46 lines
3.0 KiB
Markdown
46 lines
3.0 KiB
Markdown
#public
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# Work and energy
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| Formula | equation | Usage |
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| -------------------------------------- | ----------------------------------------------- | ----------------------------------- |
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| Gravitational Potential Energy ($U_g$) | $U_g=mgh$ | Changes in height |
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| Kinetic Energy | $K=\frac{1}{2}mv^2$ | Energy of motion |
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| Work-Energy Theorem | $\Delta E_{mec} = \Delta K+\Delta U=W_{other}*$ | calculating the effects of friction |
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| Variable | Symbol | SI Unit | Notes |
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| --- | --- | --- | --- |
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| Mass | m | kg | Convert from grams (g) if necessary. |
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| Height / Distance | h,d | m | Measures vertical or horizontal displacement. |
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| Velocity / Speed | v | m/s | Convert from km/h by dividing by 3.6.+3 |
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| Gravity | g | m/s2 | Earth's standard is approximately 9.8 m/s2. |
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| Energy / Work | $U_g$,K,W | J | 1 Joule = 1 kg⋅m2/s2. |
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# Center Of Mass (CM)
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| Formula | equation | Usage |
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| -------------------------------------- | ----------------------------------------------- | ----------------------------------- |
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| Position of COM X| $x_{com}=\frac{1}{M}\sum_{i=1}^{n}M_ix_i$ | find COM X|
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| Position of COM Y| $y_{com}=\frac{1}{M}\sum_{i=1}^{n}M_iy_i$ | find COM Y|
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| velocity of COM | $v_{com}=\frac{\sum m_iv_i}{M}$ | find the Velocity of COM |
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| Variable | Symbol | SI Unit | Notes |
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| --- | --- | --- | --- |
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| Position (X or Y) | $x_{com},y_{com}$ | m | Coordinates on the Cartesian plane.+ 1|
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| Total Mass | M | kg | The sum of all individual masses (m1+m2+…) |
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| Velocity of CM | vcom | m/s | The speed at which the entire system's balance point moves |
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# Linear Momentum and impulse
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| Formula | equation | Usage |
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| -------------------------------------- | ----------------------------------------------- | ----------------------------------- |
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| Linear Momentum | p = mv | find linear momentum |
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| Impulse | $J=\Delta p=F_{avg}\Delta t=\int F(t)dt$ | change in momentum. Also area under Force-time graph |
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| Conservation Law | $P_{initial}=P_{final}$ | if net external force is 0, totoal momentum is constant |
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| Elastic Collisions (1D) | $v_{1f}=(\frac{m_1-m_2}{m_1+m_2})v_i+(\frac{2m_2}{m_1+m_2})v_2i$| momentum and kinetic energy are conserved |
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| completely inelastic collisions | $m_1v_{1i}+m_2v_{2i}=(m_1+m_2)v_f$ | find situation where the objects stick together |
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| Variable | Symbol | SI Unit | Notes |
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| --- | --- | --- | --- |
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| Momentum | p | kg⋅m/s | Calculated as mass × velocity. |
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| Impulse | J | N⋅s | Also equivalent to kg⋅m/ s.|
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| Force | F | N | 1 Newton = 1 kg⋅m/s2.+2 |
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| Time | t,$\Delta$t | s | The duration of the force application.+1|
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