library("readODS")
## Warning: package 'readODS' was built under R version 4.4.2
file_path <- "C:/Studieren/Physics/phy_exp_1.ods"
dist_vector <- c(0.5,0.9,1.3,1.7)
df <- read_ods(file_path)
## New names:
## • `` -> `...1`
## • `` -> `...2`
mean_all_1 <-mean(df$`L1=0.5 m`, na.rm = TRUE)
mean_all_2 <-mean(df$`L2=0.9 m`, na.rm = TRUE)
mean_all_3 <- mean(df$`L3=1.3 m`, na.rm = TRUE)
mean_all_4 <- mean(df$`L4 = 1.7 m`, na.rm = TRUE)
time_all<-c(mean_all_1,mean_all_2,mean_all_3,mean_all_4)
head(df)
## # A tibble: 6 × 7
## ...1 ...2 intervals `L1=0.5 m` `L2=0.9 m` `L3=1.3 m` `L4 = 1.7 m`
## <chr> <chr> <lgl> <dbl> <dbl> <dbl> <dbl>
## 1 initial, alpha=… ex.1 NA 0.298 0.594 0.838 1.03
## 2 <NA> ex.2 NA 0.29 0.58 0.819 1.02
## 3 <NA> ex.3 NA 0.289 0.582 0.825 1.02
## 4 <NA> ex.4 NA 0.288 0.582 0.824 1.02
## 5 20g added ex.5 NA 0.288 0.582 0.824 1.02
## 6 <NA> ex.6 NA 0.299 0.597 0.841 1.04
plot(dist_vector, time_all, type = "b", col = "blue", pch = 19, xlab = "Path, meters", ylab = "Time, seconds", main = "s(t) function")
points(dist_vector, time_all, col = "red", pch = 19) # Add red dots over the blue line
grid()
diff_all <-c(mean_all_1,mean_all_2-mean_all_1,mean_all_3-mean_all_2,mean_all_4-mean_all_3)
length = 0.125
V_i <- length / diff_all
t_i_prime <- time_all + (diff_all / 2)
library(ggplot2)
plot(t_i_prime, V_i, type = "b", col = "blue", pch = 19, xlab = "Time", ylab = "Velocity", main = "v(t) function")
points(t_i_prime, V_i, col = "red", pch = 19)
grid()
ex_data <- data.frame(
time = c(0.298, 0.594, 0.838, 1.035,
0.290, 0.580, 0.819, 1.019,
0.289, 0.582, 0.825, 1.021,
0.288, 0.582, 0.824, 1.020,
0.288 ,0.582, 0.824, 1.020,
0.299, 0.597, 0.841, 1.038,
0.302, 0.602, 0.847, 1.045,
0.303, 0.603, 0.848, 1.046,
0.336, 0.652, 0.905, 1.107,
0.332, 0.669, 0.926, 1.127,
0.323, 0.665, 0.921, 1.121,
0.336, 0.661, 0.916, 1.116,
0.287, 0.581, 0.815, 1.010,
0.283, 0.574,0.806, 1.000,
0.285, 0.577, 0.810, 1.004,
0.286, 0.581, 0.813, 1.008,
0.293, 0.592, 0.826, 1.021,
0.291, 0.589, 0.834, 1.019,
0.299, 0.599, 0.835, 1.031,
0.295, 0.593, 0.829, 1.025,
0.328, 0.640, 0.882, 1.081,
0.334, 0.647, 0.890, 1.090,
0.326, 0.635, 0.876, 1.075,
0.335, 0.648, 0.89, 1.091),
displacement =rep(c(0.5,0.9,1.3,1.7), length.out = 96),
experiment_id = rep(1:24, each = 4)
)
head(ex_data)
## time displacement experiment_id
## 1 0.298 0.5 1
## 2 0.594 0.9 1
## 3 0.838 1.3 1
## 4 1.035 1.7 1
## 5 0.290 0.5 2
## 6 0.580 0.9 2
library(dplyr)
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
results <- ex_data %>%
group_by(experiment_id) %>%
do({
model <- lm(displacement ~ poly(time, 2), data = .)
coefficients <- coef(model)
a <- coefficients[3]
b <- coefficients[2]
c <- coefficients[1]
velocity_model <- function(t) { 2 * a * t + b }
acceleration <- 2 * a
tibble(a = a, b = b, c = c, velocity_model = velocity_model(0), acceleration = acceleration)
})
print(results)
## # A tibble: 24 × 6
## # Groups: experiment_id [24]
## experiment_id a b c velocity_model acceleration
## <int> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0.0798 0.891 1.1 0.891 0.160
## 2 2 0.0739 0.891 1.1 0.891 0.148
## 3 3 0.0787 0.891 1.1 0.891 0.157
## 4 4 0.0796 0.891 1.1 0.891 0.159
## 5 5 0.0796 0.891 1.1 0.891 0.159
## 6 6 0.0813 0.891 1.1 0.891 0.163
## 7 7 0.0817 0.891 1.1 0.891 0.163
## 8 8 0.0817 0.891 1.1 0.891 0.163
## 9 9 0.0881 0.890 1.1 0.890 0.176
## 10 10 0.102 0.889 1.1 0.889 0.204
## # ℹ 14 more rows
mean_acc<-mean(results$acceleration)
mean_vel<-mean(results$velocity_model)
cat("initial velocity: ", mean_vel)
## initial velocity: 0.8902275
cat("Acceleration: ", mean_acc)
## Acceleration: 0.1718807
i=0.202
i1=0.202+0.02
i2=0.202+0.12
mass <- rep(NA, 48)
mass[1:16] <- i
mass[17:32] <- i1
mass[33:48] <- i2
displacement <- rep(c(0.5,0.9,1.3,1.7), length.out = 48)
time <- c(0.298, 0.594, 0.838, 1.035,
0.290, 0.580, 0.819, 1.019,
0.289, 0.582, 0.825, 1.021,
0.288, 0.582, 0.824, 1.020,
0.288 ,0.582, 0.824, 1.020,
0.299, 0.597, 0.841, 1.038,
0.302, 0.602, 0.847, 1.045,
0.303, 0.603, 0.848, 1.046,
0.336, 0.652, 0.905, 1.107,
0.332, 0.669, 0.926, 1.127,
0.323, 0.665, 0.921, 1.121,
0.336, 0.661, 0.916, 1.116)
acceleration <- 2 * displacement / time^2
data <- data.frame(Mass = mass, Displacement = displacement, Time = time, Acceleration = acceleration)
plot(data$Mass, data$Acceleration,
xlab = "Mass (kg)", ylab = "Acceleration (m/s)",
main = "Acceleration vs Mass angle = 6",
type = "n")
model <- lm(Acceleration ~ Mass, data = data)
abline(model, col = "red")
i=0.202
i1=0.202+0.02
i2=0.202+0.12
mass <- rep(NA, 48)
mass[1:16] <- i
mass[17:32] <- i1
mass[33:48] <- i2
displacement <- rep(c(0.5,0.9,1.3,1.7), length.out = 48)
time <- c(0.287, 0.581, 0.815, 1.010,
0.283, 0.574,0.806, 1.000,
0.285, 0.577, 0.810, 1.004,
0.286, 0.581, 0.813, 1.008,
0.293, 0.592, 0.826, 1.021,
0.291, 0.589, 0.834, 1.019,
0.299, 0.599, 0.835, 1.031,
0.295, 0.593, 0.829, 1.025,
0.328, 0.640, 0.882, 1.081,
0.334, 0.647, 0.890, 1.090,
0.326, 0.635, 0.876, 1.075,
0.335, 0.648, 0.89, 1.091)
acceleration <- 2 * displacement / time^2
data_1 <- data.frame(Mass = mass, Displacement = displacement, Time = time, Acceleration = acceleration)
plot(data_1$Mass, data_1$Acceleration,
xlab = "Mass (kg)", ylab = "Acceleration (m/s)",
main = "Acceleration vs Mass angle = 10",
type = "n")
model_1 <- lm(Acceleration ~ Mass, data = data_1)
abline(model_1, col = "red")
a=6
a1=10
angles<- rep(NA, 24)
angles[1:12]<-a
angles[13:24] <-a1
accelerations<-results$acceleration
angles_rad <- angles * pi / 180
numerator <- sum(sin(angles_rad) * accelerations)
denominator <- sum(sin(angles_rad)^2)
g_estimated <- numerator / denominator
cat("Estimated gravity (g): ", g_estimated, "m/s^2\n")
## Estimated gravity (g): 9.899708 m/s^2