Matter and Interactions
4th Edition
ISBN: 9781118875865
Author: Ruth W. Chabay, Bruce A. Sherwood
Publisher: WILEY
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Chapter 2, Problem 7Q
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A planar double pendulum consists of two point masses \[m_1 = 1.00~\mathrm{kg}, \qquad m_2 = 1.00~\mathrm{kg}\]connected by massless, rigid rods of lengths \[L_1 = 1.00~\mathrm{m}, \qquad L_2 = 1.20~\mathrm{m}.\]The upper rod is hinged to a fixed pivot; gravity acts vertically downward with\[g = 9.81~\mathrm{m\,s^{-2}}.\]Define the generalized coordinates \(\theta_1,\theta_2\) as the angles each rod makes with thedownward vertical (positive anticlockwise, measured in radians unless stated otherwise).At \(t=0\) the system is released from rest with \[\theta_1(0)=120^{\circ}, \qquad\theta_2(0)=-10^{\circ}, \qquad\dot{\theta}_1(0)=\dot{\theta}_2(0)=0 .\]Using the exact nonlinear equations of motion (no small-angle or planar-pendulumapproximations) and assuming the rods never stretch or slip, determine the angle\(\theta_2\) at the instant\[t = 10.0~\mathrm{s}.\]Give the result in degrees, in the interval \((-180^{\circ},180^{\circ}]\).
What are the expected readings of the ammeter and voltmeter for the circuit in the figure below? (R = 5.60 Ω, ΔV = 6.30 V)
ammeter
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simple diagram to illustrate the setup for each law- coulombs law and biot savart law
Chapter 2 Solutions
Matter and Interactions
Ch. 2.1 - (1) Two external forces. 〈40, −70, 0〉 N and 〈20,...Ch. 2.2 - (a) In the colliding students example, how was Δt,...Ch. 2.3 - (1) You drop a piece of paper, and observe that it...Ch. 2.4 - (1) For the third time step in the iterative...Ch. 2.5 - A ball is kicked on Earth from a location 〈9.0,...Ch. 2.6 - 6 (1) You push on a spring whose stiffness is 11...Ch. 2.6 - Prob. 7CPCh. 2.6 - Prob. 8CPCh. 2.7 - Jupiter goes around the Sun in 4333 Earth days....Ch. 2.7 - Some code would need to be added in front of each...
Ch. 2 - Prob. 1QCh. 2 - An object is moving in the +y direction. Which, if...Ch. 2 - You observe three carts moving to the left. Cart A...Ch. 2 - In order to pull a sled across a level field at...Ch. 2 - Prob. 5QCh. 2 - A comet passes near the Sun. When the comet is...Ch. 2 - A ball moves in the direction of the arrow labeled...Ch. 2 - A system is acted upon by two forces, 〈18, 47,...Ch. 2 - A truck driver slams on the brakes and the...Ch. 2 - At a certain instant a particle is moving in the...Ch. 2 - At t = 16.0 s an object with mass 4 kg was...Ch. 2 - A proton (mass 1.7 × 10−27 kg) interacts...Ch. 2 - A Ping-Pong ball is acted upon by the Earth, air...Ch. 2 - In outer space a rock of mass 5 kg is acted on by...Ch. 2 - A steel safe with mass 2200 kg falls onto...Ch. 2 - In a crash test, a truck with mass 2500 kg...Ch. 2 - A tennis ball has a mass of 0.057 kg. A...Ch. 2 - An object is on a collision course with the Earth...Ch. 2 - Prob. 20PCh. 2 - You throw a metal block of mass 0.25 kg into the...Ch. 2 - A small space probe, of mass 240 kg, is launched...Ch. 2 - A soccer ball of mass 0.43 kg is rolling with...Ch. 2 - As your spaceship coasts toward Mars, you need to...Ch. 2 - A runner starts from rest and in 3 s reaches a...Ch. 2 - The driver of a car traveling at a speed of 18 m/s...Ch. 2 - On a straight road with the +x axis chosen to...Ch. 2 - A ball of mass 0.4 kg flies through the air at low...Ch. 2 - For each graph of vx vs. t numbered 1–6 in Figure...Ch. 2 - A cart rolls with low friction on a track. A fan...Ch. 2 - Consider the three experiments described in...Ch. 2 - Consider the three experiments described in...Ch. 2 - You are a detective investigating why someone was...Ch. 2 - Prob. 34PCh. 2 - A ball is kicked from a location 〈9, 0, −6〉 (on...Ch. 2 - Prob. 37PCh. 2 - Prob. 38PCh. 2 - The performance of two different cars, car 1 and...Ch. 2 - A driver starts from rest on a straight test track...Ch. 2 - The stiffness of a particular spring is 40 N/m....Ch. 2 - A spring with a relaxed length of 25 cm and a...Ch. 2 - Prob. 43PCh. 2 - Prob. 44PCh. 2 - Prob. 46PCh. 2 - Prob. 47P
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- A circular coil with 100 turns and a radius of 0.05 m is placed in a magnetic field that changes at auniform rate from 0.2 T to 0.8 T in 0.1 seconds. The plane of the coil is perpendicular to the field.• Calculate the induced electric field in the coil.• Calculate the current density in the coil given its conductivity σ.arrow_forwardAn L-C circuit has an inductance of 0.410 H and a capacitance of 0.250 nF . During the current oscillations, the maximum current in the inductor is 1.80 A . What is the maximum energy Emax stored in the capacitor at any time during the current oscillations? How many times per second does the capacitor contain the amount of energy found in part A? Please show all steps.arrow_forwardA long, straight wire carries a current of 10 A along what we’ll define to the be x-axis. A square loopin the x-y plane with side length 0.1 m is placed near the wire such that its closest side is parallel tothe wire and 0.05 m away.• Calculate the magnetic flux through the loop using Ampere’s law.arrow_forward
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- 3. An Atwood machine consists of two masses, mA and m B, which are connected by an inelastic cord of negligible mass that passes over a pulley. If the pulley has radius RO and moment of inertia I about its axle, determine the acceleration of the masses mA and m B, and compare to the situation where the moment of inertia of the pulley is ignored. Ignore friction at the axle O. Use angular momentum and torque in this solutionarrow_forwardA 0.850-m-long metal bar is pulled to the right at a steady 5.0 m/s perpendicular to a uniform, 0.650-T magnetic field. The bar rides on parallel metal rails connected through a 25-Ω, resistor (Figure 1), so the apparatus makes a complete circuit. Ignore the resistance of the bar and the rails. Please explain how to find the direction of the induced current.arrow_forwardFor each of the actions depicted, determine the direction (right, left, or zero) of the current induced to flow through the resistor in the circuit containing the secondary coil. The coils are wrapped around a plastic core. Immediately after the switch is closed, as shown in the figure, (Figure 1) in which direction does the current flow through the resistor? If the switch is then opened, as shown in the figure, in which direction does the current flow through the resistor? I have the answers to the question, but would like to understand the logic behind the answers. Please show steps.arrow_forward
- When violet light of wavelength 415 nm falls on a single slit, it creates a central diffraction peak that is 8.60 cm wide on a screen that is 2.80 m away. Part A How wide is the slit? ΟΙ ΑΣΦ ? D= 2.7.10-8 Submit Previous Answers Request Answer × Incorrect; Try Again; 8 attempts remaining marrow_forwardTwo complex values are z1=8 + 8i, z2=15 + 7 i. z1∗ and z2∗ are the complex conjugate values. Any complex value can be expessed in the form of a+bi=reiθ. Find θ for (z1-z∗2)/z1+z2∗. Find r and θ for (z1−z2∗)z1z2∗ Please show all stepsarrow_forwardCalculate the center of mass of the hollow cone shown below. Clearly specify the origin and the coordinate system you are using. Z r Y h Xarrow_forward
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