How to find data representation in physics - ACT Science
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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?
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?
The chart provides the waves in descending order of wavelength. Radio waves has a wavelength of 
, much greater than the other answer choices. Remember that a positive exponent will always be greater than a negative exponent. Furthermore, the smaller a negative exponent is, the bigger its value.
The chart provides the waves in descending order of wavelength. Radio waves has a wavelength of
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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?
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
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
In Experiment 1, how much current is most likely flowing through the circuit?
The passage provides us with a formula to calculate the amount of current running through the circuit, 
. We are told the voltage in Experiment 1 is 10 V and the resistor is 2 ohms, so 
.
The passage provides us with a formula to calculate the amount of current running through the circuit,
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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
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
Based on the formula provided in the passage and the data from the experiments, if voltage increases, current __________.
Given the formula 
, we can see that both voltage and current are in the numerator of their respective side of the equal sign; thus, these values are directly related and if voltage increases, current will also increase. This is supported by the data from the experiments.
Given the formula
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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
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
Which of the following shows a possible graphical relationship between current and voltage?
Using the formula 
, we see that voltage and current are directly related, meaning that as one increases, the other increases proportionally. The only graph that gives us this linear relationship is 
.
Using the formula .
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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
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
Which of the following shows a possible graphical relationship between current and power?
Using the formula 
, we see that current and power are directly related, meaning that as one increases, the other increases proportionally. The only graph that gives us this linear relationship is 
.
Using the formula .
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A scientist is exploring the nature of energy and work in two experimental systems.
Experiment 1
She first sets up a system with a ball on an inclined plane, and calculates the potential and kinetic energies of the ball at three positions. She places the ball at position 1, stops the ball after rolling to position 2, and then again allows it to roll to position 3. The measured kinetic and potential energies are shown in the table, along with measurements of the force of friction acting on the ball.
Ball Position Potential Energy Kinetic Energy Force of Friction 1 150 kJ X kJ 0 N 2 75 kJ 75 kJ 0 N 3 X kJ 150 kJ 0 N
Experiment 2
The same scientist then sets up another experiment with the same ball, again at three positions. The ball is provided a slight push, and then allowed to roll down three levels without any additional external input of energy.
She uses the following formulae to calculate the energy levels of the ball:
Potential Energy = Mass of the Ball x Acceleration Due to Gravity x Height of the Ball
Kinetic Energy = (1/2) x Mass of the Ball x (Velocity of the Ball)2
She also measures the internal energy of the ball, a value that she defines as the amount of energy contained in the motion of the molecules that make up the matter of the ball.
Position Potential Energy Velocity Internal Energy 1 A 1 m/s 5 kJ 2 B 5.47 m/s 6 kJ 3 C 10.94 m/s 7 kJ
In Experiment 2, the scientist wishes to approximate the total loss of potential energy from position 1 (PE1) to position 3 (PE3). Which of the following is true?
A scientist is exploring the nature of energy and work in two experimental systems.
Experiment 1
She first sets up a system with a ball on an inclined plane, and calculates the potential and kinetic energies of the ball at three positions. She places the ball at position 1, stops the ball after rolling to position 2, and then again allows it to roll to position 3. The measured kinetic and potential energies are shown in the table, along with measurements of the force of friction acting on the ball.
| Ball Position | Potential Energy | Kinetic Energy | Force of Friction |
|---|---|---|---|
| 1 | 150 kJ | X kJ | 0 N |
| 2 | 75 kJ | 75 kJ | 0 N |
| 3 | X kJ | 150 kJ | 0 N |
Experiment 2
The same scientist then sets up another experiment with the same ball, again at three positions. The ball is provided a slight push, and then allowed to roll down three levels without any additional external input of energy.
She uses the following formulae to calculate the energy levels of the ball:
Potential Energy = Mass of the Ball x Acceleration Due to Gravity x Height of the Ball
Kinetic Energy = (1/2) x Mass of the Ball x (Velocity of the Ball)2
She also measures the internal energy of the ball, a value that she defines as the amount of energy contained in the motion of the molecules that make up the matter of the ball.
| Position | Potential Energy | Velocity | Internal Energy |
|---|---|---|---|
| 1 | A | 1 m/s | 5 kJ |
| 2 | B | 5.47 m/s | 6 kJ |
| 3 | C | 10.94 m/s | 7 kJ |
In Experiment 2, the scientist wishes to approximate the total loss of potential energy from position 1 (PE1) to position 3 (PE3). Which of the following is true?
The potential energy of the ball at position one is going to be 20 times higher than the potential energy of the ball at position 3 because the ball is 20 m higher. Potential energy, according to the provided formula, is dependent on this height for its magnitude.
The potential energy of the ball at position one is going to be 20 times higher than the potential energy of the ball at position 3 because the ball is 20 m higher. Potential energy, according to the provided formula, is dependent on this height for its magnitude.
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The graph below depicts the position of three different cars over a 15-second time interval.
At the point where all three cars meet, which car is traveling the fastest?
The graph below depicts the position of three different cars over a 15-second time interval.
At the point where all three cars meet, which car is traveling the fastest?
The three cars intersect at time = 3s. At this point, one can determine the speed (or velocity) of each car by looking how many meters the car travels per second. At time = 3, car 1 is traveling 1 m per second, car 2 is traveling 2 m per second, and car 3 is traveling 4 m per second. Another way of determining which car is the fastest is by looking at the slopes of each line. The car with the greatest slope is traveling the quickest.
The three cars intersect at time = 3s. At this point, one can determine the speed (or velocity) of each car by looking how many meters the car travels per second. At time = 3, car 1 is traveling 1 m per second, car 2 is traveling 2 m per second, and car 3 is traveling 4 m per second. Another way of determining which car is the fastest is by looking at the slopes of each line. The car with the greatest slope is traveling the quickest.
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The graph below depicts the position of three different cars over a 15-second time interval.
What is the speed of Car 1 at time = 7s?
The graph below depicts the position of three different cars over a 15-second time interval.
What is the speed of Car 1 at time = 7s?
At time = 7 s, Car 1 holds the same position as it did at 6 and 8 seconds, indicating that the car is not moving. If the car is not moving, then it has a speed of 0/s. One helpful method of determining the speed of a car on this graph, or any similar problem you may encounter, is to look at the slope of the graph. A slope of 0 means the car is not moving. A positive or negative slope indicates the car is in fact moving.
At time = 7 s, Car 1 holds the same position as it did at 6 and 8 seconds, indicating that the car is not moving. If the car is not moving, then it has a speed of 0/s. One helpful method of determining the speed of a car on this graph, or any similar problem you may encounter, is to look at the slope of the graph. A slope of 0 means the car is not moving. A positive or negative slope indicates the car is in fact moving.
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The graph below depicts the position of three different cars over a 15-second time interval.
If Car 3 continues to travel at it's current speed at t = 15 seconds, what will it's position be at time = 20s?
The graph below depicts the position of three different cars over a 15-second time interval.
If Car 3 continues to travel at it's current speed at t = 15 seconds, what will it's position be at time = 20s?
At t = 15 s, Car 3 is traveling 4 m/s and is traveling away from position 0 in the negative direction. At t = 15s, Car 3 is also at position = –10 m. Five seconds later it will travel 5s x 4 m/s = 20 m; therefore, it's new position will be (-10 + -20 = -30) –30 m.
At t = 15 s, Car 3 is traveling 4 m/s and is traveling away from position 0 in the negative direction. At t = 15s, Car 3 is also at position = –10 m. Five seconds later it will travel 5s x 4 m/s = 20 m; therefore, it's new position will be (-10 + -20 = -30) –30 m.
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The graph below depicts the position of three different cars over a 15-second time interval.
What is the total distance traveled by Car 3 from time = 0 until time = 4s?
The graph below depicts the position of three different cars over a 15-second time interval.
What is the total distance traveled by Car 3 from time = 0 until time = 4s?
An important consideration in this problem is the difference between total distance traveled (which is what the question asks about) and net displacement. Total distance traveled includes every meter that Car 3 covers, even if some of that distance moved backward or toward its original position. Net displacement, often in physics referred to simply as "distance" (but not "total distance traveled") is only concerned with the beginning and end points of the object.
Here you can see that Car 3's position began at -4, moved to 4, and then returned back to 0. That means that it made a positive gain of 8 and then a negative gain of 4, for a total distance covered of 12m. The net displacement is only a net gain of 4m, but as the question asks for total distance traveled the answer is 12m.
An important consideration in this problem is the difference between total distance traveled (which is what the question asks about) and net displacement. Total distance traveled includes every meter that Car 3 covers, even if some of that distance moved backward or toward its original position. Net displacement, often in physics referred to simply as "distance" (but not "total distance traveled") is only concerned with the beginning and end points of the object.
Here you can see that Car 3's position began at -4, moved to 4, and then returned back to 0. That means that it made a positive gain of 8 and then a negative gain of 4, for a total distance covered of 12m. The net displacement is only a net gain of 4m, but as the question asks for total distance traveled the answer is 12m.
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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?
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 (
The correct answer is 
. As the passage says, the energy increases until suddenly the metal begins to emit a stream of electrons. At this point, as the passage states, the number of electrons does not change, explaining the plateau we see in this graph. The other graphs are not consistent with this information.
The correct answer is . As the passage says, the energy increases until suddenly the metal begins to emit a stream of electrons. At this point, as the passage states, the number of electrons does not change, explaining the plateau we see in this graph. The other graphs are not consistent with this information.
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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.
In Study 1, which medium tested had the greatest density?
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.
In Study 1, which medium tested had the greatest density?
The densities for the media in Study 1 can be found in Table 1. In the second column of Table 1, the densities are listed in ascending order. Lead has the highest number in that column and therefore has the greatest density.
The densities for the media in Study 1 can be found in Table 1. In the second column of Table 1, the densities are listed in ascending order. Lead has the highest number in that column and therefore has the greatest density.
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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 the data in Study 1, as density increases, what happens to the velocity of sound?
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 the data in Study 1, as density increases, what happens to the velocity of sound?
The velocity of sound in different media is listed in the third column of Table 1. Density of the media increases as you move down the column. Velocity increases along with density except between iron and lead. This means that no direct relationship between density and velocity can be drawn; the velocity of sound can either increase or decrease as density increases.
The velocity of sound in different media is listed in the third column of Table 1. Density of the media increases as you move down the column. Velocity increases along with density except between iron and lead. This means that no direct relationship between density and velocity can be drawn; the velocity of sound can either increase or decrease as density increases.
Compare your answer with the correct one above
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, water at which of the following temperatures yields the greatest velocity of sound?
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, water at which of the following temperatures yields the greatest velocity of sound?
Velocities of sound in water can be found in the third column of Table 2. The highest velocity listed in the table is 1,555 m/s. Temperatures are listed in the first column; this sound velocity occurs in water that is 80°C.
Velocities of sound in water can be found in the third column of Table 2. The highest velocity listed in the table is 1,555 m/s. Temperatures are listed in the first column; this sound velocity occurs in water that is 80°C.
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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?
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?
Table 2 lists velocity of sound in its third column. As you move down the column, each value corresponds to increasing temperatures. The velocity values increase over each interval until they drop from 1,555 m/s to 1543.05 m/s. This decrease in velocity occurs between 80°C and 100°C according to the corresponding values in the first column of the table.
Table 2 lists velocity of sound in its third column. As you move down the column, each value corresponds to increasing temperatures. The velocity values increase over each interval until they drop from 1,555 m/s to 1543.05 m/s. This decrease in velocity occurs between 80°C and 100°C according to the corresponding values in the first column of the table.
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A physicist wishes to study the trajectory of a ball launched horizontally. She varies parameters such as the launching velocity, starting height, and mass of the ball. For each trajectory, she records the time of flight (in seconds) and horizontal displacement (in meters). She assumes air resistance is negligible.
Figure 1
Using all of the data she collects, she constructs the following table:
Table 1
In Trial 1, if a fourth data point were collected in which the ball was thrown with a launching velocity of 40 m/s, what would be the approximate horizontal displacement in meters?
A physicist wishes to study the trajectory of a ball launched horizontally. She varies parameters such as the launching velocity, starting height, and mass of the ball. For each trajectory, she records the time of flight (in seconds) and horizontal displacement (in meters). She assumes air resistance is negligible.
Figure 1
Using all of the data she collects, she constructs the following table:
Table 1
In Trial 1, if a fourth data point were collected in which the ball was thrown with a launching velocity of 40 m/s, what would be the approximate horizontal displacement in meters?
Looking at the table, we see that as the launching velocity is increased by 10 m/s in Trial 1, the horizontal displacement increases by about 14 meters.
Looking at the table, we see that as the launching velocity is increased by 10 m/s in Trial 1, the horizontal displacement increases by about 14 meters.
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A physicist wishes to study the trajectory of a ball launched horizontally. She varies parameters such as the launching velocity, starting height, and mass of the ball. For each trajectory, she records the time of flight (in seconds) and horizontal displacement (in meters). She assumes air resistance is negligible.
Figure 1
Using all of the data she collects, she constructs the following table:
Table 1
If all of trial 3 were redone with a launching velocity of 20 m/s instead of 10 m/s, then compared to the data for trial 3 presented in the table, the horizontal displacement for all data points would be which of the following?
A physicist wishes to study the trajectory of a ball launched horizontally. She varies parameters such as the launching velocity, starting height, and mass of the ball. For each trajectory, she records the time of flight (in seconds) and horizontal displacement (in meters). She assumes air resistance is negligible.
Figure 1
Using all of the data she collects, she constructs the following table:
Table 1
If all of trial 3 were redone with a launching velocity of 20 m/s instead of 10 m/s, then compared to the data for trial 3 presented in the table, the horizontal displacement for all data points would be which of the following?
Trial 3 shows us that the mass of the ball does not affect horizontal displacement, so mass can be ignored for this question. Trial 1 shows us that horizontal displacement increases with launching velocity, so we can reason that a higher launching velocity in Trial 3 would result in increased horizontal displacement.
Trial 3 shows us that the mass of the ball does not affect horizontal displacement, so mass can be ignored for this question. Trial 1 shows us that horizontal displacement increases with launching velocity, so we can reason that a higher launching velocity in Trial 3 would result in increased horizontal displacement.
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Experiment 1
A scientist develops the following setup, shown in Figure 1 below, to study the charges of radioactive particles. A radioactive sample is placed into a lead box that has an open column such that the particles can only exit from one direction. A detector is placed in front of the opening. A metric ruler (centimeters (cm)), is aligned on the detector such that zero is directly in front of the opening of the column, with the positive values extending to the left and the negative values to the right. On the left side of the experimental setup, there is a device that generates a magnetic field that attracts positively charged particles and repels negatively charged particles.
Figure 1.
The device detects particles in three different places: alpha, α; beta, β; and gamma, γ; as labeled in Figure 1. The paths these particles take from the source of radioactivity are shown.
Experiment 2
A different scientist finds the following data, shown in Table 1, about the energies of the α, β, and γ particles by observing what kinds of materials through which the particles can pass. This scientist assumes that the ability of particles to pass through thicker and denser barriers is indicative of higher energy. Table 1 summarizes whether or not each type of particle was detected when each of the following barriers is placed between the radioactivity source and the detector. The paper and aluminum foil are both 1 millimeters thick, and the concrete wall is 1 meter thick.
Based on Experiment 1, which of the following particles must be positively charged?
Experiment 1
A scientist develops the following setup, shown in Figure 1 below, to study the charges of radioactive particles. A radioactive sample is placed into a lead box that has an open column such that the particles can only exit from one direction. A detector is placed in front of the opening. A metric ruler (centimeters (cm)), is aligned on the detector such that zero is directly in front of the opening of the column, with the positive values extending to the left and the negative values to the right. On the left side of the experimental setup, there is a device that generates a magnetic field that attracts positively charged particles and repels negatively charged particles.
Figure 1.
The device detects particles in three different places: alpha, α; beta, β; and gamma, γ; as labeled in Figure 1. The paths these particles take from the source of radioactivity are shown.
Experiment 2
A different scientist finds the following data, shown in Table 1, about the energies of the α, β, and γ particles by observing what kinds of materials through which the particles can pass. This scientist assumes that the ability of particles to pass through thicker and denser barriers is indicative of higher energy. Table 1 summarizes whether or not each type of particle was detected when each of the following barriers is placed between the radioactivity source and the detector. The paper and aluminum foil are both 1 millimeters thick, and the concrete wall is 1 meter thick.
Based on Experiment 1, which of the following particles must be positively charged?
As the Experiment 1 description states that the magnetic field attracts positively charge particles, and the alpha particle is the only particle with a trajectory bent toward the magnetic field, the answer must be α.
As the Experiment 1 description states that the magnetic field attracts positively charge particles, and the alpha particle is the only particle with a trajectory bent toward the magnetic field, the answer must be α.
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Experiment 1
A scientist develops the following setup, shown in Figure 1 below, to study the charges of radioactive particles. A radioactive sample is placed into a lead box that has an open column such that the particles can only exit from one direction. A detector is placed in front of the opening. A metric ruler measuring in centimeters (cm), is aligned on the detector such that zero is directly in front of the opening of the column, with positive values extending to the left and negative values extending to the right. On the left side of the experimental setup, there is a device that generates a magnetic field that attracts positively charged particles and repels negatively charged particles.
Figure 1.
The device detects particles in three different places: alpha, α; beta, β; and gamma, γ; as labeled in Figure 1. The paths these particles take from the source of radioactivity are shown.
Experiment 2
A different scientist finds the following data, shown in Table 1, about the energies of the α, β, and γ particles by observing what kinds of materials through which the particles can pass. This scientist assumes that the ability of particles to pass through thicker and denser barriers is indicative of higher energy. Table 1 summarizes whether or not each type of particle was detected when each of the following barriers is placed between the radioactivity source and the detector. The paper and aluminum foil are both 1 millimeters thick, and the concrete wall is 1 meter thick.
Based on the trajectories of the particles in Experiment 1, what can be concluded about the relative charges of the particles?
Experiment 1
A scientist develops the following setup, shown in Figure 1 below, to study the charges of radioactive particles. A radioactive sample is placed into a lead box that has an open column such that the particles can only exit from one direction. A detector is placed in front of the opening. A metric ruler measuring in centimeters (cm), is aligned on the detector such that zero is directly in front of the opening of the column, with positive values extending to the left and negative values extending to the right. On the left side of the experimental setup, there is a device that generates a magnetic field that attracts positively charged particles and repels negatively charged particles.
Figure 1.
The device detects particles in three different places: alpha, α; beta, β; and gamma, γ; as labeled in Figure 1. The paths these particles take from the source of radioactivity are shown.
Experiment 2
A different scientist finds the following data, shown in Table 1, about the energies of the α, β, and γ particles by observing what kinds of materials through which the particles can pass. This scientist assumes that the ability of particles to pass through thicker and denser barriers is indicative of higher energy. Table 1 summarizes whether or not each type of particle was detected when each of the following barriers is placed between the radioactivity source and the detector. The paper and aluminum foil are both 1 millimeters thick, and the concrete wall is 1 meter thick.
Based on the trajectories of the particles in Experiment 1, what can be concluded about the relative charges of the particles?
We know that the alpha particle must have a positive charge since it moves toward the magnetic field. We also know that the beta particle must have a negative charge since it moves away from the magnetic field. Lastly, the gamma particle must have no charge, as its trajectory is not affected by the magnetic field. Now we can look at the magnitude of deflection from 0 using the detector's ruler. As the alpha particle was deflected two units from zero, and the beta particle was deflected one unit from zero, we know that the alpha particle must have a charge twice that of the beta particle.
We know that the alpha particle must have a positive charge since it moves toward the magnetic field. We also know that the beta particle must have a negative charge since it moves away from the magnetic field. Lastly, the gamma particle must have no charge, as its trajectory is not affected by the magnetic field. Now we can look at the magnitude of deflection from 0 using the detector's ruler. As the alpha particle was deflected two units from zero, and the beta particle was deflected one unit from zero, we know that the alpha particle must have a charge twice that of the beta particle.
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The period of a simple pendulum 
is defined as the amount of time that it takes for a pendulum to swing from one end to the other and back. In studying the period of a simple pendulum, two students express their opinions.
Student 1: The period of a pendulum depends on two factors: the mass of the pendulum's bob (the object swinging at the end of the pendulum) and the length of the pendulum. The height at which the pendulum is originally dropped does not affect the period 
.
Student 2: The period of a pendulum 
only depends on the length of the pendulum. Varying the mass and the height at which the pendulum is originally dropped does not affect how long the pendulum takes to swing across.
The two students ran a series of trials to measure the period of a simple pendulum using varying weights and lengths. The students did not measure height as a factor. The results of the trials can be seen in the table below:
According to the data provided, what would we predict would happen if an experiment compared the periods of a pendulum made of a lead weight on a meter-long cord and a pendulum made of a tennis ball on a three-meter-long cord?
The period of a simple pendulum
Student 1: The period of a pendulum depends on two factors: the mass of the pendulum's bob (the object swinging at the end of the pendulum) and the length of the pendulum. The height at which the pendulum is originally dropped does not affect the period
Student 2: The period of a pendulum
The two students ran a series of trials to measure the period of a simple pendulum using varying weights and lengths. The students did not measure height as a factor. The results of the trials can be seen in the table below:
According to the data provided, what would we predict would happen if an experiment compared the periods of a pendulum made of a lead weight on a meter-long cord and a pendulum made of a tennis ball on a three-meter-long cord?
The table shows in its last two rows that changing the mass of the bob on a pendulum did not affect the pendulum's period. Therefore, only the length of the pendulum appears to affect the period. We can then ignore the lead ball versus the tennis ball, as the mass of each will not affect the periods of their respective pendulums. We can also see that if the length of a pendulum increases, the period of the pendulum also increases. Therefore, we would most likely predict that the period of the longer pendulum would be greater than the period of the shorter pendulum.
The table shows in its last two rows that changing the mass of the bob on a pendulum did not affect the pendulum's period. Therefore, only the length of the pendulum appears to affect the period. We can then ignore the lead ball versus the tennis ball, as the mass of each will not affect the periods of their respective pendulums. We can also see that if the length of a pendulum increases, the period of the pendulum also increases. Therefore, we would most likely predict that the period of the longer pendulum would be greater than the period of the shorter pendulum.
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