Sometimes scientists need to scale down experiments because collecting full-scale data may not be practical or possible. Most of the time, the data collected during a small scale-experiment is an accurate indicator of full-scale results. For example, research of craters on the Earth’s surface has indicated that the Earth has experienced a history of massive meteor collisions. It has been hypothesized that, amongst other things, these impacting meteorites caused the Earth’s oceans to vaporize. The detrimental effects associated with meteor collisions would have made the planet to be uninhabitable to humans. Due to these adverse effects, an experiment that could produce meteor-sized craters would not be possible in a full-scale setting.

Researchers have developed small-scale experiments that are exemplary of Newton’s three laws of motion. Newton’s first law states that an object in motion will stay in motion unless it is acted on by another force. This phenomenon is known as inertia. The second law comes in the form of an equation that calculates how much force is exerted on two colliding objects with respect to mass and acceleration. In other words force is equal to the mass of an object multiplied by its acceleration. The third law states that for every action there is an equal and opposite reaction. In other words, forces always occur in pairs. A counter force that is equal in magnitude and opposite in direction compliments each force in a particular direction. For example, if you push downwards on a table then the table, in theory, pushes upwards with the same force.

In a particular small-scale exercise, students were asked to design an experiment in which two “meteorites” would be dropped into a medium of sand and the subsequent crater diameters would be measured. Afterwards, the sand would be leveled and the experiment would be repeated. The students were asked to identify all of the factors that could affect the formation of the craters. This was done in order to ensure that each experiment was testing one independent and one dependent variable at a time. Otherwise, it would be unclear which variable is causing the observed effect. Possible variables that could alter the outcome of the experiment included but were not limited to the following: height of the fall, speed of the “meteorite,” angle of impact, and the mass of meteorite.

Consider an experiment that seeks to identify the mass of the meteorite analog. All other variables would have to remain constant in order to ensure accurate results.  In order to do this, the height of the fall was set to one meter. The object was placed on top of a vertical meter stick. In order to keep the acceleration and height of the drop constant, it was rolled off of the stick instead of being pushed or simply dropped. Last, a protractor was used to keep the meter stick at a ninety-degree angle. In the procedure, a marble and a golf ball were used as “meteorites” of different masses.

The results of the experiment were recorded in the table and figure provided.

What part of the experimental procedure would most likely cause the results of the experiment to be less accurate?

Sometimes scientists need to scale down experiments because collecting full-scale data may not be practical or possible. Most of the time, the data collected during a small scale-experiment is an accurate indicator of full-scale results. For example, research of craters on the Earth’s surface has indicated that the Earth has experienced a history of massive meteor collisions. It has been hypothesized that, amongst other things, these impacting meteorites caused the Earth’s oceans to vaporize. The detrimental effects associated with meteor collisions would have made the planet to be uninhabitable to humans. Due to these adverse effects, an experiment that could produce meteor-sized craters would not be possible in a full-scale setting.

Researchers have developed small-scale experiments that are exemplary of Newton’s three laws of motion. Newton’s first law states that an object in motion will stay in motion unless it is acted on by another force. This phenomenon is known as inertia. The second law comes in the form of an equation that calculates how much force is exerted on two colliding objects with respect to mass and acceleration. In other words force is equal to the mass of an object multiplied by its acceleration. The third law states that for every action there is an equal and opposite reaction. In other words, forces always occur in pairs. A counter force that is equal in magnitude and opposite in direction compliments each force in a particular direction. For example, if you push downwards on a table then the table, in theory, pushes upwards with the same force.

In a particular small-scale exercise, students were asked to design an experiment in which two “meteorites” would be dropped into a medium of sand and the subsequent crater diameters would be measured. Afterwards, the sand would be leveled and the experiment would be repeated. The students were asked to identify all of the factors that could affect the formation of the craters. This was done in order to ensure that each experiment was testing one independent and one dependent variable at a time. Otherwise, it would be unclear which variable is causing the observed effect. Possible variables that could alter the outcome of the experiment included but were not limited to the following: height of the fall, speed of the “meteorite,” angle of impact, and the mass of meteorite.

Consider an experiment that seeks to identify the mass of the meteorite analog. All other variables would have to remain constant in order to ensure accurate results.  In order to do this, the height of the fall was set to one meter. The object was placed on top of a vertical meter stick. In order to keep the acceleration and height of the drop constant, it was rolled off of the stick instead of being pushed or simply dropped. Last, a protractor was used to keep the meter stick at a ninety-degree angle. In the procedure, a marble and a golf ball were used as “meteorites” of different masses.

The results of the experiment were recorded in the table and figure provided.

Which factor, other than mass and velocity, would cause the greatest change to the results of the experiment?

Students are given an assignment to create a circuit from a given set of components. Four different students create circuits in unique manners and the professor measures the resistance of the circuit, the power output of the circuit and the heat given off by each circuit after each circuit was running for a certain amount of time. Circuits with resistors in parallel have a lower total resistance than those that have resistors in series.

What other important information should be noted by the professor? 

Scientist 1: Scientist 1 believes that light displays particle behavior. This means that rays of light have their own associated momentum. Furthermore, Scientist 1 does not believe that light will exhibit wave behavior.

Scientist 2: Scientist 2 disagrees with Scientist 1 and believes that light can exhibit wave behavior, but does not display particle behavior. In other words, this scientist believes that light does not have any momentum.

Experiment: To settle their disagreement, the scientists setup the following experiment. The scientist take dark metallic material. This material is attached to pole and the metallic material can spin if it is subjected to a force; similar to a watermill or wind turbine. This setup is then placed outside and exposed to sunlight. 

What is a potential issue with this experiment?

A scientist observed that when low energy types of electromagnetic radiation (light), such as visible light or ultraviolet light, were shone onto a conductive copper wire incorporated into a circuit with a light bulb as shown in Figure 1, the light bulb did not come on. However, when electromagnetic radiation of a higher energy, such as x-rays or gamma rays, was shone onto the wire, the light bulb did come on, indicating a current (electricity) was produced in the wire. The scientist hypothesized that this effect was due to the fact that electromagnetic radiation of a certain energy was able to overcome the attraction between electrons and protons in the individual atoms of copper in the wire, and liberate an electron to produce the electric current. He called this the photoelectric effect, and did the following experiments to further study this effect.

Figure 1

Experiment 1:

The scientist put a sample of copper in an instrument that can measure the energies of free-moving electrons. He shone a light source capable of producing specific energies of electromagnetic radiation on the metal and slowly increased the energy of the light. The instrument was used to measure the kinetic energies (energy due to motion) of any electrons that were liberated from the copper sample. The scientist recorded the energy of light used in frequency, where a low frequency corresponds to a low energy electromagnetic radiation, and a high frequency corresponds to a high frequency of electromagnetic radiation. He saw that no electrons could be detected at low frequencies, and that after a specific frequency he called the threshold frequency, the kinetic energy of liberated electrons increased linearly with increasing frequency of incident light as shown in Figure 2 below. The data was fitted with a line along which the data falls; the equation describing this line is shown in Figure 2.

Figure 2

Experiment 2:

The scientist removed the light bulb from the circuit shown in Figure 1 and replaced it with an instrument that can measure electrical charge. He then directed his x-ray source at the wire and slowly increased the intensity of the X-ray light while the frequency was held constant at . He monitored the current produced in the wire as the intensity of light increased and recorded the results in Figure 3 below. Intensity of light is measured in photons (a discrete particle, the fundamental unit of light) and charge in Coulombs, and like in Experiment 1, a linear equation is fitted to the data and shown in Figure 3.

Figure 3

The value corresponding to the binding energy of an electron to its positively charged nucleus is known as the work function, and corresponds to the y-intercept of the trend line produced when frequency of incident light is graphed against kinetic energy of liberated electrons. What is the work function for copper?

A scientist observed that when low energy types of electromagnetic radiation (light), such as visible light or ultraviolet light, were shone onto a conductive copper wire incorporated into a circuit with a light bulb as shown in Figure 1, the light bulb did not come on. However, when electromagnetic radiation of a higher energy, such as x-rays or gamma rays, was shone onto the wire, the light bulb did come on, indicating a current (electricity) was produced in the wire. The scientist hypothesized that this effect was due to the fact that electromagnetic radiation of a certain energy was able to overcome the attraction between electrons and protons in the individual atoms of copper in the wire, and liberate an electron to produce the electric current. He called this the photoelectric effect, and did the following experiments to further study this effect.

Figure 1

Experiment 1:

The scientist put a sample of copper in an instrument that can measure the energies of free-moving electrons. He shone a light source capable of producing specific energies of electromagnetic radiation on the metal and slowly increased the energy of the light. The instrument was used to measure the kinetic energies (energy due to motion) of any electrons that were liberated from the copper sample. The scientist recorded the energy of light used in frequency, where a low frequency corresponds to a low energy electromagnetic radiation, and a high frequency corresponds to a high frequency of electromagnetic radiation. He saw that no electrons could be detected at low frequencies, and that after a specific frequency he called the threshold frequency, the kinetic energy of liberated electrons increased linearly with increasing frequency of incident light as shown in Figure 2 below. The data was fitted with a line along which the data falls; the equation describing this line is shown in Figure 2.

Figure 2

Experiment 2:

The scientist removed the light bulb from the circuit shown in Figure 1 and replaced it with an instrument that can measure electrical charge. He then directed his x-ray source at the wire and slowly increased the intensity of the X-ray light while the frequency was held constant at . He monitored the current produced in the wire as the intensity of light increased and recorded the results in Figure 3 below. Intensity of light is measured in photons (a discrete particle, the fundamental unit of light) and charge in Coulombs, and like in Experiment 1, a linear equation is fitted to the data and shown in Figure 3.

Figure 3

Figure 2 shows that the threshold frequency, in Hertz, for copper is most nearly:

A scientist observed that when low energy types of electromagnetic radiation (light), such as visible light or ultraviolet light, were shone onto a conductive copper wire incorporated into a circuit with a light bulb as shown in Figure 1, the light bulb did not come on. However, when electromagnetic radiation of a higher energy, such as x-rays or gamma rays, was shone onto the wire, the light bulb did come on, indicating a current (electricity) was produced in the wire. The scientist hypothesized that this effect was due to the fact that electromagnetic radiation of a certain energy was able to overcome the attraction between electrons and protons in the individual atoms of copper in the wire, and liberate an electron to produce the electric current. He called this the photoelectric effect, and did the following experiments to further study this effect.

Figure 1

Experiment 1:

The scientist put a sample of copper in an instrument that can measure the energies of free-moving electrons. He shone a light source capable of producing specific energies of electromagnetic radiation on the metal and slowly increased the energy of the light. The instrument was used to measure the kinetic energies (energy due to motion) of any electrons that were liberated from the copper sample. The scientist recorded the energy of light used in frequency, where a low frequency corresponds to a low energy electromagnetic radiation, and a high frequency corresponds to a high frequency of electromagnetic radiation. He saw that no electrons could be detected at low frequencies, and that after a specific frequency he called the threshold frequency, the kinetic energy of liberated electrons increased linearly with increasing frequency of incident light as shown in Figure 2 below. The data was fitted with a line along which the data falls; the equation describing this line is shown in Figure 2.

Figure 2

Experiment 2:

The scientist removed the light bulb from the circuit shown in Figure 1 and replaced it with an instrument that can measure electrical charge. He then directed his x-ray source at the wire and slowly increased the intensity of the X-ray light while the frequency was held constant at . He monitored the current produced in the wire as the intensity of light increased and recorded the results in Figure 3 below. Intensity of light is measured in photons (a discrete particle, the fundamental unit of light) and charge in Coulombs, and like in Experiment 1, a linear equation is fitted to the data and shown in Figure 3.

Figure 3

An electron has a negative electric charge of . How many electrons are produced per photon with the frequency stated in Experiment 2?

A scientist observed that when low energy types of electromagnetic radiation (light), such as visible light or ultraviolet light, were shone onto a conductive copper wire incorporated into a circuit with a light bulb as shown in Figure 1, the light bulb did not come on. However, when electromagnetic radiation of a higher energy, such as x-rays or gamma rays, was shone onto the wire, the light bulb did come on, indicating a current (electricity) was produced in the wire. The scientist hypothesized that this effect was due to the fact that electromagnetic radiation of a certain energy was able to overcome the attraction between electrons and protons in the individual atoms of copper in the wire, and liberate an electron to produce the electric current. He called this the photoelectric effect, and did the following experiments to further study this effect.

Figure 1

Experiment 1:

The scientist put a sample of copper in an instrument that can measure the energies of free-moving electrons. He shone a light source capable of producing specific energies of electromagnetic radiation on the metal and slowly increased the energy of the light. The instrument was used to measure the kinetic energies (energy due to motion) of any electrons that were liberated from the copper sample. The scientist recorded the energy of light used in frequency, where a low frequency corresponds to a low energy electromagnetic radiation, and a high frequency corresponds to a high frequency of electromagnetic radiation. He saw that no electrons could be detected at low frequencies, and that after a specific frequency he called the threshold frequency, the kinetic energy of liberated electrons increased linearly with increasing frequency of incident light as shown in Figure 2 below. The data was fitted with a line along which the data falls; the equation describing this line is shown in Figure 2.

Figure 2

Experiment 2:

The scientist removed the light bulb from the circuit shown in Figure 1 and replaced it with an instrument that can measure electrical charge. He then directed his x-ray source at the wire and slowly increased the intensity of the X-ray light while the frequency was held constant at . He monitored the current produced in the wire as the intensity of light increased and recorded the results in Figure 3 below. Intensity of light is measured in photons (a discrete particle, the fundamental unit of light) and charge in Coulombs, and like in Experiment 1, a linear equation is fitted to the data and shown in Figure 3.

Figure 3

The circuit setup in Experiment 3 can be considered a solar cell as electricity is produced when the wire collects electromagnetic radiation. An important consideration in the development of solar cells is their efficiency, which can be defined as the ratio of electrons produced to photons incident on the material expressed as a percentage. What is the efficiency of the solar cell in Experiment 2? 

A scientist observed that when low energy types of electromagnetic radiation (light), such as visible light or ultraviolet light, were shone onto a conductive copper wire incorporated into a circuit with a light bulb as shown in Figure 1, the light bulb did not come on. However, when electromagnetic radiation of a higher energy, such as x-rays or gamma rays, was shone onto the wire, the light bulb did come on, indicating a current (electricity) was produced in the wire. The scientist hypothesized that this effect was due to the fact that electromagnetic radiation of a certain energy was able to overcome the attraction between electrons and protons in the individual atoms of copper in the wire, and liberate an electron to produce the electric current. He called this the photoelectric effect, and did the following experiments to further study this effect.

Figure 1

Experiment 1:

The scientist put a sample of copper in an instrument that can measure the energies of free-moving electrons. He shone a light source capable of producing specific energies of electromagnetic radiation on the metal and slowly increased the energy of the light. The instrument was used to measure the kinetic energies (energy due to motion) of any electrons that were liberated from the copper sample. The scientist recorded the energy of light used in frequency, where a low frequency corresponds to a low energy electromagnetic radiation, and a high frequency corresponds to a high frequency of electromagnetic radiation. He saw that no electrons could be detected at low frequencies, and that after a specific frequency he called the threshold frequency, the kinetic energy of liberated electrons increased linearly with increasing frequency of incident light as shown in Figure 2 below. The data was fitted with a line along which the data falls; the equation describing this line is shown in Figure 2.

Figure 2

Experiment 2:

The scientist removed the light bulb from the circuit shown in Figure 1 and replaced it with an instrument that can measure electrical charge. He then directed his x-ray source at the wire and slowly increased the intensity of the X-ray light while the frequency was held constant at . He monitored the current produced in the wire as the intensity of light increased and recorded the results in Figure 3 below. Intensity of light is measured in photons (a discrete particle, the fundamental unit of light) and charge in Coulombs, and like in Experiment 1, a linear equation is fitted to the data and shown in Figure 3.

Figure 3

Why did the scientist hold the frequency of x-rays at  in Experiment 2?

A scientist observed that when low energy types of electromagnetic radiation (light), such as visible light or ultraviolet light, were shone onto a conductive copper wire incorporated into a circuit with a light bulb as shown in Figure 1, the light bulb did not come on. However, when electromagnetic radiation of a higher energy, such as x-rays or gamma rays, was shone onto the wire, the light bulb did come on, indicating a current (electricity) was produced in the wire. The scientist hypothesized that this effect was due to the fact that electromagnetic radiation of a certain energy was able to overcome the attraction between electrons and protons in the individual atoms of copper in the wire, and liberate an electron to produce the electric current. He called this the photoelectric effect, and did the following experiments to further study this effect.

Figure 1

Experiment 1:

The scientist put a sample of copper in an instrument that can measure the energies of free-moving electrons. He shone a light source capable of producing specific energies of electromagnetic radiation on the metal and slowly increased the energy of the light. The instrument was used to measure the kinetic energies (energy due to motion) of any electrons that were liberated from the copper sample. The scientist recorded the energy of light used in frequency, where a low frequency corresponds to a low energy electromagnetic radiation, and a high frequency corresponds to a high frequency of electromagnetic radiation. He saw that no electrons could be detected at low frequencies, and that after a specific frequency he called the threshold frequency, the kinetic energy of liberated electrons increased linearly with increasing frequency of incident light as shown in Figure 2 below. The data was fitted with a line along which the data falls; the equation describing this line is shown in Figure 2.

Figure 2

Experiment 2:

The scientist removed the light bulb from the circuit shown in Figure 1 and replaced it with an instrument that can measure electrical charge. He then directed his x-ray source at the wire and slowly increased the intensity of the X-ray light while the frequency was held constant at . He monitored the current produced in the wire as the intensity of light increased and recorded the results in Figure 3 below. Intensity of light is measured in photons (a discrete particle, the fundamental unit of light) and charge in Coulombs, and like in Experiment 1, a linear equation is fitted to the data and shown in Figure 3.

Figure 3

What is the meaning of the slope in the regression equation for the data shown in Figure 1?