Physics Answer Note #62

Question 1 The magnitude of the electrostatic force between two identical ions that are separated by a distance of 5.0 × 10-10 m is 3.7 × 10-9 N. (a) What is the charge of each ion? (b) How many electrons are "missing" from each ion (thus giving the ion its charge imbalance)? Answer To answer this question, we first need to understand the concept of electrostatic force and ions. Electrostatic force is the force that exists between charged particles, and ions are atoms or molecules that have gained or lost electrons, giving them a net positive or negative charge. In this case, we are dealing with two identical ions that are separated by a distance of 5.0 × 10-10 m and exerting a force of 3.7 × 10-9 N on each other. (a) To determine the charge of each ion, we can use Coulomb's Law, which states that the magnitude of the electrostatic force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Mathematically, this can be expressed as: F = k * (q1 * q2) / d^2 Where F is the electrostatic force, k is the Coulomb's constant, q1 and q2 are the charges of the particles, and d is the distance between them. Using the given values, we can rearrange the equation to solve for the charges of the ions: q1 * q2 = (F * d^2) / k Substituting the values, we get: q1 * q2 = (3.7 × 10-9 N * (5.0 × 10-10 m)^2) / (9.0 × 10^9 N*m^2/C^2) q1 * q2 = 1.233 × 10^-26 C^2 Since both ions are identical, their charges must be equal. So we can rewrite the equation as: q^2 = 1.233 × 10^-26 C^2 Taking the square root on both sides, we get: q = ± 1.11 × 10^-13 C Therefore, the charge of each ion is ± 1.11 × 10^-13 C. (b) In order to determine the number of "missing" electrons from each ion, we need to know the charge of an electron. The charge of an electron is -1.602 × 10^-19 C. So, an ion with a charge of + 1.11 × 10^-13 C must have lost (1.11 × 10^-13 C / 1.602 × 10^-19 C) = 69368 electrons. Similarly, an ion with a charge of - 1.11 × 10^-13 C must have gained 69368 electrons. Question 2 some important features of superconductivity in easy words short answer Answer The phenomenon of superconductivity is the ability of certain materials to conduct electricity with zero resistance when they are cooled below a certain temperature. This unique property allows these materials to carry electric current with almost no loss of energy. One of the most important features of superconductivity is the critical temperature, also known as Tc, which is the temperature below which a material becomes a superconductor. This temperature varies for different materials and is typically very low, often below 10 Kelvin (-263 degrees Celsius). Some materials, such as cuprates, can have critical temperatures well above the boiling point of liquid nitrogen, making them more practical for use in everyday applications. Another key feature of superconductors is their ability to expel magnetic fields, known as the Meissner effect. When a superconductor is placed in a magnetic field, it generates an equal and opposite magnetic field, causing the magnetic field lines to bend and exit the material. This allows superconductors to levitate over magnets, making them useful in applications such as magnetic levitation trains. In addition, superconductors have the property of flux pinning, which allows them to retain small amounts of magnetic field within their structure. This is advantageous because it stabilizes the superconductor and allows it to withstand higher magnetic fields without losing its superconducting properties. Superconductivity also has potential for practical applications such as efficient power transmission, faster and more powerful electronic devices, and more powerful magnets for use in medical imaging and scientific research. To learn more about superconductivity, some useful sources include "Introduction to Superconductivity" by Michael Tinkham and "Superconductivity - A Very Short Introduction" by Stephen J. Blundell. Additionally, the websites of organizations such as the National High Magnetic Field Laboratory and the American Physical Society provide comprehensive information on superconductivity research and advancements. Question 3 3. An elevator travels at a speed of 360 m/min up from the ground floor to the top floor. The height of the top floor, above the ground floor, is 340 m. Suppose that when an elevator begins to rise from ground level, you drop a coin from the top floor down the elevator shaft. Plot the position of the elevator and the coin as a function of time. At what height does the elevator meet the coin? Answer In this scenario, we are interested in the position of an elevator and a dropped coin as a function of time. To accurately plot the position of these objects, we will need to use kinematic equations, which describe the motion of objects in terms of position, velocity, and acceleration. Before diving into calculations, let's establish some important variables: - v: velocity (in m/min) - t: time (in min) - d: distance (in m) - a: acceleration (in m/min^2) First, let's determine the kinematic equations that will be most useful for our problem: 1) v = v0 + at 2) d = v0t + 1/2at^2 3) v^2 = v0^2 + 2ad We know that the elevator travels at a constant velocity of 360 m/min, and the height of the top floor is 340 m. We also know that the elevator moves in one direction (upwards) while the coin falls in the opposite direction (downwards). This means that the velocity of the coin will be negative. To find the position of the elevator and the coin at any given time, we will need to use the above equations and solve for distance (d). To make things easier, let's set the starting point (ground floor) as the origin or d = 0. Position of the elevator (de): From equation 1, we can rearrange and solve for distance (d) to find the position of the elevator at any given time: d = vt - 1/2at^2 Since the elevator is starting from rest (v = 0) and moving upward with a constant velocity of 360 m/min, equation 1 becomes: d = 0 + 1/2(0)t^2 d=0 This means that the position of the elevator remains at ground level (d = 0) until it starts moving. After that, its position increases at a constant rate of 360 m/min. Position of the coin (dc): To find the position of the coin, we can use equation 2: d = v0t + 1/2at^2 From the above equation, we can see that the position of the coin will be affected by both the initial velocity (v0) and the acceleration (a). Let's determine these values: - Initial velocity of the coin (vco): Since the coin is dropped from rest, the initial velocity (v0) will be 0. - Acceleration of the coin (aco): In this case, the acceleration of the coin will be due to gravity acting in the downward direction. This is represented by the acceleration due to gravity, g, which is usually given as 9.8 m/s^2. But since our problem uses m/min units, we will need to convert g to m/min^2 by multiplying by 60 (since there are 60 seconds in a minute). Therefore, aco = 9.8 * 60 = 588 m/min^2. Substituting these values into equation 2, we get: d = 0(t) + 1/2(588)t^2 d = 294t^2 At this point, we have two equations that represent the positions of the elevator and the coin as a function of time. To plot these equations on a graph, we can use a graphing tool like Desmos or Wolfram Alpha. The graph will show that the position of the elevator and the coin are both increasing as time passes, but the elevator's position increases at a constant rate while the coin's position increases at an increasing rate (due to acceleration). At what height does the elevator meet the coin? To find the height at which the elevator meets the coin, we will need to set the two position equations equal to each other and solve for time (t): de = dc 360t = 294t^2 Solving for t, we get t = 0 or t = 360/294 ≈ 1.22 min. Since t = 0 represents the starting point (when the coin is dropped and the elevator has not started moving yet), we can disregard it and only use t = 1.22 min. To find the corresponding distance, we can substitute this time value into either of the position equations. Using de = 360t, we get d = 360(1.22) = 439.2 m Therefore, Question 4 what is the difference between states and phases of matter? Answer The state and phase of matter refer to the physical form and arrangement of particles in a substance. Matter can exist in three different states: solid, liquid, and gas. These states can also undergo changes known as phase transitions, such as melting, freezing, and boiling. In this answer, we will explore the differences between states and phases of matter in detail. Firstly, let's define the term "state of matter". The state of matter is determined by the arrangement and movement of the particles in a substance. In solid matter, the particles are tightly packed and have fixed positions, causing them to vibrate in place. In liquids, the particles have more space between them, allowing them to move freely but still remain in close proximity. In gases, the particles are far apart and move freely, often colliding with one another and the walls of their container. On the other hand, the term "phase of matter" refers to the physical form of matter under specific conditions, such as temperature and pressure. These conditions can cause matter to undergo phase transitions and change from one phase to another. For example, when a solid is heated, it transitions into a liquid phase, and when a liquid is heated, it turns into a gaseous phase. Now, let's discuss the main differences between states and phases of matter. 1. Particle Arrangement: In states of matter, the arrangement of particles remains constant, while in phases of matter, the arrangement can change depending on the conditions. For example, in a solid, the particles remain tightly packed, but in a liquid or gas, the particles can move freely. 2. Particle Movement: In states of matter, the movement of particles is the same, while in phases of matter, the movement can vary. For instance, in a solid, the particles only vibrate, but in a gas, the particles move around freely and collide with each other and the container walls. 3. Energy: To change the state of matter, energy is required. For example, to melt an ice cube, heat energy must be added to change the solid state to a liquid state. However, to change a substance from one phase to another, energy is not always needed. For instance, when a gas turns into a liquid, this phase transition releases heat energy, fitting the liquid phase. 4. Pressure: Changes in pressure can also affect the state of matter but has less impact on the phase of matter. For instance, an increase in pressure can cause a gas to condense into a liquid, but it will not change the phase of matter. In conclusion, states and phases of matter both refer to the physical nature and arrangement of particles in a substance. The main difference between them is that states stay constant, whereas phases can change depending on different conditions. Understanding these differences is crucial in comprehending the behavior and properties of matter in various forms. Question 5 The electrical resistivity of many metals and alloys drops suddenly to zero when the specimen is cooled to a sufficiently low temperature, often a temperature in the liquid helium range. This phenomenon, called superconductivity, was observed first by Kamerlingh Onnes in Leiden in 1911, three years after he first liquified helium. At a critical temperature Tc the specimen undergoes a phase transition from a state of normal electrical resistivity to a superconducting state, Fig. 1. Superconductivity is now very well understood. It is a field with many practical and theoretical aspects. The length of this chapter and the relevant appendices reflect the richness and subtleties of the field. Summarize it Answer Superconductivity is a fascinating phenomenon that has been studied extensively by researchers since its discovery in 1911 by Kamerlingh Onnes. This discovery marked a major breakthrough in the field of physics and has led to many practical and theoretical applications. One of the defining characteristics of superconductors is their ability to conduct electricity with no resistance when they are cooled to temperatures below a critical temperature Tc. This phenomenon is known as the Meissner effect, where the magnetic field is expelled from the material as it transitions into the superconducting state. This property has significant practical applications, such as the use of superconducting materials in highly efficient power transmission and in advanced imaging technologies. In order to understand the mechanism behind superconductivity, researchers have developed various theories and models. The most widely accepted explanation is the BCS theory, named after its creators John Bardeen, Leon Cooper, and John Schrieffer. This theory describes how the movement of electrons through a superconductor is accompanied by the formation of electron pairs, known as Cooper pairs, which allows for the flow of electricity with no resistance. The study of superconductivity has also led to the discovery of exotic materials such as high-temperature superconductors, which exhibit superconducting properties at temperatures much higher than previously thought possible. This has opened up new avenues for research and potential applications of superconductivity. To fully understand the intricacies of superconductivity, researchers have delved into various aspects such as the effects of impurities, magnetic fields, and how the transition to the superconducting state occurs. This has resulted in a wealth of knowledge and experimental techniques that continue to expand our understanding of this phenomenon. In conclusion, superconductivity is a well-established field with a wide range of practical and theoretical applications. Its discovery has revolutionized the way we think about the flow of electricity and has shown us the potential for incredibly efficient technologies. As we continue to explore the complexities of superconductivity, it is evident that this field will continue to advance and contribute to many more scientific breakthroughs.