually is denoted by W. Weight = F = mg Where g = acceleration due to gravity = 9.8 m/s2 Weight is measured in SI unit = newton or N, A unit of force  Energy ⚫ Energy is defined as the capacity of a body to do work. ⚫ Energy can be broadly categorized into two categories- Kinetic Energy and Potential Energy. ⚫ SI system – joule or J ⚫ CGS System- erg ⚫ 1 joule = 107 erg Types of energy  Kinetic Energy ⚫ Kinetic Energy is the energy associated with an object moving with a velocity. For an object of mass m and velocity, its kinetic energy is half of the product of the mass of the object with the square of its velocity. In our daily life, we observe kinetic energy while walking, cycling, throwing a ball, and others. ⚫ SI Unit: SI unit of kinetic energy is Joule (J) or kg.m2.s-2. ⚫ CGS Unit: In CGS system, the kinetic energy is defined in erg.  Potential energy ⚫ Potential energy in physics is the energy that an object possesses as a result of its position. PE = mgh where, m is the mass of the body g is the acceleration due to gravity h is the height The SI unit for measuring energy is Joule denoted as J.  Power ⚫ Power is a physical quantity that is a measure of energy transfer rate. ⚫ Therefore, it can be defined as the rate at which work is done with respect to time. where, W is the Work done, t is the Time for which work is done, and P is the Power gain or loss. ⚫ Power is the amount of Energy consumed per second. Power can also be defined as the quantity of force required to cause a unit displacement. ⚫ Power is a scalar quantity and is denoted by P. ⚫ In the SI system Watt (W) is the unit of Power. Watt is equal to one joule per second.  Work ⚫ For work to be done, a force must be exerted and there must be motion or displacement in the direction of the force. ⚫ The product of the magnitude of applied force and the distance travelled by the body equals the total work done by this force. ⚫ Work has only magnitude and no direction. Hence, work is a scalar quantity. SI unit = joule or J CGS unit = erg ⚫ We understand from the work equation that if there is no displacement, there is no work done, irrespective of how large the force is. To summarize, we can say that no work is done if: ⚫ the displacement is zero ⚫ the force is zero ⚫ the force and displacement are mutually perpendicular to each other. THANK YOU