Identifying Independent, Dependent, and Controlled Variables

A team of biomechanical engineers conducted an experiment to evaluate the impact attenuation of 3D-printed lattice structures used in protective athletic gear. In four separate trials, the engineers varied the strut angle of the elastomer lattice ($30^\circ$, $45^\circ$, $60^\circ$, and $75^\circ$) while holding the lattice density ($0.25\text{ g/cm}^3$), polymer resin formulation, and drop impact height ($2.0\text{ m}$) constant. In each trial, a drop tower released a mass onto the lattice sample, and the peak acceleration (measured in $g$) transmitted to an underlying sensor was recorded.

Match each experimental component from the investigation to its corresponding variable classification.

A team of marine biologists conducted an investigation to determine how varying concentrations of dissolved iron ($\text{Fe}^{2+}$) in seawater affect the growth rate of the phytoplankton species *Emiliania huxleyi*. Four 10 L culture vessels were filled with filtered seawater and kept at a constant temperature of $18^\circ\text{C}$ under identical 12-hour light/14-hour dark photoperiods. Each vessel received a different concentration of $\text{Fe}^{2+}$ ($0.1\ \mu\text{M}$, $0.5\ \mu\text{M}$, $1.0\ \mu\text{M}$, and $2.0\ \mu\text{M}$). After 14 days, the final cell density ($\text{cells/mL}$) of *Emiliania huxleyi* in each vessel was recorded.

Which of the following represents the independent variable in this experiment?

Atmospheric scientists conducted an experiment to evaluate how varying the ambient relative humidity ($\text{RH}$, measured as a percentage) influences the crystallization time (in seconds) of acoustically levitated ammonium sulfate ($(\text{NH}_4)_2\text{SO}_4$) microdroplets. Throughout all trials, the ambient temperature was held constant at $20.0^\circ\text{C}$ and the initial droplet radius was held constant at $5.0\,\mu\text{m}$.

Match each experimental component from the investigation to its corresponding variable classification.

A materials scientist investigated how the average pore diameter of polyurethane acoustic foam panels affects their sound absorption performance. Four foam panels of identical thickness ($50\text{ mm}$) were tested in a sound chamber at a constant ambient temperature ($22^\circ\text{C}$) and fixed incident sound frequency ($1,000\text{ Hz}$). The experimental conditions and measured outcomes are summarized in the table below:

Which of the following correctly identifies the independent variable and the dependent variable in this investigation?

A biochemist investigated how varying the pH of a reaction mixture affects the rate of hydrogen peroxide ($\text{H}_2\text{O}_2$) decomposition by the enzyme catalase. In each trial, the catalase concentration, total reaction volume, and incubation temperature ($25^\circ\text{C}$) were held constant, while the volume of oxygen gas ($\text{O}_2$) produced per minute was measured across solutions ranging from $\text{pH } 4.0$ to $\text{pH } 10.0$.

Match each experimental component from the study to its correct variable classification.

A team of environmental engineers conducted an experiment to evaluate how varying concentrations of copper sulfate ($\text{CuSO}_4$) in water affect the photosynthetic rate of *Chlorella vulgaris* algae. Four identical $500\text{ mL}$ glass bioreactors were prepared with equal initial algal cell densities. Each bioreactor received a different concentration of $\text{CuSO}_4$ ($0.0\text{ mg/L}$, $0.5\text{ mg/L}$, $1.0\text{ mg/L}$, and $1.5\text{ mg/L}$). All bioreactors were maintained at a constant temperature of $22^\circ\text{C}$ and exposed to continuous artificial light of $150\text{ }\mu\text{mol}\cdot\text{m}^{-2}\cdot\text{s}^{-1}$ for 72 hours. At the end of the trial, the total dissolved oxygen produced ($\text{mg/L}$) was measured to quantify the photosynthetic rate of the algae.

Which of the following identifies the dependent variable in this experiment?

A researcher conducted an investigation to determine how varying the strength of an external magnetic field influences the thermal conductivity of a magnetite-based ferrofluid. In each trial, a ferrofluid sample of fixed volume ($50\text{ mL}$) and fixed magnetite concentration ($5.0\%\text{ v/v}$) was placed inside a thermal cell maintained at $25^\circ\text{C}$. The applied magnetic field strength was varied from $0\text{ mT}$ to $200\text{ mT}$ in increments of $50\text{ mT}$, and the resulting thermal conductivity of the ferrofluid was measured.

Match each experimental component on the left with its correct variable classification on the right.

A group of atmospheric scientists investigated the effect of methane ($\text{CH}_4$) concentration on the rate of photochemical haze formation in a simulated planetary atmosphere. Five identical glass chambers were filled with a gas mixture consisting of nitrogen ($\text{N}_2$), carbon dioxide ($\text{CO}_2$), and varying amounts of methane ($\text{CH}_4$). All chambers were maintained at a constant temperature of $298\text{ K}$ and exposed to an ultraviolet ($\text{UV}$) light intensity of $50\text{ W/m}^2$ for $12\text{ hours}$. The optical density of the resulting haze in each chamber was measured at the end of the trial.

Based on the experimental design described, which of the following parameters served as a controlled variable?

A team of volcanologists conducted an investigation to measure how varying the silica ($\text{SiO}_2$) mass percentage in synthetic basaltic lava affects its flow viscosity. Each lava sample was melted in a specialized induction furnace maintained at a constant temperature of $1,200^\circ\text{C}$ under standard atmospheric pressure ($1\text{ atm}$). Match each experimental factor on the left with its corresponding variable role on the right.

A marine biologist conducted an experiment to investigate how varying water salinity affects the bioluminescence of the dinoflagellate *Pyrocystis fusiformis*. Four identical $500\text{ mL}$ cultures were maintained at $22^\circ\text{C}$ with a cell density of $1,000\text{ cells/mL}$. Each culture was exposed to a different salinity level ($20\text{ PSU}$, $25\text{ PSU}$, $30\text{ PSU}$, and $35\text{ PSU}$) and subjected to identical mechanical agitation to induce bioluminescence, after which the peak light intensity was measured.

Match each experimental component listed on the left to its corresponding variable classification on the right.

A materials science research group conducted an experiment to analyze the photo-degradation of polylactic acid (PLA) films. Four identical $0.5\text{ mm}$ thick PLA samples were placed into separate sealed test chambers, each maintained at a constant temperature of $25^\circ\text{C}$ and relative humidity of $50\%$. Each sample was exposed to a different UV-C radiation intensity ($2.0$, $4.0$, $6.0$, and $8.0\text{ W/m}^2$) for 48 hours, after which the percentage reduction in sample mass was measured.

Which of the following correctly identifies the independent variable and the dependent variable in this experiment?

A soil scientist investigated the effect of varying soil copper ($\text{Cu}^{2+}$) concentrations on the rate of nitrate uptake in spinach roots. Five groups of ten plants each were grown in identical hydroponic solutions containing $\text{Cu}^{2+}$ concentrations of $0\text{ }\mu\text{M}$, $5\text{ }\mu\text{M}$, $10\text{ }\mu\text{M}$, $25\text{ }\mu\text{M}$, and $50\text{ }\mu\text{M}$, respectively. Throughout the 14-day experiment, all plant groups were maintained at $22^\circ\text{C}$ under a constant 16-hour light / 8-hour dark cycle. At the conclusion of the experiment, the researcher recorded the total nitrate concentration ($\mu\text{mol/g}$) remaining in the nutrient solutions.

In this investigation, which factor serves as the independent variable?

A group of mechanical engineers conducted an experiment to evaluate how the frequency of ambient mechanical vibration affects the peak electrical voltage output of a piezoelectric cantilever beam. In each trial, a cantilever beam of identical length ($10\text{ cm}$), thickness ($1\text{ mm}$), and material composition (lead zirconate titanate) was mounted on a shaker table maintained at a constant displacement amplitude of $0.5\text{ mm}$ and a room temperature of $22^\circ\text{C}$. The vibration frequency was varied across $\text{50 Hz}$, $\text{100 Hz}$, $\text{150 Hz}$, and $\text{200 Hz}$, and the peak output voltage generated across a $100\text{ }\Omega$ load resistor was recorded.

Match each experimental component listed on the left with its corresponding variable classification on the right.

A team of atmospheric scientists investigated how varying the relative humidity inside a sealed reaction chamber affects the rate of ozone ($\text{O}_3$) depletion by aerosolized sea salt particles. In five separate trials, the relative humidity was set to 20%, 35%, 50%, 65%, and 80%, while the initial ozone concentration, temperature, and mass of sea salt particles were held constant. Based on the description of the experiment, which parameter was the dependent variable?

A team of materials engineers conducted an experiment to evaluate how different zirconium dioxide ($\text{ZrO}_2$) additive concentrations in ceramic heat-shield tiles affect peak thermal conductivity under simulated re-entry conditions. In each trial, ceramic tiles of identical dimensions were exposed to a $1200^\circ\text{C}$ plasma jet at a constant chamber atmospheric pressure of $1.0\text{ atm}$ for exactly 300 seconds. Match each experimental component to its correct variable classification.

A biochemist conducted an experiment to investigate how substrate availability influences cellular respiration rates in yeast. Five identical incubation flasks were prepared, each containing $50\text{ mL}$ of yeast suspension in a buffer solution maintained at a constant temperature of $30^\circ\text{C}$ and a $\text{pH}$ of $6.5$. Different masses of glucose—$0.5\text{ g}$, $1.0\text{ g}$, $1.5\text{ g}$, $2.0\text{ g}$, and $2.5\text{ g}$—were added to Flasks 1 through 5, respectively. The volume of carbon dioxide ($\text{CO}_2$) gas generated by each flask was measured after $10\text{ minutes}$.

Which of the following operational parameters represents the independent variable in this experiment?

A marine biologist conducted an experiment to investigate how varying water salinity affects the oxygen consumption rate of shore crabs (*Carcinus maenas*). Five identical tanks were prepared with water salinities of $10\text{ ppt}$, $15\text{ ppt}$, $20\text{ ppt}$, $25\text{ ppt}$, and $30\text{ ppt}$. All tanks were held at a constant water temperature of $18^\circ\text{C}$, and crabs of equal body mass were used in each trial.

Match each experimental component on the left with its corresponding variable classification on the right.

A team of acoustic engineers conducted an experiment to evaluate how the sound dampening efficiency of polyurethane foam panels is impacted by the concentration of embedded micro-perforated ceramic beads. Five panels of identical dimensions ($50\text{ cm} \times 50\text{ cm} \times 5\text{ cm}$) were manufactured with varying concentrations of ceramic beads ($0\%$, $5\%$, $10\%$, $15\%$, and $20\%$ by mass). Each panel was placed between a sound generator emitting a constant $1\text{-kHz}$ sine wave tone at $90\text{ dB}$ and a decibel sensor positioned $1.0\text{ m}$ away in an anechoic chamber held at $20^\circ\text{C}$. The decibel sensor measured the acoustic absorption coefficient ($\alpha$) of each panel. In this experiment, which factor served as the independent variable?

An environmental engineer conducted an experiment to evaluate wastewater purification efficiency. She prepared three identical filtration columns containing different concentrations of activated charcoal ($5\text{ g/L}$, $10\text{ g/L}$, and $15\text{ g/L}$). For all trials, she maintained a fluid temperature of $22^\circ\text{C}$, a flow rate of $10\text{ mL/min}$, and an initial methylene blue dye concentration of $50\text{ mg/L}$. She recorded the time required to achieve $99\%$ decolorization of the solution in each column.

Match each experimental component on the left with its correct variable classification on the right.