A physicist performs a series of experiments to determine the relative magnitude of electric charge on four particles. A given particle is considered to have a higher magnitude of charge than another if it will push out (or draw in) a positive test charge farther than the other particle.

A particle that pushes the test charge has positive charge, while a particle that pulls (or draws in) the test charge has negative charge. This is known as the sign of the charge. Magnitude of charge is unrelated to sign.

The experiment is conducted on a horizontal axis that measures from 20m in total: from –10m on the left to +10m on the right, with a measurement of 0m in the middle.

Experiment 1

Particle A is placed at position –5m on the horizontal axis. The test charge has a specific magnitude of charge and is located at +3m on that same axis. The result of the experiment is that the test charge is displaced to +7.5m.

Experiment 2

Particle B is placed at position –8m on the horizontal axis. The test charge has the same magnitude of charge as the previous experiment and is located at 0m on that same axis. The result of the experiment is that the test charge is displaced to –7.5m.

Experiment 3

Particle C is placed at position 0m on the horizontal axis. The test charge has the same magnitude of charge as the previous experiment and is located at +8m on that same axis. The result of the experiment is that the test charge is displaced to +10m.

Experiment 4

Particle D is placed at position –5.5m on the horizontal axis. The test charge has the same magnitude of charge as the previous experiment and is located at +2.5m on that same axis. The result of the experiment is that the test charge is displaced to +7.5m.

It can be inferred from the experiment that __________.

A particle accelerator functions by exerting a magnetic field on charged particles which are shot into the accelerator. The magnetic field causes the charged particles to move around in a circle of radius that can be predicted by the following equation, where is the mass of the particle in kilograms, is the initial speed at which the particle was shot in meters per second, is the charge of the particle in Coulombs, and is the strength of the magnetic field in Tesla.

If a given magnetic field's strength and its radius , what would the radius be at ?

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.

Which study provides stronger evidence against the students' prediction and why?

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 which trial(s) did the time of flight change between data points?

A physicist performs a series of experiments to determine the relative magnitude of electric charge on four particles. A given particle is considered to have a higher magnitude of charge than another if it will push out (or draw in) a positive test charge farther than the other particle.

A particle that pushes the test charge has positive charge, while a particle that pulls (or draws in) the test charge has negative charge. This is known as the sign of the charge. Magnitude of charge is unrelated to sign.

The experiment is conducted on a horizontal axis that measures from 20m in total: from –10m on the left to +10m on the right, with a measurement of 0m in the middle.

Experiment 1

Particle A is placed at position –5m on the horizontal axis. The test charge has a specific magnitude of charge and is located at +3m on that same axis. The result of the experiment is that the test charge is displaced to +7.5m.

Experiment 2

Particle B is placed at position –8m on the horizontal axis. The test charge has the same magnitude of charge as the previous experiment and is located at 0m on that same axis. The result of the experiment is that the test charge is displaced to –7.5m.

Experiment 3

Particle C is placed at position 0m on the horizontal axis. The test charge has the same magnitude of charge as the previous experiment and is located at +8m on that same axis. The result of the experiment is that the test charge is displaced to +10m.

Experiment 4

Particle D is placed at position –5.5m on the horizontal axis. The test charge has the same magnitude of charge as the previous experiment and is located at +2.5m on that same axis. The result of the experiment is that the test charge is displaced to +7.5m.

The results of Experiment 1 and 2 show that __________.

A physicist performs a series of experiments to determine the relative magnitude of electric charge on four particles. A given particle is considered to have a higher magnitude of charge than another if it will push out (or draw in) a positive test charge farther than the other particle.

A particle that pushes the test charge has positive charge, while a particle that pulls (or draws in) the test charge has negative charge. This is known as the sign of the charge. Magnitude of charge is unrelated to sign.

The experiment is conducted on a horizontal axis that measures from 20m in total: from –10m on the left to +10m on the right, with a measurement of 0m in the middle.

Experiment 1

Particle A is placed at position –5m on the horizontal axis. The test charge has a specific magnitude of charge and is located at +3m on that same axis. The result of the experiment is that the test charge is displaced to +7.5m.

Experiment 2

Particle B is placed at position –8m on the horizontal axis. The test charge has the same magnitude of charge as the previous experiment and is located at 0m on that same axis. The result of the experiment is that the test charge is displaced to –7.5m.

Experiment 3

Particle C is placed at position 0m on the horizontal axis. The test charge has the same magnitude of charge as the previous experiment and is located at +8m on that same axis. The result of the experiment is that the test charge is displaced to +10m.

Experiment 4

Particle D is placed at position –5.5m on the horizontal axis. The test charge has the same magnitude of charge as the previous experiment and is located at +2.5m on that same axis. The result of the experiment is that the test charge is displaced to +7.5m.

Which of the particles is negatively charged?

A particle separator functions by using a magnetic field and an electric field pointing perpendicularly. When a charged particle is launched into the particle separator, a constant electric force is exerted on the particle proportional to the particle's charge. Additionally, the magnetic field exerts a force on the particle that is in the opposite direction of the electric force and that is proportional to the particle's charge and velocity. A particle will make it through the particle separator only if the opposing magnetic forces and electric forces are equal in magnitude as they will not cause a net change in the particle's direction.

What can we infer would happen if a proton (a particle with a positive charge) were shot into the particle accelerator with an extremely low speed?

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 presented, what is the apparent relationship between mass and period ?

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.

If the temperature of iron were raised slightly in Study 1, what would be the most likely result?

Engineers are evaluating four potential technologies. These technologies are to be used as power plants that are considered "clean" energy. The estimated energy output of these plants were calculated and the resources needed to run these were also listed.

In a desert region, which two technologies can possibly be used?