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f- (@ SCALAR PRODUCT OF TWo VECTORS * Also called dot product () work * Scalar product of force and displacement is work. (3) ENERGY Capability of an object a perform work is its energy. dt a7 2 PATE a8 B lease * Work done by a force can be oA-B = BA positive, negative or zero. ) oA +e) = AB + R-é « Work done in horizontal displacement (Distributive law) of object is zero. Mechanical energy “— —_ * Work done against gravitational force is of two forms is ij = j-k= k-i =O is negative. ei-t=27-7 = k-k=ei © Work done by spring (elastic force) dod A Ler during compression is negative, . . a. - rea = : + (Ai + Ay] + ALb)-(8) a iia sate ky api Caleta) | Kinetic | Potential = + Fsin@- Foos@ during extension is positive. Ener = AgBy + Ay By + Az Bs 2 ? 4 > dis Energy - 1 pF sing cose A. Constant force W= Fed 2 . . B, Variable force W = ‘ie F(+)-d? | * Energy o body possesses 7 by virtue of its motion. C. When force-displacement graph is given, t 2 work done = Area under the graph. «KE => mv D. Werk done in stretching a spring by | | * Tes unit is joule. distance Al is W = ze (at)* ° Work is velated to KE by theorem called energy theorem. e Kinetic energy of fast moving air is used y, to generate electricity in ha ils p? Ee teen fedaten ieee a KK We" Fea « Kinetic energy of a moving mass is B= am gives shape of graph between i move than kinetic energy of fast moving ™ KE of a body and its speed is } electron and vice versa. Ke P ¥ « If fast moving stream has been am - ~ f used to generate kinetic energy of fast an fe ae J pay moving generator in hydvo- electricity. . F, = (Fr +F,)Ax = AK when both forces ave present A shape of graph between KE Fy = Conservative forces of a bedy and its speed is F,, = Non-conservative forces parabola. Fy = Conservative forces + F,. = Non-conservative forces Kinetic energy of a body of fixed mass \__is directly propertional to square of its momentum = 24 Er + Te i " *) Work, nergy and Power a Loa energy by virtue of | Some common units of energy + Wark done by gravity depends on initial and final pouition |. pacti. of Pl Cr gee te, tabla only. Zero of potential energy is arbitrary. Io cladd "ofl conservidive Proratse Unit Symbel | In joule Pe "od sf of forces. ti d * Work done by a conservative force depends only on + Potential energy is stored up as position Kilowatt hour| kWh | 3.6 x 10° initia and final points. Zero of potential energy is energy. When constraints are removed, : sores ag this energy may appear as kinetic energy. erg ae 4o7 J "yf + Change in potential energy ef bedy is z ae equal te negative of work done by the force, || Electron volt | eV [4.6 x40 5 (i Kx Kis Spring tonstant. Spring is said aul = - lig 2. at 2 | to be stiff if K is high. A cA : Calorie col | 4.486 _ . . . . . force is conservative if it is derived X = extension of spring (at x=0, U=0) from a scalar quantity uls) ig on iene — Foe - — Ax Work, Energy and Power (i) Potential Energy (iv) Conservation of a ergy Some common units of power ees ‘tation i ™ R mgh (Ge se a potential energy Ky + Uy = Ky + U, Unit Symbol In watt (ii) Work done by a spring Kilowatt kW io* Ww Woe tke Cv) Power Theorem H lorsepower (ia) Power 4k fe ee tp 746 W p= aw dt Erg per second erg/s 1077 w 4) Conservation of Mechanical Energy Law 7) Collision (F.+ Fre)Ax = AK, ® Since F,Ax =-AU, then A(K+U) = F,,.Ax or AE = F_Ax. Total Mech E! | a of Mech E: ’ If Fre= 0, AE = © Conservative Forces Ls depends only on initial /final pos. Ls path independent * Non-conservative Forces Ly path dependent * 4 Tf conservative & non-conservative forces act: 0) 5) Vertical Circular Motion ¢ General: Linear momentum conserved (Pj = Py). ° Perfect Inelastic Collision mv, = (m, +m )V mV; Com velocity V = m+, * mm Loss in KE: AK = = : (wee) ve # Inelastic KE not conserved, but momentum is; objects don't move at 90 deg for equal mass ¥ ¢ Elastic Collision Momentum & KE conserved - Final velocities (target mz at rest) ; m, amy v= (Homey, nd v= myrms % If my=mz: v,=0, Vo=\¥y (vel. exchange) Vi. Vain at C (top): V_ = ¥gt (T-=0). Vo = figl Va = {5gL. 6) P Vi = FRE. ) Power FUVRVUVUVEVESRVSUVOSOBSDIOSCERBSURBSSSLCSSEBSSY Rate ee work or ~ ‘eanaten,' Total t V Z ¢ If equal masses 2D: move at 90 degrees. * Fract.of KE of m, lost to ma: 4mm (rmytmy)* V.=.[BoL. ~ Fract. of KE, (m-rnz)* : J P= ee = . Av. m, retains:” (m,+m)* Ke Ratio: Total W —— Av. Power = ————— > Ka: Kyi Ke= 52321. Vv. Fower my mM. _, Unit: 1 hp = 746 W. 
