XI PHYSICS M. AFFAN KHAN LECTURER PHYSICS, AKHSS, K affan_414@live.co https://prootephysics.wordpress.co [MOTION] CHAPTER NO. 3 In this chapter we are going to discuss otion in one diension in which we will be learning Kineatics as well as Dynaics of soe Physical Systes with soe new concepts of Forces and Moentu.
Rest: E.g. A book kept on table Car waiting at signal Motion: E.g. Moving Car Moveent of Earth Displaceent: Displaceent is a vector quantity Its S.I. unit is eter () elocity: It is vector quantity Its S.I. unit is /s A body is said to be in rest if it doesn t change its position with respect to its surroundings. A body is said to be in otion if it continuously changes its position with respect to its surroundings. The shortest distance between two points is called as displaceent. The rate of change of position of an object is called as velocity.
Types of elocity i) Unifor elocity ii) iii) iv) If a body changes its position equally in equal interval of tie, the velocity will be called as Unifor. (i.e. velocity reains constant throughout the otion) ariable elocity If a body doesn t change its position equally in equal interval of tie, the velocity will be called as ariable. (i.e. velocity will not reain constant) Average elocity The ratio of total displaceent covered and the total tie taken during the trip is called average velocity. Instantaneous elocity The velocity of an object at a particular instant. li It is also defined as, The easureent of velocity where the tie interval approaches to zero. Acceleration: It is a vector quantity Its unit is /s 2 It is defined as the rate of change of velocity. Types of Acceleration: i) Unifor Acceleration When a body changes its velocity equally in equal interval of tie then the acceleration is called as Unifor acceleration. ii) Instantaneous Acceleration The acceleration of an object at a particular instant. li It is also defined as, The easureent of acceleration where the tie interval approaches to zero.
Three Equations of Motion: 1 st Equation: 2 nd Equation: 3 rd Equation: Gravitation Acceleration: The otion of a body under the influence of a Gravitational Force is called as Gravitational Motion, here body oves with unifor acceleration called as Gravitational Acceleration. It is denoted by g It is a vector quantity, always directed towards the center of Earth Its S.I. unit is /s 2 Now the three equations of otion can also be written as, 1 st Equation: 2 nd Equation: 3 rd Equation: where g = gravitational acceleration, h = height The value of g will be taken as negative when the body will be thrown upward and it will be taken as positive when the body will be coing downwards. Exaple: An object is dropped fro top of the hill; the object is falling freely under the action of gravity. Find its velocity after 10 seconds.
First Law of Motion: NEWTON S LAWS OF MOTION Stateent: It is also called as Law of Inertia A body will reain in rest or in unifor otion, until or unless it is subjected by an external force. Explanation: Consider the exaple of a bus, when you are sitting in a stationary bus, your present state is Rest. If the bus suddenly starts oving, you will feel a jerk and will tend to ove in opposite direction (a). Since you were in rest, you were not ready to ove that is why your body tended to be in rest. Now if that oving bus suddenly stops (b). You will feel another jerk towards the forward direction. Now again since you were in the state of Motion and you were not ready to stop yourself and as the bus stopped your body tended to be in otion that is why you felt this jerk.
Second Law of Motion: When a body is subject to an external (unbalanced) force it produces acceleration in that body. The agnitude to that acceleration is directly proportional to the force applied and inversely proportional to the ass of that object. Third Law of Motion: For every action there is an equal and opposite reaction. Explanation Consider there are two bodies about to collide. As they collide, one body (say A) will exert force on the other body (say B) as F. On the other hand, the body B will also exert force on body A and which will be equal in agnitude but opposite in direction, referred as F. F F
Tension: An opposing force, produced in a fully stretched string due to soe applied force usually weight, is called tension. The agnitude of this force is sae at all points in the string. In equilibriu position, T W; which eans that tension produced in the string due a hanging object is always equal to weight of the object. Unit: Since Tension is a force, its unit is Newtown (N) MOTION OF BODIES ATTACHED TO A STRING Case no. 1: When two bodies attached to a string and oving vertically. Consider two bodies of asses 1 and 2. Let these two bodies hang vertically with the help of a string which passes over a frictionless pulley as shown in figure. If 1 is greater than 2 then 1 will ove downwards and 2 will ove upwards with the sae acceleration. By using free body diagra, we ay write, For 1: F g T But according to Newton s second law F a, so that a g T---------- (1) For 2: F T g But again we know that F a, therefore, a T g ---------- (2) For acceleration: Add (1) & (2) a a g T T g a a g g a g g a Free Body Diagras:
For Tension: Divide (1) by (2) a g T a T g g T T g T g g T T g g T T T g g T g T g Case no. 2: When a Body is placed on a horizontal surface and other is hanging vertically Consider two bodies of asses 1 and 2 in such a anner that 2 lies on the horizontal surface and 1 hangs vertically. Both these bodies are connected to a string which passes over a frictionless pulley as shown in figure. If 1 is greater than 2 then 1 will ove downwards and 1 will slide horizontally towards right. Both bodies will ove with sae acceleration. For 1: F g T Since F a a g T ---------- (1) For 2: It is clear fro free body diagra that the forces weight and noral are cancelling each other because there no vertical oveent of the block. But we ll consider the tension force which is actually pulling it towards right. F T Since, F a a T ---------- (2)
For acceleration: Add (1) & (2) a a g T T a a g a g a For Tension: Divide (1) by (2) a g T a T g T T T g T T g T T T g T g Free Body Diagras: MOMENTUM The quantity of otion contained in a body is called as oentu. Or we ay define it in ore elaborated words A physical quantity which expresses the quantity of otion in a body and its resistance of slowing down is called as Moentu Linear oentu is a vector quantity. It has direction that of velocity. Its S.I. unit is kg s or N. s P
Explanation: Fro the definition of oentu, it becoes obvious that an object has a large oentu if both its ass and its velocity are large. Both variables are of equal iportance in deterining the oentu of an object. Consider a truck and a roller skate oving down the street at the sae speed. The considerably greater ass of the truck gives it a considerably greater oentu. Yet if the truck were at rest, then the oentu of the least assive roller skate would be the greatest. The oentu of any object that is at rest is 0. Objects at rest do not have oentu - they do not have any "ass in otion." Both variables - ass and velocity - are iportant in coparing the oentu of two objects. Stateent: Proof: LAW OF CONSERATION OF LINEAR MOMENTUM In the absence of external force the total oentu of the syste always reains constant. OR In an isolated syste the total linear oentu of a syste always conserved. Consider an isolated syste contains two asses 1 and 2 oving with velocities U1 and U2 in the sae direction. If U1 is greater than U2 than at tie interval t collision takes place between the asses and their final velocities becoe 1 and 2 respectively. Total oentu of the syste before collision U U Total oentu of the syste after collision
If the first body exerts force on second body than according to Newton s third law second body will also exert force on first body which is equal in agnitude but opposite in direction therefore we can write, F F But F a, therefore, U U t t U U U U U U Hence, FORCE IN TERMS OF LINEAR MOMENTUM The rate of change of linear oentu is called force Proof: Consider a body of ass oving with initial velocity i. Let a force F is applied to the body than it produces acceleration in the body in its own direction and its final velocity becoe f. According to Newton s second law we can write, F a Using definition of the acceleration we can write F t F t F t P P F t P F t Therefore, we ay conclude Force is tie rate of change of Linear Moentu
Types of Collisions: COLLISION OF BODIES Whenever two objects coe closer to each other such that they exert force on each other for a brief interval of tie then it is called a collision. 1. Elastic Collision 2. Inelastic Collision Elastic Collision: A collision of two or ore bodies in which the total oentu and the total kinetic energy of the syste reain conserved is called elastic collision. For exaple: The collision between olecules of a gas Inelastic Collision: A collision of two or ore bodies in which the total oentu of the syste reains constant but the total kinetic energy of the syste doesn t reain constant is called inelastic collision. For exaple: the collision between two cars Final elocities of Colliding Bodies: Consider two bodies of asses 1 and 2 oving with initial velocities U1 and U2 respectively. Let these bodies collide elastically and their final velocities becoe 1 and 2. Since collision is elastic therefore law of conservation of oentu and law of conservation of kinetic energy reains conserved.
Using law of conservation of linear oentu, Total oentu before collision Total oentu after collision U U U U U U -----------(1) Using law of conservation of kinetic energy, Total kinetic energy before collision Total kinetic energy after collision U U U U U U U U U U U U -----------(2) Dividing (2) by (1) U U U U U U U U For 1: U U U U Putting this value in (1) U U U U U U U U U U U U U
U U U U For 2: U U Putting this value in (1) U U U U U U U U U U U U U U U U U U U U U Special Cases: 1) Equal Masses: When colliding asses are equal in agnitude then For 1: U U U U U, therefore, For 2: U U U U U Conclusion: Hence the bodies will interchange their velocities
2) Target Particle at Rest: When the target particle, say 2 is at rest i.e. U2=0, then the final velocities will be, For 1: U For 2: U and if the asses are sae i.e., then U U U U Conclusion: Projectile particle will stop and the targeted particle will acquire the velocity of projectile particle. 3) Massive Target at Rest: When the target particle has ass uch higher than projected particle and it is also at rest, i.e. 2>>1 and U2=0 For 1: U U For 2: U Conclusion: The incident particle will bounce back with practically sae velocity and the targeted assive particle reains at rest.
4) Massive Projectile and Stationary Target When a assive particle collides with a very less assive particle which is at rest. i.e. 1>>2 and U2=0 For 1: U U For 2: U U Conclusion: The assive projectile practically oves with the sae velocity while the lighter target at rest reoves at twice the speed of assive projectile. FRICTION Whenever two surfaces, which are in contact, rubbed against each other then they feel opposition to their otion this opposing force is known as force of friction or siply friction. Explanation: When two surfaces are brought in contact, then uneven portions of both the surfaces griped together and thus for welds due to which they feel opposition in otion and thus friction is produced.
Matheatically, Consider two surfaces which are in contact are rubbed against each other than frictional force f will be present there, experientally it is found that friction force is directly proportional to the noral reaction R. f R f R But R W g Therefore, f g Where is constant of proportionality and called Co-efficient of Friction and it depends on the nature of the surfaces in contact. Laws of Friction: To explain friction following are soe iportant laws. 1) The direction of the friction is always opposite to the direction of otion. Friction increases with the increase of the applied force and thus called self-adjusting force. 2) If the noral reaction is kept constant, then the friction is independent to the surface area. 3) For a pair of surfaces which are in contact the ratio of the static friction and the noral reaction is constant and called as coefficient of friction. Types of Friction: There are two types of friction 1) Static Friction 2) Dynaic or Kinetic Friction Static Friction: If a force is applied on a body and the body doesn t ove, then the force of friction is called static friction. If the body is not oving then, F f Its value increases with the increase of applied force up to certain liit. The liit at which the body just began to ove is called liiting friction. Its value always greater than kinetic friction, f R Dynaic or Kinetic Friction The force of friction which is found in the oving bodies is called kinetic friction. Kinetic friction is always less then static friction and the expression for it can be written as f R
Advantages of Friction: 1) Due to friction objects can ove over each other and on the Earth. 2) Due to friction the nails and screw can bind two surfaces. 3) Due to air friction different objects fro the space burnt into the air. 4) Due to friction different parts of achines and pulleys can work properly. Disadvantages of Friction: 1) Due to friction wear and tear of different parts of achines increases. 2) Friction between parts of a achine produces heat. 3) Due to friction ore force and power are consued. 4) Due to friction it is difficult to ove objects. Methods of Reducing Friction: 1) By using grease or soe oily substance between the oving surfaces which are in contact. 2) By aking the surfaces sooth 3) By using ball bearings between the surfaces. 4) By aking the shape of fast oving objects airfoil. 5) By converting sliding friction into rolling friction.
INCLINED PLANE Inclined plane is a siple plane surface aking an angle with the horizontal. It is used to help us in rising heavy loads. Forces Acting on the Body Placed on an Inclined Plane: Consider an inclined plane akes an angle with the horizontal and a body of weight W is placed on it. The forces acting on the body will be, 1) Weight of the body W acting vertically downward, the weight W akes an angle with the noral to the inclined plane, hence W can be decoposed into two coponents i.e. W Wsin which is parallel to the surface of inclined plane, and W Wcos which is perpendicular to the surface of inclined plane. 2) Force of friction f which is opposite to W and parallel to the surface of inclined plane. 3) Noral reaction R which is perpendicular to the surface of the inclined plane. If the body is at Rest: f Wsin and R Wcos W=g Expression for the acceleration of the body oving down the inclined plane If the body on the inclined plane is oving downwards then coponent of the weight Wsin ust be greater than f. Therefore, unbalanced force can be written as, Unbalanced force F Wsin f According to Newton s second law F a so, a Wsin f a Wsin f a gsin f a gsin f This is the required expression for the acceleration of a body oving down the inclined plane.
If the force of friction between the inclined plane and the body is neglected i.e. f=0 then the above expression reduces to a gsin This equation shows that acceleration is independent of ass of the body therefore if the force of friction is neglected then all objects regardless of ass will coe down with the sae acceleration. Special Cases: 1) If the angle of the inclined plane is then a gsin 2) If the angle plane is then the body will fall freely. a gsin g a g