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Pure Physics Mechanics Summary Notes Summary of Physics (Formula and definition) Definition Formula/Example Speed of a body is defined as the distance moved per Spd= Distance Moved / Time Taken unit time. Ave. Spd= Total Dist. Moved Total Time Taken V = s / t S.I unit m/s. Other units km/hr, km/s Displacement is the distance travelled in a stated E.g. displacement = 0 even when it travels much distance direction. and eventually ending at the start point. Velocity of a body is the distance travelled per unit time Vel=Dist. travelled in stated direction / Time Taken in a stated direction. Vel= Displacement Time Taken Average Vel = Total Displacement Total Time Taken Ave. vel = S / t S.I unit m/s. Other unit km/hr, km/s 1/2 (v + u) = S / t Acceleration is the rate of change of velocity. Acc = Change in Velocity / Time taken Acc = (final Velocity – initial Velocity) / Time taken 2 2 a = (v-u) / t S.I. unit m/s . Other unit km/hr u – initial velocity and v- final velocity Using the equations and for constant acceleration, 1 s (v u ) ------------ Equ 1.1 2 t (v u ) a ------------ Equ 1.2 t From equ 1.2; t = (v – u) /a subst into equ 1.1 1 s (v u ) 2 (v u ) a (v u)(v u) 2as v 2 u 2 2as therefore; v 2 u 2 2as From equ 1.2; v = u + at subst into equ 1.1 1 s (u at u ) 2 t 1 1 ut at 2 s therefore; s ut at 2 2 2 Mechanics – Summary Notes Page 1 of 6 a v s g t t t Object hits the floor Free Falling Object Acceleration due to Gravity Free Fall Without Air Resistance. Object under free fall is subjected to a constant acceleration provided that the effect of air resistance is negligible. In such a case, we can use the following equations: 2 1) a = g, where g = 10 m/s (2) v = u + gt v 2 s (3) s = ut + ½ gt a t Free Fall With Air Resistance. One key consideration is that ; Air resistance velocity Hence the acceleration will gradually decrease from g to 0m/s over time as the velocity & air resistance 2 The velocity will start from 0 m/s and climb to a steady and constant velocity, this velocity is termed as the terminal velocity Displacement graph will start from 0 and be gradual, until it hits terminal velocity, when the gradient will be constant. s v a t When a = 0, i.e. gravitational force = air resistance Effects of forces on motion Newton’s first law of motion states that a body continues in its state of rest or uniform motion in a straight line unless compelled by a force to do otherwise. The reluctance of the object to change its state of motion is known as inertia. All objects with mass have inertia. Newton’s second law of motion states that the net force acting on an object is equal to the product of the mass and the acceleration of the object; the direction of the force is in the same direction as the object’s acceleration. 2 F = ma where F is force in N, m is mass in kg ; a is acceleration in m/s Mechanics – Summary Notes Page 2 of 6 Newton’s third law of motion states that for every action there is an equal and opposite reaction. illustrations of action-reaction are as follows: Summation of forces differs from include both the scalar component and its direction. They can be expressed in the form of vectors as shown, where R is the net resultant force. F2 R F1 F2 F1 R F2 F1 R The turning effect of a force is termed as moment. Moment is the product of force and the perpendicular distance from the the line-of-action of the force to the pivot (Line-of-action of a force is the line along which the force acts.) Moment = Force x Perpendicular Distance SI unit is Nm =Fxd Centre of Gravity of an object is the point on the body where the entire weight seems to act. Centre of Mass is the point where if the object changed such that all of the mass of the object were concentrated at that point, the motion of the object were unchanged. The stability of a body is its ability to return to its original position when displaced. The stability of a body is increased by lowering its CG or increasing its base area. G When CG lowers, d or When base area is increased, d CG the ability that CG goes beyond FG is d more difficult. F Stable Equilibrium: object returns to its original position when displaced slightly Unstable Equilibrium: object does not return to its original position when displaced slightly Neutral Equilibrium: a displacement will neither raise or lower the CG Work is done when a force produces a motion of an object through a distance in the direction of the force applied. Work done = Force x Distance Moved SI unit is Joule =Fxd 1 J = 1 Nm Energy is defined as the capacity to do work. Units of energy is same as work done, i.e. in Joules. Law of conservation of energy states that energy cannot be created or destroyed, but only changes from one form to another. Energy Form Definition/Example Mechanics – Summary Notes Page 3 of 6 Kinetic Energy Energy possessed by a body due to its motion 2 ½ mv KE can be translational (moving car), rotational or vibrational F x s = ma x s = mas = m [ ½ 2 2 v –u ] Potential Energy Energy possessed because of its position relative to centre of Gravitational the earth mgh PE is measured relative to a reference PE = 0 at ground F x s = mg x h level, thus h is the difference in physical height Elastic Potential Energy Energy possessed by a body because of its compressed or stretched state E.g. compressed spring Power is the rate of doing work. SI unit of power is Watt (W). 1 W is defined as the power required to obtain 1 J of work done per second. 1 W = 1 J /s Power/P (W) = Work Done (J) = Energy (J) Time taken (s) Time taken (s) Efficiency is the ratio of energy output to energy input. It is expressed in percentage form. Efficiency /E = useful output energy x 100% input energy Energy wasted = 1 – E % Pressure is the force acting per unit area. Pressure = Force Area SI unit = Pascal -2 Other : Nm , mmHg, Patm -2 SI unit for Pressure is Pascal. 1 Pa = 1 Nm Atmospheric Pressure is the pressure exerted by the weight of the atmosphere. At sea level, the atmospheric 5 pressure is 10 Pa. 5 The unit for pressure used for meterological purpose is called the bar. 1 bar = 10 Pa. Pressure dips as the altitude increases. Liquid Pressure A liquid exerts a pressure because of its weight. Pressure = hg Given as density of liquid, Mechanics – Summary Notes Page 4 of 6 Gas Pressure Gas pressure is measured with manometer. Liquid in the manometer can be water or mercury. Calculation of gas pressure is as demonstrated: Pressure of Gas at B > Pressure of Gas at A Pb = Pa + Pressure difference due to AB Pa Pb = Pa + hg Pb Formula can be used to find pressure at any point in the liquid A st 1 Example: Finding Pb Liquid is mercury. h Pa = atmospheric pressure = 760mm Hg B x h = 20mm C Pb = Pa + Pressure difference due to AB = 760mm + 20mm = 780mm Hg nd 2 Example: Finding Pc Pc = Pb + xg, where h = x Pc = Pa + (h+x)g Kinetic Theory of Matter states that all matter is made up of large number of atoms/molecules in continuous motion. An increase in temperature increases the motion of the vibrations of the atoms/molecules. Brownian motion is the random movement of the gases and liquids. Diffusion is the differential movement of molecules from a region of higher concentration to a region of lower concentration. Pressure-Volume Relationship of Gas Boyle’s Law states that pressure of a gas is inversely proportional to its volume, provided the mass and temperature of the gas is kept constant. PV = k P P 11 V V Decrease Volume Increase P & Decrease Volume Increase P Explaining using the Kinetic Theory of Molecules: (1) P = Force/Area (2) Volume reduces ½ No. of molecules per unit volume increases by 2x (3) No. of collusions on the wall increases by 2x Force exerted on the wall increases by 2x Pressure increases by 2x PV = constant P P 11 V V Mechanics – Summary Notes Page 5 of 6 When Initial Vol, V1(Ax) is halved, Rate of collusion on wall increases by twice Force on wall increases by half due to change in momentum over time Mechanics – Summary Notes Page 6 of 6