SPH3U2 Formula Sheet

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SPH3U2 Formula Sheet Δ𝑑𝑑⃗ = π‘£π‘£βƒ—π‘Žπ‘Žπ‘Žπ‘Žπ‘Žπ‘Ž Δ𝑑𝑑 𝑣𝑣⃗1 + 𝑣𝑣⃗2 Δ𝑑𝑑⃗ = οΏ½ οΏ½ Δ𝑑𝑑 2

𝐸𝐸𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 = 𝐸𝐸𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 β€²

1 Δ𝑑𝑑⃗ = 𝑣𝑣⃗1 Δ𝑑𝑑 + π‘Žπ‘Žβƒ—Ξ”π‘‘π‘‘ 2 2 1 Δ𝑑𝑑⃗ = 𝑣𝑣⃗2 Δ𝑑𝑑 βˆ’ π‘Žπ‘Žβƒ—Ξ”π‘‘π‘‘ 2 2 𝑣𝑣⃗22 = 𝑣𝑣⃗12 + 2π‘Žπ‘Žβƒ—Ξ”π‘‘π‘‘βƒ— 𝑣𝑣⃗2 = 𝑣𝑣⃗1 + π‘Žπ‘Žβƒ—Ξ”π‘‘π‘‘ Ξ”π‘₯π‘₯ =

𝐸𝐸𝑔𝑔 = π‘šπ‘šπ‘šπ‘šΞ”β„Ž 𝑃𝑃 =

π‘Šπ‘Š 𝑑𝑑

1 πΈπΈπ‘˜π‘˜ = π‘šπ‘šπ‘£π‘£ 2 2

Efficiency = οΏ½

𝐹𝐹𝐹𝐹 𝐹𝐹𝑁𝑁 where FN is the normal force πœ‡πœ‡ =

πΊπΊπ‘šπ‘š1 π‘šπ‘š2 (Δ𝑑𝑑)2

π‘Šπ‘Š = 𝐹𝐹𝐴𝐴 Δ𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑

1 1 π‘šπ‘šπ‘šπ‘šΞ”β„Ž1 + π‘šπ‘šπ‘£π‘£12 = π‘šπ‘šπ‘šπ‘šΞ”β„Ž2 + π‘šπ‘šπ‘£π‘£22 2 2

𝑣𝑣𝑖𝑖2 𝑠𝑠𝑠𝑠𝑠𝑠2πœƒπœƒ 𝑔𝑔

𝐹𝐹𝑛𝑛𝑛𝑛𝑛𝑛 = π‘šπ‘šπ‘Žπ‘Žβƒ—

𝐹𝐹𝑔𝑔 =

π‘Šπ‘Š = 𝐹𝐹𝐴𝐴 Δ𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑

βˆ’11

𝐺𝐺 = 6.673 Γ— 10 𝐹𝐹𝑔𝑔 = π‘šπ‘šπ‘”π‘”βƒ—

π‘Žπ‘Ž = 100(𝑑𝑑2 βˆ’ 𝑑𝑑1 ) in rapid analysis

π‘π‘π‘šπ‘š2 π‘˜π‘˜π‘”π‘”2

Useful energy out οΏ½ Γ— 100% Energy in

𝑄𝑄 = π‘šπ‘šπ‘šπ‘šΞ”π‘‘π‘‘ where c is the specific heat capacity in J/kgΒ°C

𝑄𝑄𝑙𝑙𝑙𝑙 = π‘šπ‘š Γ— 𝑙𝑙𝑣𝑣 where lv is the latent heat of vaporization constant 𝑄𝑄𝑙𝑙𝑙𝑙 = π‘šπ‘š Γ— 𝑙𝑙𝑓𝑓 where lf is the latent heat of fusion constant 1 𝐸𝐸𝑒𝑒 = π‘˜π‘˜π‘₯π‘₯ 2 2 where k is the spring constant and x is the extension/compression 𝐹𝐹 = π‘˜π‘˜π‘˜π‘˜

𝑝𝑝⃗ = π‘šπ‘šπ‘£π‘£βƒ— Δ𝑝𝑝⃗ = 𝐹𝐹⃗ Δ𝑑𝑑

𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑙𝑙𝑖𝑖 = 𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑓𝑓

π‘šπ‘š1 𝑣𝑣1 + π‘šπ‘š2 𝑣𝑣2 = π‘šπ‘š1 𝑣𝑣1β€² + π‘šπ‘š2 𝑣𝑣2 β€² π‘šπ‘š1 𝑣𝑣1 + π‘šπ‘š2 𝑣𝑣2 = (π‘šπ‘š1 + π‘šπ‘š2 )𝑣𝑣 β€² πΈπΈπ‘˜π‘˜ > πΈπΈπ‘˜π‘˜ β€² in inelastic collisions

1 1 1 = + 𝑓𝑓 π‘‘π‘‘π‘œπ‘œ 𝑑𝑑𝑖𝑖 𝑀𝑀 = 𝑛𝑛 =

1 𝑇𝑇 𝑐𝑐 = 𝑓𝑓𝑓𝑓 𝑓𝑓 =

β„Žπ‘–π‘– 𝑑𝑑𝑖𝑖 =βˆ’ β„Žπ‘œπ‘œ π‘‘π‘‘π‘œπ‘œ

𝑣𝑣𝑠𝑠 𝑓𝑓2 = 𝑓𝑓1 οΏ½ οΏ½ 𝑣𝑣𝑠𝑠 Β± π‘£π‘£π‘œπ‘œ where + is receding and – is approaching

𝑐𝑐

π‘£π‘£π‘šπ‘šπ‘šπ‘šπ‘šπ‘šπ‘šπ‘šπ‘šπ‘šπ‘šπ‘š

𝑛𝑛1 π‘ π‘ π‘ π‘ π‘ π‘ πœƒπœƒ1 = 𝑛𝑛2 π‘ π‘ π‘ π‘ π‘ π‘ πœƒπœƒ2

index of refraction =

𝑐𝑐 𝑣𝑣

𝑛𝑛2 𝑖𝑖𝑐𝑐𝑐𝑐𝑐𝑐 = arcsin οΏ½ οΏ½ 𝑛𝑛1 where n2 is the refractive index of the optically less dense medium

𝑣𝑣𝑠𝑠 𝑓𝑓2 = 𝑓𝑓1 οΏ½ οΏ½ 𝑣𝑣𝑠𝑠 Β± π‘£π‘£π‘œπ‘œ where + is receding and – is approaching 𝑣𝑣 = 332 + 0.6𝑇𝑇 𝐼𝐼 =

𝑃𝑃 4πœ‹πœ‹π‘Ÿπ‘Ÿ 2

𝐼𝐼1 π‘Ÿπ‘Ÿ22 = 𝐼𝐼2 π‘Ÿπ‘Ÿ12

𝐼𝐼2 𝛽𝛽 = 10 log οΏ½ οΏ½ 𝐼𝐼1 πœ†πœ†1 𝑣𝑣1 = πœ†πœ†2 𝑣𝑣2

2𝑛𝑛 βˆ’ 1 πœ†πœ† 4 in closed air columns 𝐿𝐿 =

𝑛𝑛 πœ†πœ† 2 in open air columns 𝐿𝐿 =

𝑓𝑓1 𝐿𝐿2 = 𝑓𝑓2 𝐿𝐿1

𝑓𝑓1 �𝑇𝑇1 = 𝑓𝑓2 �𝑇𝑇2 𝑓𝑓1 𝑑𝑑2 = 𝑓𝑓2 𝑑𝑑1

𝑓𝑓1 �ρ2 = 𝑓𝑓2 �ρ1 where rho is the density

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