Title NEWTON'S LAWS OF MOTION & FRICTIOM.pdf ✅

 Digital www.allendigital.in [ 217 ] Force According to Aristotle, a constant continuous force is required to keep a body in uniform motion. This is called Aristotle's Fallacy. This cause was first understood in the late 1600s by Sir Isaac Newton. Any push or pull which either changes or tends to change the state of rest or of uniform motion (constant velocity) of a body is known as force. Effects of force: - A non-zero resultant force may produce the following effects on a body: (i) It may change the speed of the body. (ii) It may change the direction of motion. (iii) It may change both the speed and direction of motion. (iv) It may change the size and the shape of the body. Units for measurement of force: - Absolute units: (i) S.I  Newton (N) (ii) C.G.S  Dyne Conversion: 1N = 5 10 Dyne Force is a vector quantity, with magnitude and direction. Force: Push and Pull: - For instance, the force has been defined as an interaction that changes the motion of an object if unopposed. When this statement is examined closely, we see the role of push-pull in this. A force that changes the direction of an object towards you, that would be a pull. On the other hand, if it moves away, it is a push. Sometimes, force is simply defined as a push or pull upon an object resulting from the object’s interaction with another object. Hence, any kind of force is basically a push or a pull. Spring and elastic are also types of forces. The moment you push against it, it tends to resist and react or springs back with the same magnitude. Push and Pull Examples Push is defined as the force that is responsible for an object to move from the state of rest. Examples of push: • Pushing the trolley. • Pushing of the car when it breaks down. • Pushing the table from one place to another. The pull is defined as the force that is responsible for an object to move from the state of rest but in the opposite direction when compared to the push. Examples of pull: • Pulling the curtain. • Dragging the box. • Opening of the door. Newton's Laws of Motion 04 & Friction
NEET : Physics [ 218 ] www.allendigital.in  Digital Whenever we consider a force in a given scenario, it can act as an internal as well as an external force depending on the system we have considered. This is how we have introduced this topic from the basic and it emphasizes on the fact that we have to be careful about the system chosen whenever we are labelling a force as an internal or an external force. Balanced and Unbalanced Forces: - Balanced Forces If the resultant force of all the forces acting on a body sums up to zero, then the forces acting on the body are known as balanced forces. Let us look at some examples of balanced forces and understand how the body’s state of motion remains unaffected. Unbalanced Forces If force or forces acting on an object change the state of rest or uniform motion then it is called unbalanced forces. Practically anything that moves is a result of the exertion of unbalanced forces on it. If you kick a football and it moves from one place to another, it means that the unbalanced troops are acting upon it. The ball moves from one place to another after it’s kicked. Laws of Motion Newton formulated three laws, which we call Newton's laws of motion. 1. Newton’s First Law of Motion or Law of Inertia 2. Newton’s Second Law of Motion 3. Newton’s Third Law of Motion Newton’s First law of motion If a body is at rest, then it remains at rest and if it is moving with constant velocity then it continues to move with constant velocity until or unless it is acted upon by an external force. 3. Inertia Inertia is property of a body by virtue of which it opposes any change in its state of rest or state of motion. Mass of a body is quantitative or numerical measure of a body's inertia. Inertia  Mass • Mass of a body is quantitative or numerical measure of a body's inertia. • Larger the inertia of a body, more will be its mass. Inertia of Rest It is the inability of a body to change its state of rest by itself. Example: • When we shake a branch of a mango tree, the mangoes fall down. • When a bus or train starts suddenly, the passengers sitting inside tends to fall backwards. • When a horse starts off suddenly, its rider falls backwards. • A coin is placed on cardboard and this cardboard is placed over a tumbler such that coin is above the mouth of tumbler. Now if the cardboard is removed with a sudden jerk, then the coin falls into the tumbler. • The dust particles in a blanket fall off when it is beaten with a stick.
Newton's Laws of Motion & Friction  Digital www.allendigital.in [ 219 ] Inertia of Motion It is the inability of a body to change its state of uniform motion by itself. Example: • When a bus or train stops suddenly, the passengers sitting inside lean forward. • A person who jumps out of a moving train may fall in the forward. • A bowler runs with the ball before throwing it, so that his speed of running gets added to the speed of the ball at the time of throw. • An athlete runs through a certain distance before taking a long jump because the velocity acquired during the running gets added to the velocity of athlete at the time of jump and hence he can jump over a longer distance. • A ball is thrown in the upward direction by a passenger sitting inside a moving train then the ball will fall: - • back to the hands of the passenger, if the train is moving with constant velocity. • ahead of the passenger, if the train is retarding (slowing down) • behind of the passenger, if the train is accelerating (speeding up) Inertia of Direction It is the inability of a body to change its direction of motion by itself. Example: • When a straight running car turns sharply, the person sitting inside feels a force radially outwards. • Rotating wheels of vehicle throw out mud, mudguard fitted over the wheels prevent this mud from spreading. • When a knife is pressed against a grinding stone, the sparks produced move in the tangential direction. Linear Momentum The total amount of motion possessed by a moving body is known as the momentum of the body.  It is the product of the mass and velocity of a body.  It is a vector quantity whose direction is along instantaneous velocity. Momentum p mv = Momentum = Mass × Velocity  The equation illustrates that momentum is directly proportional to an object's mass and directly proportional to the object's velocity.  The direction of the momentum vector is the same as the direction of the velocity vector. SI unit : kg-m/s, N-s ; Dimension : [MLT–1] Illustration 1: Describe the momentum of 5 kg ball moving westward at 2 m/s you must include information about both the magnitude and the direction of the ball? Solution: Linear momentum is P m v =  The magnitude of momentum is |P| = |5| × |2| = 10 kg-m/s. The direction of momentum vector is the same as the direction of the velocity of the ball. As a vector quantity the momentum of an object is fully described by both magnitude and direction is 10 kg-m/s, westward.
NEET : Physics [ 220 ] www.allendigital.in  Digital Illustration 2: A block having mass 2 kg moving with velocity ˆ ˆ ˆ v 2i 3j k m /s = + + . Find momentum of the block. Solution: Linear momentum is P m v =  = ˆ ˆ ˆ 2 (2i 3j k m/s)  + + The magnitude of momentum is 2 2 2 P 4 6 2 kg m/s = + + − =2 14 kg m/s − Change in Momentum Change in any physical quantity can be calculated by Change = Final – Initial Similarly change in momentum can be calculated by  = − p p p f i = − mv mv f i =  m v Illustration 3: A ball of 0.20 kg hits a wall with a velocity of 25 m/s at an angle of 45° with horizontal. if the ball rebounds at 90° to the direction of incidence with same speed, calculate the magnitude of change in momentum of the ball. Solution: Initial momentum i i ( ) P m v m v(cos45 )i mvsin45 j =  =   +  − ˆ ˆ Final momentum f f ( ) ( ) P m v m v(cos45 ) i mvsin45 j =  =   − +  − ˆ ˆ Change in momentum = (–mv cos45°) – (mv cos45°) = –2mv cos45° 1 p 2mv cos45 2 0.2 25 5 2N s 2  =  =    = − Newton’s Second Law of Motion According to this law, "rate of change of momentum of any system is directly proportional to the applied external force". net dp dp F F k dt dt   = [In S.I. units k = 1] net dp F dt = Change in momentum takes place in the direction of the applied force. net dp F dt = d(mv) md(v) vdm dt dt dt = = + If m is constant dm 0 dt   =      net md(v) F dt = =ma dp dt = net d(mv) md(v) vdm F dt dt dt = = + If v is constant dv 0 dt   =     net vdm F dt = (variable mass system e.g. conveyor belt, rocket) The slope of momentum-time graph is equal to the force on the particle at that instant. dp F tan slope dt = =  = p t  mv cos   –mv cos v v =45° mv sin   mv sin