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Review work and force and energy

step inference rule input feed output step validity (as per SymPy)
1
  • 0000111981: declare initial expression
  • number of inputs: 0; feeds: 0; outputs: 1
  • Eq.~\ref{eq:#1} is an initial equation.
  1. 1590774089
    \(dW = F dx\)
 no validation is available for declarations
2
  • 0000111408: integrate
  • number of inputs: 1; feeds: 0; outputs: 1
  • Integrate Eq.~ref{eq:#1}; yields Eq.~ref{eq:#2}.
  1. 1590774089
    \(dW = F dx\)
  1. 5542528160
    \(\int dW = F \int_0^x dx\)
 recognized infrule but not yet supported
3
  • 0000111662: evaluate definite integral
  • number of inputs: 1; feeds: 0; outputs: 1
  • Evaluate definite integral Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.
  1. 5542528160
    \(\int dW = F \int_0^x dx\)
  1. 3512166162
    \(W = F x\)
 valid
4
  • 0000111556: substitute LHS of expr 1 into expr 2
  • number of inputs: 2; feeds: 0; outputs: 1
  • Substitute LHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.
  1. 5345738321
    \(F = m a\)
  2. 3512166162
    \(W = F x\)
  1. 8953094349
    \(W = m a x\)
 valid
5
  • 0000111236: change three variables in expression
  • number of inputs: 1; feeds: 6; outputs: 1
  • Change of variable $#1$ to $#2$ and $#3$ to $#4$ and $#5$ to $#6$ in Eq.~\ref{eq:#7}; yields Eq.~\ref{eq:#8}.
  1. 5611024898
    \(d = \frac{1}{2 a} (v^2 - v_0^2)\)
  1. 3183197515
    \(v_1\)
  2. 5398681502
    \(v\)
  3. 6701855578
    \(v_2\)
  4. 3652511721
    \(v\)
  5. 8111389082
    \(x\)
  6. 9623791270
    \(d\)
  1. 3253234559
    \(x = \frac{v_2^2 - v_1^2}{2 a}\)
 LHS diff is pdg0001943 - pdg0004037 RHS diff is (pdg0001357**2 + pdg0002473**2 - pdg0004770**2 - pdg0005153**2)/(2*pdg0009140)
6
  • 0000111556: substitute LHS of expr 1 into expr 2
  • number of inputs: 2; feeds: 0; outputs: 1
  • Substitute LHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.
  1. 8953094349
    \(W = m a x\)
  2. 3253234559
    \(x = \frac{v_2^2 - v_1^2}{2 a}\)
  1. 9413699705
    \(W = m a \frac{v_2^2 - v_1^2}{2 a}\)
 LHS diff is pdg0004037 - pdg0006789 RHS diff is (-pdg0002473**2 + pdg0004770**2 + pdg0005156*pdg0009140*(pdg0002473**2 - pdg0004770**2))/(2*pdg0009140)
7
  • 0000111457: simplify
  • number of inputs: 1; feeds: 0; outputs: 1
  • Simplify Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.
  1. 9413699705
    \(W = m a \frac{v_2^2 - v_1^2}{2 a}\)
  1. 4811121942
    \(W = \frac{1}{2} m v_2^2 - \frac{1}{2} m v_1^2\)
 valid
8
  • 0000111732: substitute LHS of two expressions into expression
  • number of inputs: 3; feeds: 0; outputs: 1
  • Substitute LHS of Eq.~\ref{eq:#1} and LHS of Eq.~\ref{eq:#2} into Eq.~\ref{eq:#3}; yields Eq.~\ref{eq:#4}.
  1. 4811121942
    \(W = \frac{1}{2} m v_2^2 - \frac{1}{2} m v_1^2\)
  2. 4928007622
    \(KE_1 = \frac{1}{2} m v_1^2\)
  3. 7676652285
    \(KE_2 = \frac{1}{2} m v_2^2\)
  1. 3360172339
    \(W = KE_2 - KE_1\)
 recognized infrule but not yet supported
9
  • 0000111341: declare final expression
  • number of inputs: 1; feeds: 0; outputs: 0
  • Eq.~\ref{eq:#1} is one of the final equations.
  1. 3360172339
    \(W = KE_2 - KE_1\)
no validation is available for declarations

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