SPH3U2 Formula Sheet Δ𝑑𝑑⃗ = 𝑣𝑣⃗𝑎𝑎𝑎𝑎𝑎𝑎 Δ𝑡𝑡 𝑣𝑣⃗1 + 𝑣𝑣⃗2 Δ𝑑𝑑⃗ = � � Δ𝑡𝑡 2

𝐸𝐸𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = 𝐸𝐸𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 ′

1 Δ𝑑𝑑⃗ = 𝑣𝑣⃗1 Δ𝑡𝑡 + 𝑎𝑎⃗Δ𝑡𝑡 2 2 1 Δ𝑑𝑑⃗ = 𝑣𝑣⃗2 Δ𝑡𝑡 − 𝑎𝑎⃗Δ𝑡𝑡 2 2 𝑣𝑣⃗22 = 𝑣𝑣⃗12 + 2𝑎𝑎⃗Δ𝑑𝑑⃗ 𝑣𝑣⃗2 = 𝑣𝑣⃗1 + 𝑎𝑎⃗Δ𝑡𝑡 Δ𝑥𝑥 =

𝐸𝐸𝑔𝑔 = 𝑚𝑚𝑚𝑚Δℎ 𝑃𝑃 =

𝑊𝑊 𝑡𝑡

1 𝐸𝐸𝑘𝑘 = 𝑚𝑚𝑣𝑣 2 2

Efficiency = �

𝐹𝐹𝐹𝐹 𝐹𝐹𝑁𝑁 where FN is the normal force 𝜇𝜇 =

𝐺𝐺𝑚𝑚1 𝑚𝑚2 (Δ𝑑𝑑)2

𝑊𝑊 = 𝐹𝐹𝐴𝐴 Δ𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑

1 1 𝑚𝑚𝑚𝑚Δℎ1 + 𝑚𝑚𝑣𝑣12 = 𝑚𝑚𝑚𝑚Δℎ2 + 𝑚𝑚𝑣𝑣22 2 2

𝑣𝑣𝑖𝑖2 𝑠𝑠𝑠𝑠𝑠𝑠2𝜃𝜃 𝑔𝑔

𝐹𝐹𝑛𝑛𝑛𝑛𝑛𝑛 = 𝑚𝑚𝑎𝑎⃗

𝐹𝐹𝑔𝑔 =

𝑊𝑊 = 𝐹𝐹𝐴𝐴 Δ𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑

−11

𝐺𝐺 = 6.673 × 10 𝐹𝐹𝑔𝑔 = 𝑚𝑚𝑔𝑔⃗

𝑎𝑎 = 100(𝑑𝑑2 − 𝑑𝑑1 ) in rapid analysis

𝑁𝑁𝑚𝑚2 𝑘𝑘𝑔𝑔2

Useful energy out � × 100% Energy in

𝑄𝑄 = 𝑚𝑚𝑚𝑚Δ𝑡𝑡 where c is the specific heat capacity in J/kg°C

𝑄𝑄𝑙𝑙𝑙𝑙 = 𝑚𝑚 × 𝑙𝑙𝑣𝑣 where lv is the latent heat of vaporization constant 𝑄𝑄𝑙𝑙𝑙𝑙 = 𝑚𝑚 × 𝑙𝑙𝑓𝑓 where lf is the latent heat of fusion constant 1 𝐸𝐸𝑒𝑒 = 𝑘𝑘𝑥𝑥 2 2 where k is the spring constant and x is the extension/compression 𝐹𝐹 = 𝑘𝑘𝑘𝑘

𝑝𝑝⃗ = 𝑚𝑚𝑣𝑣⃗ Δ𝑝𝑝⃗ = 𝐹𝐹⃗ Δ𝑡𝑡

𝑝𝑝𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑖𝑖 = 𝑝𝑝𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑓𝑓

𝑚𝑚1 𝑣𝑣1 + 𝑚𝑚2 𝑣𝑣2 = 𝑚𝑚1 𝑣𝑣1′ + 𝑚𝑚2 𝑣𝑣2 ′ 𝑚𝑚1 𝑣𝑣1 + 𝑚𝑚2 𝑣𝑣2 = (𝑚𝑚1 + 𝑚𝑚2 )𝑣𝑣 ′ 𝐸𝐸𝑘𝑘 > 𝐸𝐸𝑘𝑘 ′ in inelastic collisions

1 1 1 = + 𝑓𝑓 𝑑𝑑𝑜𝑜 𝑑𝑑𝑖𝑖 𝑀𝑀 = 𝑛𝑛 =

1 𝑇𝑇 𝑐𝑐 = 𝑓𝑓𝑓𝑓 𝑓𝑓 =

ℎ𝑖𝑖 𝑑𝑑𝑖𝑖 =− ℎ𝑜𝑜 𝑑𝑑𝑜𝑜

𝑣𝑣𝑠𝑠 𝑓𝑓2 = 𝑓𝑓1 � � 𝑣𝑣𝑠𝑠 ± 𝑣𝑣𝑜𝑜 where + is receding and – is approaching

𝑐𝑐

𝑣𝑣𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚

𝑛𝑛1 𝑠𝑠𝑠𝑠𝑠𝑠𝜃𝜃1 = 𝑛𝑛2 𝑠𝑠𝑠𝑠𝑠𝑠𝜃𝜃2

index of refraction =

𝑐𝑐 𝑣𝑣

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

𝑣𝑣𝑠𝑠 𝑓𝑓2 = 𝑓𝑓1 � � 𝑣𝑣𝑠𝑠 ± 𝑣𝑣𝑜𝑜 where + is receding and – is approaching 𝑣𝑣 = 332 + 0.6𝑇𝑇 𝐼𝐼 =

𝑃𝑃 4𝜋𝜋𝑟𝑟 2

𝐼𝐼1 𝑟𝑟22 = 𝐼𝐼2 𝑟𝑟12

𝐼𝐼2 𝛽𝛽 = 10 log � � 𝐼𝐼1 𝜆𝜆1 𝑣𝑣1 = 𝜆𝜆2 𝑣𝑣2

2𝑛𝑛 − 1 𝜆𝜆 4 in closed air columns 𝐿𝐿 =

𝑛𝑛 𝜆𝜆 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