Physics Formulas & Concepts: Uncertainty to Radioactivity Study Guide

Chapter #1- Uncertainty 𝑥 =𝐴+𝐵 𝑥 =𝐴−𝐵 𝑥 =𝐴×𝐵 𝑥= } } 𝑥=𝐴 𝑥 = 𝑐𝑜𝑛𝑠𝑡. 𝐴 𝛿𝑥 = 𝛿𝐴 + 𝛿𝐵 𝛿𝑥 𝛿𝐴 𝛿𝐵 = + 𝑥 𝐴 𝐵 } 𝛿𝑥 𝛿𝐴 = 𝐵. 𝑥 𝐴 ∆𝑥 = 𝑥 − 𝑥 Vectors: 𝑑= 𝑑 +𝑑 𝑐𝑜𝑠 𝜃 = 𝑑 𝑑 𝑑 = 𝑑 𝑐𝑜𝑠 𝜃 𝑠𝑖𝑛 𝜃 = d 𝑑 𝑑 𝑑 = 𝑑 𝑠𝑖𝑛 𝜃 dy θ 𝑜𝑝𝑝 𝑠𝑖𝑛 𝜃 = ℎ𝑦𝑝 dx 𝑎𝑑𝑗 𝑐𝑜𝑠 𝜃 = ℎ𝑦𝑝 𝑡𝑎𝑛 𝜃 = 𝑜𝑝𝑝 𝑎𝑑𝑗 Chapter #2- Kinematics ∆ 𝑎=∆ a=acceleration; v= velocity; t=time 𝑎= v= final velocity; u= initial velocity 𝑣 = 𝑢 + 𝑎𝑡 𝑠 = 𝑣𝑡 𝑣 = s= displacement 𝑢+𝑣 2 𝑠 = 𝑢𝑡 + 1 2 𝑎𝑡 For flight time from rest: 𝑡 = g=acceleration of free fall; h=height of fall; t=time 𝐾𝐸 = 𝐾𝐸 + 𝑔𝑎𝑖𝑛 𝑖𝑛 𝐾𝐸 𝐺𝑎𝑖𝑛 𝑖𝑛 𝐾𝐸 = 𝐾𝐸 − 𝐾𝐸 𝐾𝐸 = 1 2 𝑚𝑣 ∆𝐾𝐸 = 1 2 𝑚(𝑣 − 𝑣 ) ∆𝑃𝐸 = ∆𝐾𝐸 with no external force, friction 𝑃𝐸 = 𝑚𝑔ℎ ∆𝑃𝐸 = 𝑚𝑔(ℎ − ℎ ) Momentum: 𝑃 = 𝑚𝑣 P=momentum; m=mass-kg; v=velocity ∆𝑃 = 𝑚. ∆𝑣 ∆𝑃 ∆𝑣 = 𝑚. ∆𝑡 ∆𝑡 ∆𝑃 = 𝑚. 𝑎 ∆𝑡 𝐹 = 𝑚𝑎 ∆ 𝐹=∆ 2nd law of motion ∆𝑃 = 𝐹 × ∆𝑡 ∆P= impulse of force 𝑃 = 𝑚𝑣 𝑃 = (𝑚𝑣) 𝑃 = 𝑚 .𝑣 𝑃 = 𝑚. 𝑚. 𝑣 𝑃 = 𝑚𝑣 𝑚 𝑃 1 = 𝑚𝑣 2𝑚 2 𝑃 = 𝐾𝐸 2𝑚 𝑃 = √2𝑚𝐾𝐸 Law of conservation of momentum 𝐹 = −𝐹 ∆𝑃 ∆𝑃 =− ∆𝑡 ∆𝑡 (𝑃 − 𝑃 ) = −(𝑃 − 𝑃 ) 𝑚 𝑢 − 𝑚 𝑢 = −𝑚 𝑣 + 𝑚 𝑣 𝑀𝑜𝑚𝑒𝑛𝑡𝑢𝑚 𝑜𝑓 𝑠𝑦𝑠𝑡𝑒𝑚 𝑏𝑒𝑓𝑜𝑟𝑒 𝑐𝑜𝑙𝑙𝑖𝑠𝑖𝑜𝑛 = 𝑀𝑜𝑚𝑒𝑛𝑡𝑢𝑚 𝑜𝑓 𝑠𝑦𝑠𝑡𝑒𝑚 𝑎𝑓𝑡𝑒𝑟 𝑐𝑜𝑙𝑙𝑖𝑠𝑖𝑜𝑛 𝑚 𝑢 − 𝑚 𝑢 = (𝑚 + 𝑚 )𝑉 for if the bodies stick together after collision for a perfectly elastic collision 𝑢 +𝑢 =𝑣 +𝑣 𝐹 = 𝜌𝐴𝑣 F=force of flow of fluid; p=density; A=cross-sectional area; v=velocity 𝐹 = 𝜌𝐴𝑣 FR = flow rate (kg s-1 ); 𝑚 = 𝜌𝐴𝑣𝑡 m=mass of fluid; t= time taken for ’m’ to flow Chapter#3- Work, energy and Power W=work; f=force; d=distance in direction of force 𝑊 = 𝑓×𝑑 𝑊 = 𝑓𝑑 𝑐𝑜𝑠 𝜃 for an inclined plane P=pressure; V=volume 𝑊 = 𝑃(𝑉 − 𝑉 ) 𝑊 = 𝑓𝑑 𝑊 = 𝑃𝐴𝑑 𝑊 = 𝑃 × 𝐴𝑥 𝑊 = 𝑃 × ∆𝑉 𝑊 = 𝑃(𝑉 − 𝑉 ) Wf=work against friction 𝐺𝑃𝐸 − 𝐾𝐸 = 𝑊 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 = 𝑃= 𝑜𝑢𝑡𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑟 × 100% 𝑖𝑛𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑟 P=Power; W=work; t=time F=force; v=velocity 𝑃 = 𝐹𝑣 Chapter #4-Forces, density and pressure 𝑃= P=pressure; f=force; a= surface area 𝑃 = 𝜌𝑔ℎ for liquids Po=atmospheric pressure 𝑃 = 𝑃 + 𝜌𝑔ℎ 𝐹 = 𝜌𝑉𝑔 F=upthrust; V=volume of liquid displaced; p=density of liquid 𝑇 =𝐹×𝑙 T=moment of force; F=force; l=length from pivot 𝑇 = 𝐹 × 𝑙 𝑐𝑜𝑠 𝜃 𝑇=𝐹× F R F 𝑙 2 F θ F 𝑇 = 𝐹 × 2𝑅 l 𝜌= 𝑚 𝑣 P=density; m=mass; v=volume F Chapter#5- Deformation of solids F=force/load; k=spring constant; x=extension 𝑘= 𝐹 = 𝑘𝑥 𝑆𝑡𝑟𝑎𝑖𝑛 𝑒𝑛𝑒𝑟𝑔𝑦 = 1 2 𝐹𝑥 𝑆𝑡𝑟𝑎𝑖𝑛 𝑒𝑛𝑒𝑟𝑔𝑦 = 1 2 𝑘𝑥 𝜎= σ=stress; F=force/load; A=cross-sectional area 𝜀= ε=strain; e=extension; l=length of spring 𝐸= E=Young’s modulus 𝐸= 𝐹𝑙 𝑒𝐴 Chapter#6-Electricity I=current; Q=Charge; t=time 𝐼= 𝑄 = 𝐼𝑡 𝑁𝑜. 𝑜𝑓 𝑒 𝑠 𝑝𝑒𝑟 𝑠𝑒𝑐 = 𝑄 = 𝑛𝑒 =𝑛 Q=Amount of charge on object; n=integer; e=elementary charge N=Total no. of 𝑒 𝑠 𝑝𝑒𝑟 𝑠𝑒𝑐; no. of 𝑒 𝑠 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑣𝑜𝑙𝑢𝑚𝑒; 𝑉 = 𝑣𝑜𝑙𝑢𝑚𝑒 I=current; A=cross-sectional area of wire; q=elementary charge; n=no. of 𝑒 𝑠 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑣𝑜𝑙𝑢𝑚𝑒; V=volume 𝐼 = 𝑛𝐴𝑞𝑉 R=resistance; ρ=resistivity; l=length; A=cross sectional area 𝑅= 𝜌= 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑒𝑙𝑒𝑚𝑒𝑛𝑡𝑎𝑟𝑦 𝑐ℎ𝑎𝑟𝑔𝑒 𝑅𝐴 𝑙 W=energy consumed; V=voltage; Q=transferred charge 𝑉= 𝑊 = 𝑉𝑄 𝑉 = 𝐼𝑅 𝐼= 𝑉 𝑅 𝑅= 𝑉 𝐼 𝑉 =𝑉 +𝑉 V=voltage; I=current; R=resistance energy conservation principle; Kirchoff’s 2nd law 𝐼 𝑅 =𝐼 𝑅 +𝐼 𝑅 𝑅 =𝑅 +𝑅 for series only 𝑉 𝑅 = 𝑉 𝑅 𝐼= 𝑉 𝑅 +𝑅 𝑉 = 𝑉 ×𝑅 𝑅 +𝑅 𝑉 = 𝑉 ×𝑅 𝑅 +𝑅 𝐼 =𝐼 +𝐼 = + 𝑅 = 𝑅 𝑅 𝑅 +𝑅 Principle of Kirchoff’s charge; 1st law of conservation for parallel only 𝐼 = 𝐼 ×𝑅 𝑅 +𝑅 𝐼 = 𝐼 ×𝑅 𝑅 +𝑅 𝑃 = 𝑉𝐼 𝑃=𝐼 𝑅 𝑃= P=power; V=voltage; I=current; R=resistance 𝑉 𝑅 𝑉 = 𝐸 − 𝐼𝑅 𝑉 = 𝐸 + 𝐼𝑅 battery being used up battery being charged null method = Chapter #7- Waves and superposition 𝑣 = 𝑓λ v=speed of wave; f=frequency of wave; λ=wavelength 𝑓= T=time period for one oscillation 𝐼= I=intensity of wave; P=power; A=cross sectional area 𝐼∝𝐴 A=Amplitude 𝐼 𝐼 = 𝐴 𝐴 Doppler effect: 𝑓 =𝑓 𝑣 𝑣+𝑣 𝑓𝑜𝑟 𝑤ℎ𝑒𝑛 𝑠𝑜𝑢𝑟𝑐𝑒 𝑖𝑠 𝑚𝑜𝑣𝑖𝑛𝑔 𝑎𝑤𝑎𝑦 𝑓𝑟𝑜𝑚 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑟 𝑓 =𝑓 𝑣 𝑣−𝑣 𝑓𝑜𝑟 𝑤ℎ𝑒𝑛 𝑠𝑜𝑢𝑟𝑐𝑒 𝑖𝑠 𝑚𝑜𝑣𝑖𝑛𝑔 𝑡𝑜𝑤𝑎𝑟𝑑𝑠 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑟 𝑓 = 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑓 = 𝑠𝑜𝑢𝑟𝑐𝑒 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 v=speed of sound 𝑣 = 𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑠𝑜𝑢𝑟𝑐𝑒 𝑝𝑎𝑡ℎ 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 𝑛λ for constructive interference 𝑝𝑎𝑡ℎ 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = (𝑛 + 1 2)λ for destructive interference a=slit separation; λ=wavelength; x=fringe separation; D=distance between slits and screen 𝜆= d=distance between consecutive slits; θ=angle of nth order from central maxima; n=order of maxima 𝑑 sin 𝜃 = 𝑛λ d=distance between consecutive slits; N=Number of slits per metre 𝑑= 𝜆 = 2(𝑙 − 𝑙 ) 𝑙 =length of tube for second harmonic 𝑙 =length of tube for first harmonic 𝑣 = 2𝑓(𝑙 − 𝑙 ) v=speed of wave; f=frequency Chapter #8-Radioactivity 𝑋→ 𝑌 + 𝐻𝑒 alpha decay 𝑋→ 𝑌+ beta decay 𝑒 gamma decay 𝑋 → 𝑋+𝛾 𝑛→ 𝑝+ 𝑒+ῡ 𝛽 − 𝑑𝑒𝑐𝑎𝑦 𝑝→ 𝑛+ 𝑒+𝑣 𝛽 + 𝑑𝑒𝑐𝑎𝑦

Physics Formulas & Concepts: Uncertainty to Radioactivity Study Guide

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