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Review. A light, unstressed spring has length d. Two identical particles, each with charge q, are connected to the opposite ends of the spring. The particles are held stationary a distance d apart and then released at the same moment. The system then oscillates on a frictionless, horizontal table. The spring has a bit of internal kinetic friction, so the oscillation is damped. The particles eventually stop vibrating when the distance between them is 3d. Assume the system of the spring and two charged particles is isolated. Find the increase in internal energy that appears in the spring during the oscillations.
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Chapter 25 Solutions
Physics for Scientists and Engineers, Technology Update, Hybrid Edition (with Enhanced WebAssign Multi-Term LOE Printed Access Card for Physics)
- Four charged particles are at rest at the corners of a square (Fig. P26.14). The net charges are q1 = q2 = 2.65 C and q3 = q4 = 5.15 C. The distance between particle 1 and particle 3 is r13 = 1.75 cm. a. What is the electric potential energy of the four-particle system? b. If the particles are released from rest, what will happen to the system? In particular, what will happen to the systems kinetic energy as their separations become infinite? FIGURE P26.14 Problems 14, 15, and 16.arrow_forwardReview. Two insulating spheres have radii 0.300 cm and 0.500 cm, masses 0.100 kg and 0.700 kg, and uniformly distributed charges 2.00 C and 3.00 C. They are released from rest when their centers are separated by 1.00 m. (a) How fast will each be moving when they collide? (b) What If? If the spheres were conductors, would the speeds be greater or less than those calculated in part (a)? Explain.arrow_forwardFour charged particles are at rest at the corners of a square (Fig. P26.14). The net charges are q1 = q2 = +2.65 C and q3 = q4 = 5.15 C. The distance between particle 1 and particle 3 is r13 = 1.75 cm. a. What is the electric potential energy of the four-particle system? b. If the particles are released from rest, what will happen to the system? In particular, what will happen to the systems kinetic energy?arrow_forward
- An electroscope is a device used to measure the (relative) charge on an object (Fig. P23.20). The electroscope consists of two metal rods held in an insulated stand. The bent rod is fixed, and the straight rod is attached to the bent rod by a pivot. The straight rod is free to rotate. When a positively charged object is brought close to the electroscope, the straight movable rod rotates. Explain your answers to these questions: a. Why does the rod rotate in Figure P23.20? b. If the positively charged object is removed, what happens to the electroscope? c. If a negatively charged object replaces the positively charged object in Figure P23.20, what happens to the electroscope? d. If a charged object touches the top of the fixed conducting rod and is then removed, what happens to the electroscope?arrow_forwardOne end of a light spring with force constant k = 125 N/m is attached to a wall, and the other end to a metal block with charge qA = 2.00 C on a horizontal, frictionless table (Fig. P23.34). A second block with charge qB = 3.60 C is brought close to the first block. The spring stretches as the blocks attract each other so that at equilibrium, the blocks are separated by a distance d = 12.0 cm. What is the displacement x of the spring? Figure P23.34arrow_forwardA Two positively charged particles, each with charge Q, are held at positions (a, 0) and (a, 0) as shown in Figure P23.73. A third positively charged particle with charge q is placed at (0, h). a. Find an expression for the net electric force on the third particle with charge q. b. Show that the two charges Q behave like a single charge 2Q located at the origin when the distance h is much greater than a. Figure P23.73 Problems 73 and 74.arrow_forward
- Two small beads having positive charges q1 = 3q and q2 = q are fixed at the opposite ends of a horizontal insulating rod of length d = 1.50 m. The bead with charge q1 is at the origin. As shown in Figure P19.7, a third small, charged bead is free to slide on the rod. (a) At what position x is the third bead in equilibrium? (b) Can the equilibrium be stable?arrow_forwardFour balls, each with mass m, are connected by four nonconducting strings to form a square with side a as shown in Figure P25.74. The assembly is placed on a nonconducting. frictionless. horizontal surface. Balls 1 and 2 each have charge q, and balls 3 and 4 are uncharged. After the string connecting halls 1 and 2 is cut, what is the maximum speed of balls 3 and 4?arrow_forwardTwo 5.00-nC charged particles are in a uniform electric field with a magnitude of 625 N/C. Each of the particles is moved from point A to point B along two different paths, labeled in Figure P26.65. a. Given the dimensions in the figure, what is the change in the electric potential experienced by the particle that is moved along path 1 (black)? b. What is the change in the electric potential experienced by the particle that is moved along path 2 (red)? c. Is there a path between the points A and B for which the change in the electric potential is different from your answers to parts (a) and (b)? Explain. FIGURE P26.65 Problems 65, 66, and 67.arrow_forward
- Problems 72, 73, and 74 are grouped. 72. A Figure P26.72 shows a source consisting of two identical parallel disks of radius R. The x axis runs through the center of each disk. Each disk carries an excess charge uniformly distributed on its surface. The disk on the left has a total positive charge Q, and the disk on the right has a total negative charge Q. The distance between the disks is 3R, and point A is 2R from the positively charged disk. Find an expression for the electric potential at point A between the disks on the x axis. Approximate any square roots to three significant figures. FIGURE P26.72 Problems 72, 73, and 74.arrow_forwardReview. A block having mass m and charge + Q is connected to an insulating spring having a force constant k. The block lies on a frictionless, insulating, horizontal track, and the system is immersed in a uniform electric field of magnitude E directed as shown in Figure P24.6. The block is released from rest when the spring is unstretched (at x = 0). We wish to show that the ensuing motion of the block is simple harmonic. (a) Consider the system of the block, the spring, and the electric field. Is this system isolated or nonisolated? (b) What kinds of potential energy exist within this system? (c) Call the initial configuration of the system that existing just as the block is released from rest. The final configuration is when the block momentarily comes to rest again. What is the value of x when the block comes to rest momentarily? (d) At some value of x we will call x = x0, the block has zero net force on it. What analysis model describes the particle in this situation? (c) What is the value of x0? (f) Define a new coordinate system x such that x = x x0. Show that x satisfies a differential equation for simple harmonic motion. (g) Find the period of the simple harmonic motion. (h) How does the period depend on the electric field magnitude? Figure P24.6arrow_forwardA proton is located at the origin, and a second proton is located on the x-axis at x = 6.00 fm (1 fm = 10-15 m). (a) Calculate the electric potential energy associated with this configuration. (b) An alpha particle (charge = 2e, mass = 6.64 1027 kg) is now placed at (x, y) = (3.00, 3.00) fm. Calculate the electric potential energy associated with this configuration. (c) Starting with the three-particle system, find the change in electric potential energy if the alpha particle is allowed to escape to infinity while the two protons remain fixed in place. (Throughout, neglect any radiation effects.) (d) Use conservation of energy to calculate the speed of the alpha particle at infinity. (e) If the two protons are released from rest and the alpha panicle remains fixed, calculate the speed of the protons at infinity.arrow_forward
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