Newton's Laws of Motion PDF

SKCH PUC COLLEGE DEPARTMENT OF PHYSICS Chapter-4 Laws of motion The branch of physics which deals with cause for motion is known as Dynamics. ARISTOTLE’S FALLACY According to Aristotelian law of motion, an extern...

SKCH PUC COLLEGE DEPARTMENT OF PHYSICS Chapter-4 Laws of motion The branch of physics which deals with cause for motion is known as Dynamics. ARISTOTLE’S FALLACY According to Aristotelian law of motion, an external force is required to keep a body in motion. Flaw in Aristotle’s argument: A body moving on a floor stops because of external frictional force between the body and the floor and also due to air resistance. If there were no opposing forces the moving body would never stop. The opposing forces such as friction (solids) and viscous forces (for fluids) are always present in the natural world. This explains why forces by external agencies are necessary to overcome the frictional forces to keep bodies in uniform motion. THE LAW OF INERTIA Galileo studied motion of objects on an inclined plane. Objects (i) moving down an inclined plane accelerate, while those (ii) moving up retard. (iii) Motion on a horizontal plane is an intermediate situation. Galileo concluded that an object moving on a frictionless horizontal plane must neither have acceleration nor retardation, i.e. it should move with constant velocity. Galileo thus, arrived at a new insight on motion,the state of rest and the state of uniform linear motion (motion with constant velocity) are equivalent. In both cases, there isno net force acting on the body. It is incorrect to assume that a net force is needed to keep a body in uniform motion. To maintain a body in uniform motion, we need to apply an external force to ecounter the frictional force, so that the two forces sum up to zero net external force. To summarise, if the net external force is zero, a body at rest continues to remain at rest and a body in motion continues to move with a uniform velocity. This property of the body is called inertia. Inertia:The term inertia means ‘resistance to change’. It is defined as the inherent property of the body by virtue of which it continues to be in the same sate of rest or uniform motion. Due to inertia, the body always opposes the change in the position of rest or of uniform motion. Inertia of a body is directly proportional to its mass. SKCH PUC COLLEGE DEPARTMENT OF PHYSICS Different types of inertia: (i) Inertia of rest: The tendency of a body to remain in its position of rest is called inertia of rest Ex: A person standing in a bus falls backward when the bus suddenly starts moving forward. (ii) Inertia of motion: The tendency of a body to remain in its state of uniform motion in a straight line is called inertia of motion. Ex: When a moving bus suddenly stops, a person sitting in it falls forward. (iii) Inertia of direction: The inability of a body to change the direction of motion by itself is called inertia of direction. Ex: When a bus takes a sharp turn, a person sitting in the bus experiences a force acting away from the curved path due to his tendency to move in the original direction. Newton’s laws of motion: Sir Isaac Newton made a systematic study of motion and arrived at three laws of motion. First law of motion: Statement: Everybody continues in its state of rest or of uniform motion in a straight line unless it is compelled by some external force to change that state. The state of rest or uniform linear motion, both imply zero acceleration. Therefore, the first law can be simply expressed as follows: “If the net external force on the body is zero, its acceleration on is zero. Acceleration can be non-zero only if there is net external force acting on the body”. Newton’s first law of motion is also called law of inertia: According to Newton’s first law of motion, everybody continues in its state of rest or uniform motion unless an external force acts on it. This shows that a body, by itself, cannot change its state of rest or uniform motion. This inability of a body to change its state of rest or of uniform motion along a straight line is called inertia of the body. Thus first law defines inertia and hence it is called law of inertia’. Illustrations of Newton’s first law of motion: (a) Based on inertia of rest: (i) When a horse suddenly starts running, the rider falls backward: this is because the lower part of the rider, which is intact with the horse, comes into motion while his upper part tends to remain at rest due to inertia. (ii) Dust is removed from a hanging carpet by beating it with a stick: As the carpet is beaten, it suddenly moves forward while the dust particles tends to remain at rest due to inertia of rest and so fall off. (b) Based on inertia of motion: SKCH PUC COLLEGE DEPARTMENT OF PHYSICS (i) When a horse running fast suddenly stops the rider is thrown forward: This is because the lower part of the rider’s body, which is in contact with the horse, comes to rest while the upper part of his body tends to keep moving due to inertia. (ii) A person getting out of a moving bus or train falls in the forward direction: As the man jumps out of a moving bus his feet suddenly comes to rest on touching the ground while the upper part of his body continues to move forward. That is why he falls with his head forward. (iii)A ball thrown upward in a moving train comes back into the thrower’s hands: The ball acquires the horizontal velocity of the train and maintains it (inertia of motion) during its upward and downward motion. In this period, the ball covers the same horizontal distance as the train, so it comes back into the thrower’s hands. Force: It is defined as an external agency which changes or tends to change the state of rest or of uniform motion or the direction of motion of a body. Effects produced by a force: A force applied on an object can produce three types of changes: (i) Force can change speed of an object, making it to move slower or faster. (ii) Force can change the direction of motion of an object. (iii) Force can change the shape of the object. Linear momentum(P):It represents the quantity of motion present in a body which depends on mass and velocity of the body. Definition: Momentum of a body is defined as the product of mass and velocity of the body. Momentum = mass x velocity P  mv It is a vector quantity. Its direction is same as that of the velocity of the body. It’s magnitude is given by P = mv SI unit is kgms1 and dimensional formula is [MLT-1] Note: (i) The linear momenta of bodies having equal masses are proportional to their velocities. p1 v1 P when m1 = m2,    constant P2 v2 v (ii) The linear momenta of bodies having equal velocities are proportional to their masses. p1 m1 P when v1 = v2,    constant P2 m2 m SKCH PUC COLLEGE DEPARTMENT OF PHYSICS (iii) The velocities of bodies having equal linear momenta are inversely proportional to their masses ie., when two objects have equal linear momentum, the lighter object will move faster than the heavier one v m when P1 = P2, 1  2  mv  constant v2 m1 Newton’s Second law of motion: Statement:The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts”. Explanation: The second law can be divided into two parts. (i) The rate of change of momentum is directly proportional to the applied force: The larger the force acting on the body greater is the change in momentum. As P = mv, and mass remains constant, force is directly proportional to the change in velocity ie., acceleration. (ii) The change of momentum occurs in the direction of the force: If a body is at rest, a force will set it in motion. If a body is moving with a certain velocity, a force will increase or decrease this velocity accordingly as the force acts in its same or opposite direction. Expression for force(F = ma): Consider a body of mass m moving with an initial velocity v along a straight line.Let a force F acts on the body for time interval t. let the velocity of the body changes from v to v + v. correspondingly, let the momentum of the body changes from p to p+p. Then, change of momentum in time t = p Rate of change of momentum = ⃗⃗⃗⃗⃗ ∆𝑝 ∆𝑡 According to Newton’s second law of motion, applied force  rate of change of momentum. ⃗⃗⃗⃗⃗ ∆𝑝 ⃗⃗𝐹𝛼 ∆𝑡 ⃗⃗⃗⃗⃗ ∆𝑝 ⃗⃗ = 𝑘 𝐹 ∆𝑡 Where k is a constant of proportionality.The instantaneous momentum can be obtained by the limiting value of change in momentum ie., t 0 SKCH PUC COLLEGE DEPARTMENT OF PHYSICS   ⃗⃗𝑭 = k. lim  p  t 0  t    ⃗⃗⃗⃗⃗ 𝑑𝑝 ⃗⃗𝐹 = 𝑘 𝑑𝑡 But momentum, p = mv ⃗⃗𝐹 = 𝑘 𝑑(𝑚𝑣⃗) 𝑑𝑡 When the velocity of the body is very much less than the velocity of light (v