Illustrate only the following questions: Two identical, small insulating balls are suspended by separate 0.25 m threads that are attached to a common point on the ceiling. Each ball has a mass of 2 x 10-3 kg. Initially the balls are uncharged and hang straight down. They are then given identical positive charges and, as a result, spread apart with an angle 36° between the threads. Determine a) the charge on each ball and b) the tension in the threads.
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- In 1910 Rutherford performed a classic experiment in which he directed a beam of alpha particles at a thin gold foil. He unexpectedly observed a few of the particles scattered almost directly backward. This result was not consistent with then current models of atomic structure and led Rutherford to propose the existence of a very dense concentration of positive charge at the center of an atom—the atomic nucleus. The alpha particle has a charge of +2e and the gold nucleus a charge of +79e. Suppose that an alpha particle is initially a great distance from the gold, has a kinetic energy of 5.70 MeV (5.70 106 eV), and is headed directly at a gold nucleus. How close will the particle come to the center of the nucleus? Treat the nucleus and the alpha particle as point charges.Two hard rubber spheres, each of mass m = 14.9 g, are rubbed with fur on a dry day and are then suspended with two insulating strings of length L = 5.25 cm whose support points are a distance d = 3.06 cm from each other as shown in the figure below. During the rubbing process, one sphere receives exactly twice the charge of the other. They are observed to hang at equilibrium, each at an angle of 0 = 10.4° with the vertical. Find the amount of charge on each sphere. (Enter your answers from smallest to largest.)Suppose Earth and the Moon each carried a net negative charge −Q. Approximate both bodies as point asses and point charges.(a) What value of Q is required to balance the gravitational attraction between Earth and the Moon?(b) Does the distance between Earth and the Moon affect your answer? Explain.(c) How many electrons would be needed to produce this charge?
- A small metal sphere, carrying a net charge of qt= +7.5 mC, is held in a stationary position by insulating supports. A second small metal sphere, with net charge of 2' +3 mC and mass 2 g is projected toward q . When two spheres are 0.8 m apart, sa is moving toward qt with speed 22.0 mls, see Figure. Assume that the two spheres can be treated as point charges. Neglect the force of gravity. a) What is the speed ofqt when the spheres are 0.5 m apart† How close can q2 approach to q1 ?The dipole moment of the water molecule (H2O) is 6.17×10−30C⋅m. Consider a water molecule located at the origin whose dipole moment p⃗ points in the positive x direction. A chlorine ion (Cl−), of charge −1.60×10−19C, is located at x=3.00×10−9 meters. Assume that this x value is much larger than the separation d between the charges in the dipole, so that the approximate expression for the electric field along the dipole axis can be used. Find the magnitude of the electric force, ignoring the sign, that the water molecule exerts on the chlorine ion.In 1910 Rutherford performed a classic experiment in which he directed a beam of alpha particles at a thin gold foil. He unexpectedly observed a few of the particles scattered almost directly backward. This result was not consistent with then current models of atomic structure and led Rutherford to propose the existence of a very dense concentration of positive charge at the center of an atom—the atomic nucleus. The alpha particle has a charge of +2e and the gold nucleus a charge of +79e. Suppose that an alpha particle is initially a great distance from the gold, has a kinetic energy of 2.31 MeV (2.31 106 eV), and is headed directly at a gold nucleus. How close will the particle come to the center of the nucleus? Treat the nucleus and the alpha particle as point charges.
- Two identical balloons are inflated and charged in the same manner. They are tied by threads and hung from the same pivot point on the ceiling. The balloons hang down, with the threads making an angle of 13.9° with each other and the balloons being separated by a distance of 71.9 cm (center-to-center). Each balloon has a charge of -3.59x10-7 C. Draw a free-body diagram for the balloons and consider them to act as point objects. a. Calculate the force of electrical repulsion between the balloons. Force of Repulsion x-Component of Tension b. What is the horizontal component of force in the thread that supports either one of the balloons? y-Component of Tension d. What is the mass of either one of the balloons? x10^ Balloon Mass c. What is the vertical component of force in the thread that supports either one of the balloons? x10^ x10^ N x10^ kg N N I IIn 1910 Rutherford performed a classic experiment in which he directed a beam of alpha particles at a thin gold foil. He unexpectedly observed a few of the particles scattered almost directly backward. This result was not consistent with then current models of atomic structure and led Rutherford to propose the existence of a very dense concentration of positive charge at the center of an atom-the atomic nucleus. The alpha particle has a charge of +2e and the gold nucleus a charge of +79e. Suppose that an alpha particle is initially a great distance from the gold, has a kinetic energy of 5.44 MeV (5.44 x 106 eV), and is headed directly at a gold nucleus. How close will the particle come to the center of the nucleus? Treat the nucleus and the alpha particle as point charges.Jwo metal spheres, each of radius 4.2 cm, have a center-to-center separation of 1.9 m. Sphere 1 has a charge of + 1.5 x 10 C; sphere 2 has a charge of - 3.4 x 10 C. Assume that the separation is large enough for us to assume that the charge on each sphere is uniformly distributed (the spheres do not affect each other). With V = 0 at infinity, calçulate in volts (a) the potential at the point halfway between their centers and the potential on the surface of (b) sphere 1 and (c) sphere 2. (a) Number i Units (b) Number i Units (c) Number i Units
- Two hard rubber spheres, each of mass m = 14.9 g, are rubbed with fur on a dry day and are then suspended with two insulating strings of length L = 5.25 cm whose support points are a distance d = 3.06 cm from each other as shown in the figure below. During the rubbing process, one sphere receives exactly twice the charge of the other. They are observed to hang at equilibrium, each at an angle of 0 = 10.4° with the vertical. Find the amount of charge on each sphere. (Enter your answers from smallest to largest.) с C Need Help? Submit Answer m Read It L 18 mTwo very small spheres are initially neutral and separated by a distance of 0.590 m. Suppose that 2.21 x 1018 electrons are removed from one sphere and placed on the other. (a) What is the magnitude of the electrostatic force that acts on each sphere? (b) Is the force attractive or repulsive? (a) Number i Units (b) The force isIdentical 42 μC charges are fixed on an x axis at x = ±3.4 m. A particle of charge q = –20 μC is then released from rest at a point on the positive part of the y axis. Due to the symmetry of the situation, the particle moves along the y axis and has kinetic energy 1.2 J as it passes through the point x = 0, y = 4.5 m. (a) What is the kinetic energy of the particle as it passes through the origin? (b) At what negative value of y will the particle momentarily stop?