Tiêu đề 5.Laws of Motion-f.pdf ✅

1 | P a g e NEET-2022 Ultimate Crash Course PHYSICS Laws of Motion
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3 | P a g e Important Points to Remember EQUILIBRIUM OF CONCURRENT FORCES We know that a body is at rest or in a state of uniform motion in a straight line when the resultant force acting on it is zero. If a number of forces, 1 2 3 , , ,..... F F F F n are acting at a point, these are said to be concurrent and their resultant F is given by 1 2 3 = + + + + ..... F F F F F n ---------------(1) In case F = 0, the point at which these forces are acting is said to be in equilibrium. Let us now consider three concurrent forces 1 2 F F, and F3 acting at the point O along OA OB , and OC respectively, see in the figure. The resultant of F1 and F2 is given by OD , where OD F F = +1 2 . In case, OD OC = , F F F 1 2 3 + = − or 1 2 3 F F F + + = 0 -----------(2) Obviously, 1 2 F F, and F3 are three such concurrent forces which are in equilibrium. These is another important result called Lami’s theorem which is of interest in case of three concurrent forces in equilibrium. According to this theorem, 1 2 3 sin sin sin = = F F F    ----------------(3) ➢ p mv = , where p is the linear momentum of a particle of mass m moving with a velocity v. ➢ (a) F ma = , where F is the resultant force acting on a body of mass m moving with acceleration a. (b)     = = +         dp dv dm F m v dt dt dt (in case both m and v are changing) (c)   =     dv F m dt (in case m is constant and v is changing) (d)   =     dm F v dt (in case v is constant and m is changing) Eqns. (a), (b), (c) and (d), all represent Newton’s second law of motion. ➢ Ft = impulse of a force F acting for a time t. ➢ Ft mv mv = − 0 = change in momentum. This result is called Impulse-momentum theorem. ➢ F F AB BA = − where FAB = force acting on body A due to body B (action) and FBA = force acting on body B due to body A (reaction). This is the mathematical representation of Newton’s third law of motion.
4 | P a g e ➢ m v m v m v m v 1 01 1 02 1 1 2 2 + = + where 1 2 m m, = masses of two bodies 01 02 v v, = initial velocities of the bodies and 1 2 v v, = final velocities of the bodies. This is in accordance with the Law of conservation of linear momentum. ➢ = − mv V M where V is the velocity of recoil of a gun (of mass M) which fires a bullet of mass m with velocity v . ➢ (a) 0 0 = + ln m v v u m and (b) = dm F u dt , are the equations of motion of a rocket, where u = velocity of exhaust gases, 0 v v, = initial velocity and velocity of the rocket at any instant t. 0 m m, = initial mass and mass of the rocket at instant t, F = thrust exerted on the rocket. ➢ (a) ( ) ( ) 2 1 1 2 − = + m m a g m m and (b) ( ) 1 2 1 2 2 = + m m T g m m where a is the acceleration produced in case of connected motion of two masses m1 and m2 (m m 1 2  ) at the ends of a massless string passing over a massless and frictionless pulley. T is the tension in the string. ➢ F ma 0 0 = , where F0 is called the force of inertia, fictitious force of pseudo-force acting on a body of mass m placed in an acceleration frame (non-inertial frame). 0 a is the acceleration of the non-inertia frame relative to the inertial one. F0 acts in a direction opposite to 0 a . In vector form, F ma 0 0 = − ➢ The forces of interaction between portions of a system of bodies being considered are called internal forces. The forces exerted on bodies of a given system by bodies not included in the system are called external forces. A system of bodies on which no external forces act is called a dosed (isolated) system