This problem is a continuation of Problem 45. You are part of a team working in a machine parts mechanic’s shop. An important customer has asked your company to provide springs with a very precise force constant k. You devise the electrical circuit shown in Figure P25.45 to measure the spring constant of each of the springs to be provided to the customer.
The circuit consists of two identical, parallel metal plates connected to identical metal springs, a switch, and a battery with emf ΔV. With the switch open, the plates are uncharged, are separated by a distance d, and have a capacitance C.
To provide a comparison value for the spring constant that you found in Problem 45, you slide a slab of material with dielectric constant κ and thickness t between the plates, so that it is in contact with one of the plates as shown in Figure P25.50. When the switch is closed, the plates become charged and attract each other. The distance between the plates changes by a factor f, after which the plates are in equilibrium between the spring forces and the attractive electric force between the plates. To keep the plates from going into oscillations, you hold each plate with insulating gloves as the switch is closed and apply a force on the plates that allows them to move together at a slow constant speed until they are at the equilibrium separation, at which point you can release the plates. Find an expression for the spring constant in terms of C, d, ΔV, k, t, and f.
Figure P25.50
Trending nowThis is a popular solution!
Chapter 25 Solutions
Physics for Scientists and Engineers
- This problem is a continuation of Problem 45. You are part of a team working in a machine parts mechanics shop. An important customer has asked your company to provide springs with a very precise force constant k. You devise the electrical circuit shown in Figure P25.45 to measure the spring constant of each of the springs to be provided to the customer. The circuit consists of two identical, parallel metal plates connected to identical metal springs, a switch, and a battery with emf V. With the switch open, the plates are uncharged, are separated by a distance d, and have a capacitance C. To provide a comparison value for the spring constant that you found in Problem 45, you slide a slab of material with dielectric constant and thickness t between the plates, so that it is in contact with one of the plates as shown in Figure P25.50. When the switch is closed, the plates become charged and attract each other. The distance between the plates changes by a factor f, after which the plates are in equilibrium between the spring forces and the attractive electric force between the plates. To keep the plates from going into oscillations, you hold each plate with insulating gloves as the switch is closed and apply a force on the plates that allows them to move together at a slow constant speed until they are at the equilibrium separation, at which point you can release the plates. Find an expression for the spring constant in terms of C, d, V, k, t, and f. Figure P25.50arrow_forward(a) What is the average power output of a heart defibrillator that dissipates 400 J of energy in 10.0 ms? (b) Considering the high-power output, why doesn’t the defibrillator produce serious bums?arrow_forwardYou are part of a team working in a machine parts mechanics shop. An important customer has asked your company to provide springs with a very precise force constant k. You dense the electrical circuit shown in Figure P25.45 to measure the spring constant of each of the springs to be provided to the customer. The circuit consists of two identical, parallel metal plates free to move, other than being connected to identical metal springs, a switch, and a battery with terminal voltage V. With the switch open, the plates are uncharged, are separated by a distance d, and have a capacitance C. When the switch is closed, the plates become charged and attract each other. The distance between the plates changes by a factor f, after which the plates are in equilibrium between the spring forces and the attractive electric force between the plates. To keep the plates from going into oscillations, you hold each plate with insulating gloves as the switch is closed and apply a force on the plates that allows them to move together at a slow constant speed until they are at the equilibrium separation, at which point you can release the plates. You determine an expression for the spring constant in terms of C, d, V, and f. Figure P25.45 Problems 45 and 50.arrow_forward
- The circuit shown in Figure P28.78 is set up in the laboratory to measure an unknown capacitance C in series with a resistance R = 10.0 M powered by a battery whose emf is 6.19 V. The data given in the table are the measured voltages across the capacitor as a function of lime, where t = 0 represents the instant at which the switch is thrown to position b. (a) Construct a graph of In (/v) versus I and perform a linear least-squares fit to the data, (b) From the slope of your graph, obtain a value for the time constant of the circuit and a value for the capacitance. v(V) t(s) In (/v) 6.19 0 5.56 4.87 4.93 11.1 4.34 19.4 3.72 30.8 3.09 46.6 2.47 67.3 1.83 102.2arrow_forwardFigure CQ20.7 shows a slidewire generator with motional cmf 0 when the wire at A slides across the top and bottom rails at constant velocity v0. (a) When the wire reaches B so that the area enclosed by the circuit is doubled, determine the ratio of the new cmf to the original cmf, /0. (b) If the wire's speed is doubled so that v = 2v0 determine the ratio /0. Figure CQ20.7arrow_forwardUnreasonable Results An inventor wants to generate 120V power by moving a 1.00mlong wire perpendicular to the Earth’s 5.00105T field. (a) Find the speed with which the wire must move. (b) What is unreasonable about this result? (c) Which assumption is responsible?arrow_forward
- Figure CQ20.7 shows a slidewire generator with motional cmf 0 when the wire at A slides across the top and bottom rails at constant velocity v0. (a) When the wire reaches B so that the area enclosed by the circuit is doubled, determine the ratio of the new cmf to the original cmf, /0. (b) If the wire's speed is doubled so that v = 2v0 determine the ratio /0. Figure CQ20.7arrow_forwardA student stands on a thick piece of insulating material, places her hand on top of a Van de Graaffgenerator, and then turns on the generator. Does she receive a shock?arrow_forwardThe values for the components of the circuit shown in the figure are V = 15 V, C = 3.5 μF, and L = 150 mH. When the capacitor is fully charged, you simultaneously open switch S1 and close switch S2. f = 219.65 Hz qmax = 5.25 * 10-5 C io = 0.07245 A What is the electromagnetic energy of the oscillating circuit, in joules?arrow_forward
- The plane of a square loop of wire with edge length a=0.200m is oriented Vertically and along an east west axis. The Earth’s magnitude field at this Points is of magnitude B=35.0 µT and is directed north ward at 35.0° below The horizontal.The total resistance of the loop and the wires connecting it To a sensitive ammeter is 0.500Ω. If the loop is suddenly collapsed by horizontal Forces are shown in figure p30.37, what total charge enters one terminal of the Ammeter?arrow_forward(a) What is the final speed (in m/s) of an electron accelerated from rest through a voltage of 87.5 MV by a negatively charged Van de Graaff terminal? (Ignore relativistic effects.) (b) What is unreasonable about this result? (c) Which assumptions are responsible?arrow_forwardAn 80 kg astronaut has gone outside his space capsule to do some repair work. Unfortunately, he forgot to lock his safety tether in place , and he has drifted 5.0 m away from the capsule . Fortunately, he has a 1000 W portable laser with fresh batteries that will operate it for 1.0 h. His only chance is to accelerate him self toward the space capsule by firing the laser in the opposite direction. He has a 10-h supply of oxygen. How long will it take him to reach safety ?arrow_forward
- Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning