f8c7e274-b26b-44a1-8a3b-df32fe29893c 349 Alvaro Diaz Falconi 4 5 false false 0 0 decimal
&[PAGENUM] / &[COUNT]

Evaluating a Formula like in a Texbook

 <content> <p>EvalSF with mathcad blocks</p> </content>

Use all digitis in equation constants

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Use significant figures only

Sintaxis

Assign to y the result of the euqation in the block ME using the values in the block MV with n significant figures, in the string of the unit U, and returns some intermediate steps of the algebra involved, suitable for show in a Table.

Examples

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Example

Simple case

 m_a force F m force ''k EvalSF F m force m_a ''k EvalSF F m force
S:F≈m*a≈{1.73*'kg}*{3.54*'m/{'s^2}}≈{6.12}*{'N}
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F m_a force 'N 3 EvalSF 1 el
6.12 N *

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Example

 vals eq_exp

Some values and an equation

 in 33.516993782 in 33.53

Using only 4 sigificant figures

 Ev y θ k y.t t A eq_exp a F m force ''k EvalSF y θ k y.t t A eq_exp vals a F m force m_a ''k EvalSF y θ k y.t t A eq_exp a F m force
S:y.t≈{A*cos(θ)}/{e^{k*t}}≈{{4.1*'ft}*cos({30*'°})}/{e^{{2.4*'Hz}*{0.1*'s}}}≈{{{1.25*'m}*cos({0.5236})}/{e^{{2.4*1/'s}*{0.1*'s}}}}*{{39.37}*{'in}/{'m}}≈{33.53}*{'in}
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Ev 1 el

Algebra steps

k and θ are "exact"

Adding some measure errors

 in 35.28 31.78 2 1 sys

Result with error propagation

 Δt ΔA Ev θ k y.t t A eq_exp a F m force ''k EvalSF Δt ΔA y θ k y.t t A eq_exp vals a F m force m_a ''k EvalSF Δt ΔA θ k y.t t A eq_exp a F m force
S:Δy.t≈{abs(cos(θ)/{e^{k*t}})}*ΔA+{abs(-{A*cos(θ)*k}/{e^{k*t}})}*Δt≈{abs(cos({30*'°})/{e^{{2.4*'Hz}*{0.1*'s}}})}*{0.00254*'m}+{abs(-{{4.1*'ft}*cos({30*'°})*{2.4*'Hz}}/{e^{{2.4*'Hz}*{0.1*'s}}})}*{0.01*'s}≈{{abs(cos({0.5236})/{e^{{2.4*1/'s}*{0.1*'s}}})}*{0.00254*'m}+{abs(-{{1.25*'m}*cos({0.5236})*{2.4*1/'s}}/{e^{{2.4*1/'s}*{0.1*'s}}})}*{0.01*'s}}*{{39.37}*{'in}/{'m}}≈{0.8727}*{'in}
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Ev 2 el

Spliting into y±Δy

 in 3.5 in 33.53

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Example

 vals eq psf min / 40.318 P.a E q' B q L eq Δy Δt ΔA Ev y θ k y.t t A eq_exp a F m force ''k EvalSF P.a q' B q L eq Δy Δt ΔA y θ k y.t t A eq_exp vals a F m force m_a ''k EvalSF P.a q' B q L eq Δy Δt ΔA y θ k y.t t A eq_exp a F m force
S:q≈P.a/{L*B}≈{500*'kgf/'min}/{{3.3333*'m}*{2.5*'ft}}≈{{81.722*{'kg*'m}/{'s^3}}/{{3.3333*'m}*{0.762*'m}}}*{{1.2531}*{'psf/'min}/{'kg/{'m*'s^3}}}≈{40.318}*{'psf/'min}
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q' vals eq 'psf/'min 5 EvalSF 1 el

Notice that q' have five significant figures in the given unit, buton not at other

 Pa s / 32.173938026

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Example

Unitless, use use 'k for mask constants with decimals.

 vals eq 529.834245597 c P.a E q' B q L eq Δy Δt ΔA Ev y θ k y.t t A eq_exp F m force ''k EvalSF c P.a q' B q L eq Δy Δt ΔA y θ k y.t t A eq_exp vals F m force m_a ''k EvalSF c P.a q' B q L eq Δy Δt ΔA y θ k y.t t A eq_exp F m force
S:t≈{5*(a*c+b*cos(c))}/{5*c^2+2502}≈{5*({1.944*10^5}*{1.309}+{44640}*cos({1.309}))}/{5*{1.309}^2+2502}≈529.8
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t vals eq 1 4 EvalSF 1 el
529.8

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Example

Using ± for defining uncertainities.

 vals eq kgf 2.149 1.237 2 1 sys m.2 m.1 g c P.a E q' B q L eq Δy Δt ΔA Ev y θ k y.t t A eq_exp F m force ''k EvalSF m.2 m.1 T g c P.a q' B q L eq Δy Δt ΔA y θ k y.t t A eq_exp vals F m force m_a ''k EvalSF m.2 m.1 g c P.a q' B q L eq Δy Δt ΔA y θ k y.t t A eq_exp F m force
S:T≈{2*m.1*m.2*g}/{m.1+m.2}≈{2*{3.333*'kg}*{2.5*'lb}*{1*'g.e}}/{{3.333*'kg}+{2.5*'lb}}≈{{2*{3.333*'kg}*{1.134*'kg}*{9.807*'m/{'s^2}}}/{{3.333*'kg}+{1.134*'kg}}}*{{0.102}*{'kgf}/{{'m*'kg}/{'s^2}}}≈{1.693}*{'kgf}
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Ev 1 el
m.2 m.1 g c P.a E q' B q L eq Δy Δt ΔA Ev y θ k y.t t A eq_exp F m force ''k EvalSF m.2 m.1 T g c P.a q' B q L eq Δy Δt ΔA y θ k y.t t A eq_exp vals F m force m_a ''k EvalSF m.2 m.1 g c P.a q' B q L eq Δy Δt ΔA y θ k y.t t A eq_exp F m force
S:ΔT≈{abs({2*m.2^2*g}/{(m.1+m.2)^2})}*Δm.1+{abs({2*m.1^2*g}/{(m.1+m.2)^2})}*Δm.2≈{abs({2*{2.5*'lb}^2*{1*'g.e}}/{({3.333*'kg}+{2.5*'lb})^2})}*{0.2*'kg}+{abs({2*{3.333*'kg}^2*{1*'g.e}}/{({3.333*'kg}+{2.5*'lb})^2})}*{0.4*'lb}≈{{abs({2*{1.134*'kg}^2*{9.807*'m/{'s^2}}}/{({3.333*'kg}+{1.134*'kg})^2})}*{0.2*'kg}+{abs({2*{3.333*'kg}^2*{9.807*'m/{'s^2}}}/{({3.333*'kg}+{1.134*'kg})^2})}*{0.1814*'kg}}*{{0.102}*{'kgf}/{{'m*'kg}/{'s^2}}}≈{0.2278}*{'kgf}
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Ev 2 el

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Example

Using a unit as undefined variable

 vals eq 0.531042751 γ * m * β κ α m.2 m.1 g c P.a E q' B q L eq Δy Δt ΔA Ev y θ k y.t t A eq_exp F m force ''k EvalSF β κ α m.2 m.1 T g c P.a q' B q L eq Δy Δt ΔA y θ k y.t t A eq_exp vals F m force m_a ''k EvalSF β κ α m.2 m.1 g c P.a q' B q L eq Δy Δt ΔA y θ k y.t t A eq_exp F m force
S:κ≈{'γ*(α^2+β^2)^{1/2}}/4≈{'γ*({1.386*'m}^2+{1.609*'m}^2)^{1/2}}/4≈0.5309*'γ*'m
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κ vals eq 1 4 EvalSF 1 el
0.5309 γ * m *

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Further examples

 V.2 V.3 V.1 V'.2 V'.3 V'.1 force

Equation

 F.1 V'.1 V'.3 V'.2 V.1 V.3 V.2 β κ α m.2 m.1 T g c P.a E q' B q L eq Δy Δt ΔA Ev y θ k y.t t A eq_exp vals a F m force m_a ''k EvalSF F.1 V'.1 V'.3 V'.2 V.1 V.3 V.2 β κ α m.2 m.1 T g c P.a q' B q L eq Δy Δt ΔA y θ k y.t t A eq_exp vals a F m force m_a ''k EvalSF F.1 V'.1 V'.3 V'.2 V.1 V.3 V.2 β κ α m.2 m.1 g c P.a q' B q L eq Δy Δt ΔA y θ k y.t t A eq_exp vals F force m_a
S:F≈m*a≈{1.732}*{3.536}≈6.124
S:ΔF≈0≈0≈0
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F.1 V.1 force 1 4 EvalSF transpose
6.124 F.2 F.1 V'.1 V'.3 V'.2 V.1 V.3 V.2 β κ α m.2 m.1 T g c P.a E q' B q L eq Δy Δt ΔA Ev y θ k y.t t A eq_exp vals a F m force m_a ''k EvalSF F.2 F.1 V'.1 V'.3 V'.2 V.1 V.3 V.2 β κ α m.2 m.1 T g c P.a q' B q L eq Δy Δt ΔA y θ k y.t t A eq_exp vals a F m force m_a ''k EvalSF F.2 F.1 V'.1 V'.3 V'.2 V.1 V.3 V.2 β κ α m.2 m.1 g c P.a q' B q L eq Δy Δt ΔA y θ k y.t t A eq_exp vals F force m_a
S:F≈m*a≈{1.732*'kg}*{3.536*'m/{'s^2}}≈{6.124}*{'N}
S:ΔF≈0≈0≈0
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F.2 V.2 force 'N 4 EvalSF transpose
N 6.124 F.3 F.2 F.1 V'.1 V'.3 V'.2 V.1 V.3 V.2 β κ α m.2 m.1 T g c P.a E q' B q L eq Δy Δt ΔA Ev y θ k y.t t A eq_exp vals a F m force m_a ''k EvalSF F.3 F.2 F.1 V'.1 V'.3 V'.2 V.1 V.3 V.2 β κ α m.2 m.1 T g c P.a q' B q L eq Δy Δt ΔA y θ k y.t t A eq_exp vals a F m force m_a ''k EvalSF F.3 F.2 F.1 V'.1 V'.3 V'.2 V.1 V.3 V.2 β κ α m.2 m.1 g c P.a q' B q L eq Δy Δt ΔA y θ k y.t t A eq_exp vals F force m_a
S:F≈m*a≈{3.818*'lb}*{3.536*'m/{'s^2}}≈{{1.732*'kg}*{3.536*'m/{'s^2}}}*{{1}*{'N}/{{'m*'kg}/{'s^2}}}≈{6.124}*{'N}
S:ΔF≈0≈0≈0≈0
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F.3 V.3 force 'N 4 EvalSF transpose
N 6.124 F'.1 F.3 F.2 F.1 V'.1 V'.3 V'.2 V.1 V.3 V.2 β κ α m.2 m.1 T g c P.a E q' B q L eq Δy Δt ΔA Ev y θ k y.t t A eq_exp vals a F m force m_a ''k EvalSF F'.1 F.3 F.2 F.1 V'.1 V'.3 V'.2 V.1 V.3 V.2 β κ α m.2 m.1 T g c P.a q' B q L eq Δy Δt ΔA y θ k y.t t A eq_exp vals a F m force m_a ''k EvalSF F.3 F.2 F.1 V'.1 V'.3 V'.2 V.1 V.3 V.2 β κ α m.2 m.1 g c P.a q' B q L eq Δy Δt ΔA y θ k y.t t A eq_exp vals F force m_a
S:F≈m*a≈{1.732}*{3.536}≈6.124
S:ΔF≈{abs(a)}*Δm+{abs(m)}*Δa≈{abs({3.536})}*{0.2}+{abs({1.732})}*{0.04}≈0.7765
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F'.1 V'.1 force 1 4 EvalSF transpose
7.677 4.571 2 1 sys F'.2 F'.1 F.3 F.2 F.1 V'.1 V'.3 V'.2 V.1 V.3 V.2 β κ α m.2 m.1 T g c P.a E q' B q L eq Δy Δt ΔA Ev y θ k y.t t A eq_exp vals a F m force m_a ''k EvalSF F'.2 F'.1 F.3 F.2 F.1 V'.1 V'.3 V'.2 V.1 V.3 V.2 β κ α m.2 m.1 T g c P.a q' B q L eq Δy Δt ΔA y θ k y.t t A eq_exp vals a F m force m_a ''k EvalSF F.3 F.2 F.1 V'.1 V'.3 V'.2 V.1 V.3 V.2 β κ α m.2 m.1 g c P.a q' B q L eq Δy Δt ΔA y θ k y.t t A eq_exp vals F force m_a
S:F≈m*a≈{1.732*'kg}*{3.536*'m/{'s^2}}≈{6.124}*{'N}
S:ΔF≈{abs(a)}*Δm+{abs(m)}*Δa≈{abs({3.536*'m/{'s^2}})}*{0.2*'kg}+{abs({1.732*'kg})}*{0.04*'m/{'s^2}}≈{0.7765}*{'N}
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F'.2 V'.2 force 'N 4 EvalSF transpose
N 7.677 4.571 2 1 sys F'.3 F'.2 F'.1 F.3 F.2 F.1 V'.1 V'.3 V'.2 V.1 V.3 V.2 β κ α m.2 m.1 T g c P.a E q' B q L eq Δy Δt ΔA Ev y θ k y.t t A eq_exp vals a F m force m_a ''k EvalSF F'.3 F'.2 F'.1 F.3 F.2 F.1 V'.1 V'.3 V'.2 V.1 V.3 V.2 β κ α m.2 m.1 T g c P.a q' B q L eq Δy Δt ΔA y θ k y.t t A eq_exp vals a F m force m_a ''k EvalSF F.3 F.2 F.1 V'.1 V'.3 V'.2 V.1 V.3 V.2 β κ α m.2 m.1 g c P.a q' B q L eq Δy Δt ΔA y θ k y.t t A eq_exp vals F force m_a
S:F≈m*a≈{3.818*'lb}*{3.536*'m/{'s^2}}≈{{1.732*'kg}*{3.536*'m/{'s^2}}}*{{1}*{'N}/{{'m*'kg}/{'s^2}}}≈{6.124}*{'N}
S:ΔF≈{abs(a)}*Δm+{abs(m)}*Δa≈{abs({3.536*'m/{'s^2}})}*{0.4409*'lb}+{abs({3.818*'lb})}*{0.04*'m/{'s^2}}≈{{abs({3.536*'m/{'s^2}})}*{0.2*'kg}+{abs({1.732*'kg})}*{0.04*'m/{'s^2}}}*{{1}*{'N}/{{'m*'kg}/{'s^2}}}≈{0.7765}*{'N}
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F'.3 V'.3 force 'N 4 EvalSF transpose
N 7.677 4.571 2 1 sys 1.1.8763.0