0-aceleracao-g-Julia.ipynb

Kernel: Julia 1.8

ACELERAÇÃO DE QUEDA LIVRE g

Este arquivo deve ser utilizado para calcular a propagação das incertezas no cálculo da aceleração de queda livre g. Os valores medidos devem ser digitados com ponto não com vírgula.

ANTES DE INICIAR O EXPERIMENTO LEIA TODO O ROTEIRO, POIS ALGUNS PASSOS PODEM SER DECISIVOS NA COLETA DE DADOS E LER ANTES O ROTEIRO REDUZ O RETRABALHO DO EXPERIMENTO.

Consulte o guia introdutório "Elementos Python Julia Fisica experimental" em bit.ly/fisica-experimental . Para aprender mais sobre Python ou Julia use: bit.ly/tutorial-basico-python-julia-fisica

Pacotes

# para instalar os pacotes
# só funcionará no Jupyter off-line
# se já instalou não precisa executar
# execute com shift + enter

using Pkg
Pkg.add("Measurements")
Pkg.add("DataFrames")
Pkg.add("CSV")
Pkg.add("Plots")
Pkg.add("StatsBase")

   Resolving package versions...
  No Changes to `~/.julia/environment/v1.8/Project.toml`
  No Changes to `~/.julia/environment/v1.8/Manifest.toml`
   Resolving package versions...
  No Changes to `~/.julia/environment/v1.8/Project.toml`
  No Changes to `~/.julia/environment/v1.8/Manifest.toml`
   Resolving package versions...
  No Changes to `~/.julia/environment/v1.8/Project.toml`
  No Changes to `~/.julia/environment/v1.8/Manifest.toml`
   Resolving package versions...
  No Changes to `~/.julia/environment/v1.8/Project.toml`
  No Changes to `~/.julia/environment/v1.8/Manifest.toml`
   Resolving package versions...
  No Changes to `~/.julia/environment/v1.8/Project.toml`
  No Changes to `~/.julia/environment/v1.8/Manifest.toml`

# importar os pacotes
# execute com shift + enter

using Measurements, DataFrames, CSV, StatsBase, Statistics, Plots
gr()

┌ Info: Precompiling CSV [336ed68f-0bac-5ca0-87d4-7b16caf5d00b]
└ @ Base loading.jl:1664
ERROR: LoadError: UndefVarError: PosLen not defined
Stacktrace:
 [1] top-level scope
   @ ~/.julia/packages/WeakRefStrings/31nkb/src/poslenstrings.jl:6
 [2] include(mod::Module, _path::String)
   @ Base ./Base.jl:419
 [3] include(x::String)
   @ WeakRefStrings ~/.julia/packages/WeakRefStrings/31nkb/src/WeakRefStrings.jl:1
 [4] top-level scope
   @ ~/.julia/packages/WeakRefStrings/31nkb/src/WeakRefStrings.jl:547
 [5] include
   @ ./Base.jl:419 [inlined]
 [6] include_package_for_output(pkg::Base.PkgId, input::String, depot_path::Vector{String}, dl_load_path::Vector{String}, load_path::Vector{String}, concrete_deps::Vector{Pair{Base.PkgId, UInt64}}, source::String)
   @ Base ./loading.jl:1554
 [7] top-level scope
   @ stdin:1
in expression starting at /home/user/.julia/packages/WeakRefStrings/31nkb/src/poslenstrings.jl:6
in expression starting at /home/user/.julia/packages/WeakRefStrings/31nkb/src/WeakRefStrings.jl:1
in expression starting at stdin:1
ERROR: LoadError: Failed to precompile WeakRefStrings [ea10d353-3f73-51f8-a26c-33c1cb351aa5] to /home/user/.julia/compiled/v1.8/WeakRefStrings/jl_mqN5SM.
Stacktrace:
  [1] error(s::String)
    @ Base ./error.jl:35
  [2] compilecache(pkg::Base.PkgId, path::String, internal_stderr::IO, internal_stdout::IO, keep_loaded_modules::Bool)
    @ Base ./loading.jl:1707
  [3] compilecache
    @ ./loading.jl:1651 [inlined]
  [4] _require(pkg::Base.PkgId)
    @ Base ./loading.jl:1337
  [5] _require_prelocked(uuidkey::Base.PkgId)
    @ Base ./loading.jl:1200
  [6] macro expansion
    @ ./loading.jl:1180 [inlined]
  [7] macro expansion
    @ ./lock.jl:223 [inlined]
  [8] require(into::Module, mod::Symbol)
    @ Base ./loading.jl:1144
  [9] include
    @ ./Base.jl:419 [inlined]
 [10] include_package_for_output(pkg::Base.PkgId, input::String, depot_path::Vector{String}, dl_load_path::Vector{String}, load_path::Vector{String}, concrete_deps::Vector{Pair{Base.PkgId, UInt64}}, source::Nothing)
    @ Base ./loading.jl:1554
 [11] top-level scope
    @ stdin:1
in expression starting at /home/user/.julia/packages/CSV/mgO6B/src/CSV.jl:1
in expression starting at stdin:1

Failed to precompile CSV [336ed68f-0bac-5ca0-87d4-7b16caf5d00b] to /home/user/.julia/compiled/v1.8/CSV/jl_MIb8x2.

Stacktrace:
  [1] error(s::String)
    @ Base ./error.jl:35
  [2] compilecache(pkg::Base.PkgId, path::String, internal_stderr::IO, internal_stdout::IO, keep_loaded_modules::Bool)
    @ Base ./loading.jl:1707
  [3] compilecache
    @ ./loading.jl:1651 [inlined]
  [4] _require(pkg::Base.PkgId)
    @ Base ./loading.jl:1337
  [5] _require_prelocked(uuidkey::Base.PkgId)
    @ Base ./loading.jl:1200
  [6] macro expansion
    @ ./loading.jl:1180 [inlined]
  [7] macro expansion
    @ ./lock.jl:223 [inlined]
  [8] require(into::Module, mod::Symbol)
    @ Base ./loading.jl:1144
  [9] eval
    @ ./boot.jl:368 [inlined]
 [10] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String)
    @ Base ./loading.jl:1428

Análise de dados

# importação dos dados da aceleração

# dados aceleração g e tempo 
dados_aceleracao_g = DataFrame(CSV.File("dadost1t2.csv"))
dados_aceleracao_g

UndefVarError: CSV not defined

Stacktrace:
 [1] top-level scope
   @ In[7]:4
 [2] eval
   @ ./boot.jl:368 [inlined]
 [3] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String)
   @ Base ./loading.jl:1428

# calcular a quantidade de dados da aceleração
# Para processar o cálculo execute shit+enter no teclado ou toque em Run

n = length(dados_aceleracao_g.g)
n

# quantidade de classes dada pela fórmula de Sturges
# o valor deve ser arredondado para um número inteiro
K = round(Int, 1.0 + 3.3*log(10,n))

# histograma
# observe a semelhança com a curva normal

histogram(dados_aceleracao_g.g, xlabel = "g", ylabel = "freq", bins = K)

# média aritmética
g_med = mean(dados_aceleracao_g.g)

# desvio padrão
s = std(dados_aceleracao_g.g)

# desvio da média
s_med =  s / sqrt(n)

# procure na tabela t-student o valor de t (veja slide metrologia).
t = 

# incerteza Δg
Δg = t*s_med

# incerteza equipamento digital do sensor g do celular (veja o slide metrologia)

Δg_equip = 

# incerteza combinada (equipamento e cálculada)

Δgc = sqrt(Δg^2 + Δg_equip^2)

# impressão aceleração g

g_exp = measurement(g_med, Δgc)

using Roots, Measurements

T(t) = 80*exp(-measurement(-0.004527, 0.000037)*t)-50

T (generic function with 1 method)

find_zero(T,measurement(55,0))

-103.82 ± 0.85

FIM