Tiêu đề SP-1_Ch-5_Laws of Motion.pdf ✅

Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 Chapter Contents Chapter 5 FORCE Force is a action of one body upon another. The force may either produce deformation (change in the size or shape of bodies) or acceleration, in the motion of body. It is a vector quantity with unit newton (N). Types of Forces (i) Weight : Weight of a body is the force with which earth attracts it. It is also defined as force of gravity. (ii) Contact forces : Whenever two bodies come in contact they exert forces on each other, that are called contact forces. Contact force has two component. (a) Normal reaction (N or R) : It is the component of contact force normal to the surface. It measures how strongly the surfaces in contact are pressed together. (b) Frictional force (f) : It is the component of contact force parallel to the surface. It opposes the relative motion (or attempted motion) of the two surfaces in contact. (iii) Tension : The force exerted by the end of a taut string, rope or chain is called the tension. The direction of tension is always pulling in nature. (iv) Spring force : Every spring resists any attempt to change its length, the more you change its length the harder it resists. The force exerted by a spring is given by F kx   , -where x is the change in length and k is spring constant or stiffness constant (units N/m). LINEAR MOMENTUM ( ) P It is the measure of total quantity of motion contained in body. The momentum of a body is given by product of mass and velocity of body. P mv  It is a vector quantity. The direction of P is in the direction of v. Force Linear Momentum Newton’s Laws of Motion Law of conservation of Linear Momentum Rocket Propulsion Frame of Reference Equilibrium of a Particle Application of Newton’s Laws of Motion Friction Circular Motion Banking of Roads Laws of Motion
112 Laws of Motion NEET Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456 NEWTON’S LAWS OF MOTION Newton’s First Law It states that a body continues to be in its state of rest or of uniform motion until and unless it is acted upon by some external force to change the state If Fv a  0, Constant, 0     (i) This law defines force. (ii) The body opposes any external change in its state of rest or of uniform motion Mass is the measure of inertia. Heavier the body, larger is its inertia. Inertia is of three types (1) Inertia of rest (2) Inertia of motion (3) Inertia of direction Newton’s Second Law The rate of change of linear momentum of a body, is directly proportional to the applied external force on the body. dP F dt  from experiments K = 1 dP F dt  F = Resultant external force. Direction of force is in the direction of change of momentum.   ( ) dP d F mv dt dt   dm dv Fv m dt dt Case 1: If constant, 0 dv v dt   dm F v dt   Case 2: If m = constant, 0 dm dt  F ma  F  Resultant external force in the direction of acceleration ˆˆˆ ˆ ˆ ˆ F i F j F k ma i ma j ma k xy z x y z    External force acting on a body may accelerate in following ways. (i) If force is parallel or antiparallel to motion: It change magnitude of v, and the path followed by body is a straight line. (ii) If force is acting  to the motion of body, it change the direction of v, not the magnitude of velocity, and path followed by body is circle (UCM). (iii) If the force at an angle to motion of body, it change both magnitude and direction of velocity. And path followed by body may be elliptical, parabolic, hyperbolic or non uniform circular motion.
NEET Laws of Motion 113 Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456 Newton’s Third Law To every action force there is an equal and opposite reaction force. F F 12 21   Action and reaction force acts on different bodies. Any one of the force can be assumed as action and other as reaction. Impulse ( )I Impulse is defined as the product of force and the time for which that force acts (i) If force is constant I Ft   (ii) If force is variable I F dt   (iii) Impulse is measured by change in momentum produced in the body I P mv mu    (iv) Area under (F – t) graph gives the magnitude of impulse. Example 1 : A force ˆ ˆ 2 F ti t j N   (2 3 ) -acts on an object moving in xy plane. Find magnitude of change in momentum of the object in time interval t = 0 to t = 2 s. Solution : Given, ˆ ˆ 2   2 3 F ti t j ˆ ˆ 2 2 3 dp ti t j dt    ˆ ˆ 2    2 3 dp tdti t dtj 2 2 2 0 0    2 3 ˆ ˆ   dp tdti t dtj 2 2 2 3 0 0      ˆ ˆ   p t it j    4 8 ˆ ˆ pi j    p 16 64  80  9 kg m/s Example 2 : A ball of mass m strikes a rigid wall with speed v and gets reflected without any loss of speed, as shown in the figure. 30° 30° v v (a) What is the magnitude of the impulse imparted to the ball by the wall? (b) What is the direction of the force on the wall due to the ball?
114 Laws of Motion NEET Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456 Solution : Considering x-axis and y-axis as shown, (a) ˆ ˆ p mv i mv j i    sin30 cos30 ˆ ˆ p mv i mv j f     sin30 cos30    p p p f i ˆ ˆ    2 sin30 mv i mvi | |   p mv (b) Negative sign of the impulse shows that it is along negative x-direction. Since impulse and force are in the same direction, the force on the ball is along the negative direction of x-axis. Hence the force on the wall will be along positive x-axis. LAW OF CONSERVATION OF LINEAR MOMENTUM If net external force on a system is zero, then linear momentum of system remains constant or linear momentum of an isolated system remains constant ext  dP F dt If ext   0, 0 dP F dt or P = constant or P P i f  Law of conservation of linear momentum is applicable in the direction in which external force is zero i.e. If 0, 0 x x dP F dt   then Constant Px  If 0, 0 y y dP F dt   then Constant Py  If 0, 0 z z dP F dt   then Constant Pz  Area under (F – t) graph represent impulse or change in momentum Area (1) = I P or  -= Positive Area (2) = I P or  -= Negative F t 1 2 Since av P F t    Therefore, for a certain momentum change as time interval increases, then the average force exerted on body decreases.