🔑:A great question about a classic experiment in physics!The Tolman-Stewart experiment, conducted by Richard Chace Tolman and Thomas Dale Stewart in 1916, was a landmark study that helped establish the electron theory of metals. The primary outcome of the experiment was the measurement of the ratio of the mass of an electron to its charge, which provided strong evidence for the existence of electrons as particles and their role in carrying electric current in metals.In the experiment, Tolman and Stewart used a rotating cylinder of metal, which was initially charged with a certain amount of electricity. As the cylinder rotated, the electrons in the metal were expected to be thrown outward due to centrifugal force, causing a potential difference between the center and the edge of the cylinder. By measuring this potential difference, the researchers were able to calculate the ratio of the mass of an electron to its charge.The experiment yielded a value for the electron's mass-to-charge ratio that was consistent with the predictions of the electron theory, which posited that electric current in metals is carried by electrons. This result provided strong evidence for the existence of electrons as particles and their role in conducting electricity in metals.The Tolman-Stewart experiment contributed significantly to our understanding of the composition of electric current in metals in several ways:1. Confirmation of the electron theory: The experiment provided direct evidence for the existence of electrons as particles and their role in carrying electric current in metals, confirming the predictions of the electron theory.2. Measurement of electron properties: The experiment allowed for the measurement of the electron's mass-to-charge ratio, which was an important step in understanding the properties of electrons and their behavior in metals.3. Understanding of conduction in metals: The experiment helped establish that electric current in metals is carried by electrons, which are free to move within the metal lattice. This understanding has had a profound impact on our knowledge of electrical conduction in metals and the development of electronic devices.4. Foundation for quantum mechanics: The Tolman-Stewart experiment, along with other experiments of the time, laid the foundation for the development of quantum mechanics, which has revolutionized our understanding of the behavior of electrons and other particles at the atomic and subatomic level.In summary, the Tolman-Stewart experiment was a groundbreaking study that provided strong evidence for the existence of electrons as particles and their role in carrying electric current in metals, contributing significantly to our understanding of the composition of electric current in metals and the development of modern physics.

🔑:## Step 1: Understand the problem and the given valuesThe individual has a near point of 15 cm, meaning they can see objects clearly at a distance of 15 cm without corrective lenses. The far point is 60 cm, indicating that without corrective lenses, the person can see objects clearly only at distances of 60 cm or more. We need to find the lens power required to correct this nearsightedness and the new near point when wearing corrective lenses.## Step 2: Calculate the focal length of the corrective lensFor a nearsighted person, the corrective lens is diverging, which means it spreads out light rays. The focal length (f) of the lens can be found using the formula for a thin lens, where the object distance is the far point (60 cm) and the image distance is the near point (15 cm) of the normal eye, which we want to achieve with correction. However, the correct approach involves using the lensmaker's equation and considering the relationship between the far point, near point, and the focal length of the corrective lens.## Step 3: Apply the lensmaker's equationThe lensmaker's equation is ( frac{1}{f} = frac{1}{d_o} + frac{1}{d_i} ), where ( f ) is the focal length of the lens, ( d_o ) is the object distance, and ( d_i ) is the image distance. For a corrective lens to correct nearsightedness, it should make the far point of the eye (60 cm) appear at infinity (or a very large distance) when looking through the lens. Thus, we want the lens to create an image at the near point of the normal eye (25 cm, which is the standard near point for a normal eye, not the given 15 cm near point of the nearsighted individual) when the object is at 60 cm. However, the question asks us to work with the given near point of 15 cm for the nearsighted individual, which is not standard.## Step 4: Calculate the lens powerThe power of a lens (P) is given by ( P = frac{1}{f} ), where ( f ) is in meters. To correct the nearsightedness, we need to find ( f ) for a lens that makes an object at 60 cm appear at 15 cm (the nearsighted person's near point, which we are using as the basis for our calculation, even though typically we'd consider correction to the standard near point). However, for a diverging lens to correct nearsightedness, we consider the far point (60 cm) as the object distance and aim for an image distance that would correct the vision to normal, but the question's framing suggests calculating the power needed based on given parameters.## Step 5: Correct calculation approachGiven that the near point is 15 cm and the far point is 60 cm, the lens should correct the vision so that the far point appears at infinity. The correct formula to use is ( frac{1}{f} = frac{1}{60} - frac{1}{15} ) because we're considering the change in the focal length needed to correct the vision from the far point to the near point of the individual, not to the standard near point.## Step 6: Perform the calculation( frac{1}{f} = frac{1}{60} - frac{1}{15} = frac{1}{60} - frac{4}{60} = -frac{3}{60} = -frac{1}{20} ) meters. The power ( P = frac{1}{f} = -frac{1}{20} ) diopters.## Step 7: Determine the new near pointWhen wearing corrective lenses, the new near point would theoretically be the standard near point for a normal eye, which is about 25 cm, as the corrective lens adjusts the focal length to match the normal eye's capabilities. However, the question asks for calculations based on the given near point, and the primary calculation was to find the lens power needed to correct the vision.The final answer is: boxed{-5.0}

🔑:## Step 1: Calculate the initial potential energy of the dipole in the electric field.The potential energy (U) of a dipole in an electric field is given by the equation U = -pEcos(θ), where p is the magnitude of the dipole moment, E is the magnitude of the electric field, and θ is the angle between the dipole moment and the electric field. Given p = 0.1 C-m, E = 400 N/C, and θ = 135º, we can calculate the initial potential energy.## Step 2: Substitute the given values into the equation for potential energy.U = -0.1 C-m * 400 N/C * cos(135º). Recall that cos(135º) = -√2/2.## Step 3: Perform the calculation of the initial potential energy.U = -0.1 * 400 * (-√2/2) = 20√2 J.## Step 4: Consider the conversion of potential energy to kinetic energy.As the dipole moves in the electric field, its potential energy converts into kinetic energy. The maximum kinetic energy (K) will be equal to the initial potential energy (U) when the dipole is aligned with the electric field, assuming no energy is lost to other forms.## Step 5: Calculate the maximum kinetic energy.Since energy is conserved in this system (ignoring friction or other losses), the maximum kinetic energy (K_max) that the dipole will attain is equal to the initial potential energy. Therefore, K_max = U.The final answer is: boxed{20sqrt{2}}

🔑:## Step 1: Understand the scenarioWe have a negative mass and a positive mass, with the negative mass rotating around the fixed positive mass. According to Newton's law of universal gravitation, every point mass attracts every other point mass by a force acting along the line intersecting both points.## Step 2: Determine the force between the massesGiven that the force of gravity between two masses is given by (F = G frac{m_1 m_2}{r^2}), where (G) is the gravitational constant, (m_1) and (m_2) are the masses, and (r) is the distance between the centers of the masses, we can see that if one of the masses is negative, the force will be repulsive because the product (m_1 m_2) will be negative.## Step 3: Apply Newton's second lawNewton's second law states that (F = ma), where (F) is the net force acting on an object, (m) is its mass, and (a) is its acceleration. For the positive mass (let's call it (M)) which is fixed, the force acting on it due to the negative mass (let's call it (-m)) is (F = G frac{M (-m)}{r^2}), and for the negative mass, the force is (F = G frac{(-m) M}{r^2}). The accelerations of the two masses can be found by dividing these forces by their respective masses.## Step 4: Calculate the accelerationsFor the positive mass (M), the acceleration (a_M) is given by (a_M = frac{F}{M} = frac{G frac{M (-m)}{r^2}}{M} = -G frac{m}{r^2}). For the negative mass (-m), the acceleration (a_{-m}) is given by (a_{-m} = frac{F}{-m} = frac{G frac{(-m) M}{r^2}}{-m} = -G frac{M}{r^2}).## Step 5: Analyze the accelerationsThe acceleration of the positive mass (M) is directed towards the negative mass because the force is attractive but since (M) is fixed, it doesn't move. The acceleration of the negative mass is in the direction away from the positive mass because the force is repulsive. However, the negative mass is rotating around the positive mass, which implies a centripetal acceleration towards the positive mass. The repulsive force provides the centripetal force needed for this rotation, which is unusual because typically, attraction provides the centripetal force.## Step 6: Relate the accelerationsSince the negative mass is rotating, its acceleration towards the center (centripetal acceleration) is (a_{-m} = frac{v^2}{r}), where (v) is the velocity of the negative mass. This acceleration is provided by the repulsive force due to the positive mass. Thus, (-G frac{M}{r^2} = frac{v^2}{r}), which can be rearranged to find (v) in terms of (G), (M), and (r).The final answer is: boxed{-G frac{M}{r^2} = frac{v^2}{r}}