As part of an engineering competition, a group of students are asked to design a flying robot that simulates the way real birds fly. Below, three of the students give their explanations for how bird flight occurs.

Student 1:

Birds are able to fly due to the shape of their wings. Bird wings are convex on their upper sides, while their lower sides are usually concave. This type of shape is called an airfoil. When a wing travels through the air, air passing over the top of the wing must travel a greater distance than air passing under the wing. The stream of air passing over the wing and the stream of air passing under the wing meet together at the tail end of the wing. In order for both streams of air to meet at the same point behind the wing, the air above the wing, which travels a greater distance, must travel faster than the air below the wing.

When a volume of air travels more quickly over a distance, its molecules are spread out over a greater distance. As a result, the air traveling over the top of a wing has a lower pressure than the air traveling under the wing. Because the wing has a region of low pressure above it and a region of relative high pressure below it, it experiences a net upward force. When this upward force is greater than or equal to the bird's weight, or the force exerted on a bird by gravity, the bird is able to fly.

The magnitude of the upward force depends on the speed at which air flows across the wing and on the corresponding difference in pressure over and under the wing. When birds flap their wings, they increase the speed of air flowing across their wings, thus producing a greater upward force.

Student 2:

There are two components to bird flight: lift and thrust. "Lift" refers to the upward force that allows a bird to stay aloft in the air despite its weight, while "thrust" refers to the horizontal force that allows a bird to move forward through the air. Birds are able to fly because they do not hold their wings perfectly horizontally. Instead, their wings are angled slightly upward. The angle at which a wing is inclined upward, with respect to the horizontal, is called its "angle of attack."

Air is not an ideal gas; instead, it has viscosity. This means that the air flowing close to a solid object tends to follow the curves of that object. When air encounters a bird's wing, it follows the incline of the wing. Because of the wing's angle of attack, the air is directed downward and back. The air continues to move downward, even after it has left the wing. This movement of the air creates an opposing force that pushes the bird upward and forward.

Thus, the angle of attack of a bird's wings accounts for both the lift and thrust components of a bird's flight.

Student 3:

Birds are able to fly because the way in which they move their wings allows them to create a net movement of air downward and backward. The flapping of a bird's wings can be understood as being composed of two parts: a downstroke, during which the bird moves its wings down, and an upstroke, during which the bird moves its wings up. During a downstroke, a bird displaces a quantity of air downward and behind it. During an upstroke, however, the bird's wings are angled upward in a way that displaces less air, and its wing feathers rotate to allow air to pass through them. Thus, on the upstroke, the bird much exerts less force on the air than it does on the downstroke.

Suppose that a robot is designed with stationary wings in the shape of airfoils; however, it is found that the robot is still not able to fly. Which of the following suggestions would Student 1 most likely not make about how to change the design of the robot?

As part of an engineering competition, a group of students are asked to design a flying robot that simulates the way real birds fly. Below, three of the students give their explanations for how bird flight occurs.

Student 1:

Birds are able to fly due to the shape of their wings. Bird wings are convex on their upper sides, while their lower sides are usually concave. This type of shape is called an airfoil. When a wing travels through the air, air passing over the top of the wing must travel a greater distance than air passing under the wing. The stream of air passing over the wing and the stream of air passing under the wing meet together at the tail end of the wing. In order for both streams of air to meet at the same point behind the wing, the air above the wing, which travels a greater distance, must travel faster than the air below the wing.

When a volume of air travels more quickly over a distance, its molecules are spread out over a greater distance. As a result, the air traveling over the top of a wing has a lower pressure than the air traveling under the wing. Because the wing has a region of low pressure above it and a region of relative high pressure below it, it experiences a net upward force. When this upward force is greater than or equal to the bird's weight, or the force exerted on a bird by gravity, the bird is able to fly.

The magnitude of the upward force depends on the speed at which air flows across the wing and on the corresponding difference in pressure over and under the wing. When birds flap their wings, they increase the speed of air flowing across their wings, thus producing a greater upward force.

Student 2:

There are two components to bird flight: lift and thrust. "Lift" refers to the upward force that allows a bird to stay aloft in the air despite its weight, while "thrust" refers to the horizontal force that allows a bird to move forward through the air. Birds are able to fly because they do not hold their wings perfectly horizontally. Instead, their wings are angled slightly upward. The angle at which a wing is inclined upward, with respect to the horizontal, is called its "angle of attack."

Air is not an ideal gas; instead, it has viscosity. This means that the air flowing close to a solid object tends to follow the curves of that object. When air encounters a bird's wing, it follows the incline of the wing. Because of the wing's angle of attack, the air is directed downward and back. The air continues to move downward, even after it has left the wing. This movement of the air creates an opposing force that pushes the bird upward and forward.

Thus, the angle of attack of a bird's wings accounts for both the lift and thrust components of a bird's flight.

Student 3:

Birds are able to fly because the way in which they move their wings allows them to create a net movement of air downward and backward. The flapping of a bird's wings can be understood as being composed of two parts: a downstroke, during which the bird moves its wings down, and an upstroke, during which the bird moves its wings up. During a downstroke, a bird displaces a quantity of air downward and behind it. During an upstroke, however, the bird's wings are angled upward in a way that displaces less air, and its wing feathers rotate to allow air to pass through them. Thus, on the upstroke, the bird much exerts less force on the air than it does on the downstroke.

Many birds can fly by soaring. During soaring flight, birds do not move their wings. Which of the three students' explanations cannot be used to give any explanation of how soaring flight occurs?

As part of an engineering competition, a group of students are asked to design a flying robot that simulates the way real birds fly. Below, three of the students give their explanations for how bird flight occurs.

Student 1:

Birds are able to fly due to the shape of their wings. Bird wings are convex on their upper sides, while their lower sides are usually concave. This type of shape is called an airfoil. When a wing travels through the air, air passing over the top of the wing must travel a greater distance than air passing under the wing. The stream of air passing over the wing and the stream of air passing under the wing meet together at the tail end of the wing. In order for both streams of air to meet at the same point behind the wing, the air above the wing, which travels a greater distance, must travel faster than the air below the wing.

When a volume of air travels more quickly over a distance, its molecules are spread out over a greater distance. As a result, the air traveling over the top of a wing has a lower pressure than the air traveling under the wing. Because the wing has a region of low pressure above it and a region of relative high pressure below it, it experiences a net upward force. When this upward force is greater than or equal to the bird's weight, or the force exerted on a bird by gravity, the bird is able to fly.

The magnitude of the upward force depends on the speed at which air flows across the wing and on the corresponding difference in pressure over and under the wing. When birds flap their wings, they increase the speed of air flowing across their wings, thus producing a greater upward force.

Student 2:

There are two components to bird flight: lift and thrust. "Lift" refers to the upward force that allows a bird to stay aloft in the air despite its weight, while "thrust" refers to the horizontal force that allows a bird to move forward through the air. Birds are able to fly because they do not hold their wings perfectly horizontally. Instead, their wings are angled slightly upward. The angle at which a wing is inclined upward, with respect to the horizontal, is called its "angle of attack."

Air is not an ideal gas; instead, it has viscosity. This means that the air flowing close to a solid object tends to follow the curves of that object. When air encounters a bird's wing, it follows the incline of the wing. Because of the wing's angle of attack, the air is directed downward and back. The air continues to move downward, even after it has left the wing. This movement of the air creates an opposing force that pushes the bird upward and forward.

Thus, the angle of attack of a bird's wings accounts for both the lift and thrust components of a bird's flight.

Student 3:

Birds are able to fly because the way in which they move their wings allows them to create a net movement of air downward and backward. The flapping of a bird's wings can be understood as being composed of two parts: a downstroke, during which the bird moves its wings down, and an upstroke, during which the bird moves its wings up. During a downstroke, a bird displaces a quantity of air downward and behind it. During an upstroke, however, the bird's wings are angled upward in a way that displaces less air, and its wing feathers rotate to allow air to pass through them. Thus, on the upstroke, the bird much exerts less force on the air than it does on the downstroke.

Suppose that a tarp covers the back of a truck and is attached to the truck at its edges. When the truck is driven on the highway, the tarp bulges outward.

Given that Student 1's explanation is correct, how might the above situation be explained?

Mary is performing an experiment involving the electromagnetic spectrum. She observes several different types of waves and records their wavelength, frequency, and speed.

Which type of radiation has the greatest wavelength?

A student was interested in determining the relationship between the current, voltage, and resistance in a direct circuit, such as those exemplified by batteries connected to light bulbs. The student built the circuit presented in Figure 1 using a 2 ohm resistor.

Figure 1:

The current that flows through the circuit can be calculated using the equation , where  is the voltage of the battery,  is the current flowing through the circuit, and  is the resistance of the resistor.

The student used a 2 ohm resistor and batteries of various voltages to obtain the results in Table 1. The currents shown in the table are NOT calculated using the formula , but instead directly measured from the circuit using an ammeter. It is important to note that the measured current will only exactly equal the calculated current if the system contains no internal resistance.

Based on the formula provided in the passage and the data from the experiments, if voltage increases, current __________.

A student was interested in determining the relationship between the current, voltage, and resistance in a direct circuit, such as those exemplified by batteries connected to light bulbs. The student built the circuit presented in Figure 1 using a 2 ohm resistor.

Figure 1:

The current that flows through the circuit can be calculated using the equation , where  is the voltage of the battery,  is the current flowing through the circuit, and  is the resistance of the resistor.

The student used a 2 ohm resistor and batteries of various voltages to obtain the results in Table 1. The currents shown in the table are NOT calculated using the formula , but instead directly measured from the circuit using an ammeter. It is important to note that the measured current will only exactly equal the calculated current if the system contains no internal resistance.

Which of the following shows a possible graphical relationship between current and voltage?

A student was interested in determining the relationship between the current, voltage, and resistance in a direct circuit, such as those exemplified by batteries connected to light bulbs. The student built the circuit presented in Figure 1 using a 2 ohm resistor.

Figure 1:

The current that flows through the circuit can be calculated using the equation , where  is the voltage of the battery,  is the current flowing through the circuit, and  is the resistance of the resistor.

The student used a 2 ohm resistor and batteries of various voltages to obtain the results in Table 1. The currents shown in the table are NOT calculated using the formula , but instead directly measured from the circuit using an ammeter. It is important to note that the measured current will only exactly equal the calculated current if the system contains no internal resistance.

Which of the following shows a possible graphical relationship between current and power?

A student was interested in determining the relationship between the current, voltage, and resistance in a direct circuit, such as those exemplified by batteries connected to light bulbs. The student built the circuit presented in Figure 1 using a 2 ohm resistor.

Figure 1:

The current that flows through the circuit can be calculated using the equation , where  is the voltage of the battery,  is the current flowing through the circuit, and  is the resistance of the resistor.

The student used a 2 ohm resistor and batteries of various voltages to obtain the results in Table 1. The currents shown in the table are NOT calculated using the formula , but instead directly measured from the circuit using an ammeter. It is important to note that the measured current will only exactly equal the calculated current if the system contains no internal resistance.

In Experiment 1, how much current is most likely flowing through the circuit?

The photoelectric effect is a phenomenon that has led to many important scientific discoveries. Light of a particular wavelength is shined onto a piece of metal, showering the metal with photons. Wavelength is inversely related to a photon's energy. That is, with a smaller wavelength, the photon has greater energy. The wavelength of the light is decreased until a detector next to the metal senses that electrons are being ejected from the metal. This sensor also tells us how many electrons are ejected per second, which we call electrical current. At this point, any additional decrease in wavelength does not affect the number of electrons ejected. This point is called the metal's work function. However, if we then begin to increase the intensity of the light being shone (meaning the amount of light as opposed to the light's wavelength), the number of electrons picked up by the sensor increases. 

Which of the following graphs comparing photon energy () and amount of electrons ejected () would best represent the information provided in the passage?

Sound waves travel through a medium by mechanically disturbing the particles of that medium. As particles in the medium are displaced by the sound wave, they in turn act upon neighboring particles. In this fashion, the wave travels through the medium through a parallel series of disturbed particles. Like in other forms of motion, the rate at which the sound wave travels can be measured by dividing the distance over which the wave travels by the time required for it to do so.  

Study 1
A group of students hypothesizes that the velocity of sound is dependent upon the density of the medium through which it passes. They propose that with more matter in a given space, each particle needs to travel a shorter distance to disturb the adjacent particles. Using two microphones and a high speed recording device, the students measured the delay from the first microphone to the second. They chose a variety of media, shown in Table 1, and measured the velocity of sound through each using their two-microphone setup. The results are found in Table 1.

Study 2
The students wanted to test their hypothesis by using the same medium at different densities. To do this, they heated pure water to various temperatures and repeated the procedure described in Study 1. Their results can be found in Table 2.

According to Study 2, over what temperature interval does velocity begin to decrease as water temperature rises?