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.

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.

In Experiment 1, if the vertical distance drop is the same from points 2 to 3 as it is from points 1 to 2, which of the following most nearly approximates the value of X?

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.

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.

The Law of Conservation of Energy states that energy in the universe cannot be created or destroyed. Which of the following is most likely true in Experiment 2 as the ball moves from position 1 to position 3?

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.

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.

The work-energy theorem states that the work done on an object is equal to that object's change in kinetic energy:  

As the ball rolls from position 1 to position 2 in Experiment 1, which of the following is most likely 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.

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.

As the velocity of an object is increased fourfold, its kinetic energy most likely increases by a factor of:

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 associated table, along with measurements of the force of friction acting on the ball.

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.

As the height of an object is increased fourfold, its potential energy most likely increases by a factor of:

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.

It is discovered that a certain element in the Earth's crust emits beta particles, and furthermore, that beta particles can cause cancer. Should architects building houses in the areas where this phenomenon is found in high abundance be mandated to build basements with concrete walls with a minimum thickness of one meter?

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 2, the scientist could conclude that the particles, in order of increasing energy, are __________.

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.

A new type of radioactive material is discovered. A sample of it is placed into the lead chamber of the experimental setup described in Experiment 1. The detector detects radioactive particles at +1 cm. Which one of the following statements is true?

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 students' hypotheses were correct, what might be a worthwhile question for them to study next?

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.

Suppose a second group of students hypothesizes that the velocity of sound is inversely dependent upon the density of the substance through which the sound travels. Which study would best support their hypothesis and why?