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Physics 1 Final exam cheat sheet

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Final Exam Chit Sheet : SHM, Waves and Fluids
ο‚·
Simple harmonic motion (mass-Spring system)
Hooke’s Law
𝐹 = −π‘˜π‘₯
Basic defns
π‘˜
2πœ‹
πœ” = √ = 2πœ‹π‘“ =
π‘š
𝑇
𝑇=
2πœ‹
π‘š
= 2πœ‹√
πœ”
π‘˜
Position as a function of time
π‘₯(𝑑) = 𝐴 π‘π‘œπ‘ πœ”π‘‘
Velocity and acceleration
π‘£π‘šπ‘Žπ‘₯ = 𝑣(π‘šπ‘–π‘‘π‘‘π‘™π‘’) = πœ”π΄
π‘Žπ‘šπ‘Žπ‘₯ = π‘Ž(𝑒𝑑𝑔𝑒𝑠) = πœ”2 𝐴
Energy
1 2
π‘˜π‘₯
2
1
𝐾. 𝐸 = π‘šπ‘£ 2
2
𝑃𝐸 =
πΈπ‘‘π‘œπ‘‘ = 𝑃. 𝐸 + 𝐾. 𝐸 =
1 2
π‘˜π΄
2
Simple Pendulum (small oscillations hence simple harmonic like spring)
𝑙
𝑇 = 2πœ‹√
𝑔
ο‚·
Waves
Transverse Wave eqn
𝑦(π‘₯, 𝑑) = 𝐴 sin(π‘˜π‘₯ − πœ”π‘‘)
Basic defns
2πœ‹
, πœ” = 2πœ‹π‘“
πœ†
πœ”
𝑣 = = π‘“πœ†
π‘˜
π‘˜=
π‘£π‘šπ‘Žπ‘₯ = πœ”π΄
Max transverse speed
Speed of waves do not change unless they change medium
ο‚·
Fluid Statics
𝐹
𝐴
π‘š
𝜌=
𝑉
𝑃 = β„ŽπœŒπ‘”
𝑃=
π‘ƒπ‘‘π‘œπ‘‘ = β„ŽπœŒπ‘” + π‘ƒπ‘Žπ‘‘π‘š
π‘˜π‘”
π‘˜π‘”
π‘˜π‘”
(πœŒπ‘€ = 1000 π‘š3 , πœŒπ‘Žπ‘–π‘Ÿ = 1.20 π‘š3 , πœŒπ»π‘” = 13560 π‘š3 , π‘ƒπ‘Žπ‘‘π‘š = 101 π‘˜π‘ƒπ‘Ž)
𝐹𝑏 = 𝑀𝑑 π‘œπ‘“ π‘‘π‘–π‘ π‘π‘™π‘Žπ‘π‘’π‘‘ π‘€π‘Žπ‘‘π‘’π‘Ÿ = πœŒπ‘€ 𝑉𝑖𝑛𝑠𝑖𝑑𝑒 𝑔
π‘Šπ‘Žπ‘π‘ = (πœŒπ‘œπ‘π‘— − πœŒπ‘€ )𝑉𝑖𝑛 𝑔
πœŒπ‘œπ‘π‘—
πœŒπ‘œπ‘π‘—
π‘‰π‘œπ‘’π‘‘ = π‘‰π‘‘π‘œπ‘‘ (1 −
) 𝑉𝑖𝑛 = π‘‰π‘‘π‘œπ‘‘
πœŒπœ”
πœŒπœ”
πœŒπ‘€
π‘Žπ‘‘π‘œπ‘€π‘›π‘€π‘Žπ‘Ÿπ‘‘ = (1 −
)𝑔
πœŒπ‘œπ‘π‘—
π‘šΜ‡ = πœŒπ‘‰Μ‡ = πœŒπ΄π‘£
Steady flow (π‘šΜ‡ 1 = π‘šΜ‡ 2 ) leads to Continuity eqn
𝑣1 𝐴1 = 𝑣2 𝐴2
Bernoulli s eqn
1
1
𝑃1 + πœŒπ‘£12 + πœŒπ‘”π‘¦1 = 𝑃2 + πœŒπ‘£22 + πœŒπ‘”π‘¦2
2
2
For horizontal pipe: Narrow pipe, more pressure
For vertical pipe: More depth, more pressure
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