Practice Problem 4.4.8: The 90-kg man, whose center of gravity is at G, is climbing a uniform ladder. The length of the ladder is 5 m, and its mass is 20 kg. Friction may be neglected. (a) Compute the magnitudes of the reactions at A and B for x = 1.5m.(b) Find the distance x for which the ladder will be ready to fall. L=5 m 1.2 m -1.6 m–|

Practice Problem 4.4.8: The 90-kg man, whose center of gravity is at G, is climbing a uniform ladder. The length of the ladder is 5 m, and its mass is 20 kg. Friction may be neglected. (a) Compute the magnitudes of the reactions at A and B for x = 1.5m.(b) Find the distance x for which the ladder will be ready to fall. L=5 m 1.2 m -1.6 m–|

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Exercise 2 A naval cannon (105 mm, scale 35) fires a shell of mass M = 18 kg with a speed of magnitude Vo = 700 m/s. and at an angle of shooting a. Given g = 9.8 m/s, Alpha=D45° %3D A Study in the abscense of air resistance. Taking : Origin of time : the launching instant; Origin of position : the launching point O; (xOy) : the vertical plane of motion of the shell. yt Vo a X 1) Determine the acceleration vector of the shell. 2) Determine, in term of t, the velocity vector of thr shell 3) Calculate the magnitude of the velocity vextor at the maximum height. 4) Determine, in term of t, the position vector of the shell.
Exercise 5 Suppose that the motion of a continuous medium is given by the 1D mapping olge, x = (1+ t)X and the temperature distribution along X in the reference description is described by P(X, t) = Xt² %3D Compute the material time derivative field (x, t) written in the spatial configuration.
Problem 2. 4.6 The homogeneous triangular plate has a mass of 12 kg. Draw the FBD of the plate for each set of supports shown in (a)–(d) and determine the number of unknowns. 210 mm Friction 120 mm Friction Frictionless 60 30° (a) (b) 45° Friction Fig. P4.6
A block of mass m = 1 kg is sliding at 2 m/s [E] on a frictionless surface. A curved frictionless ramp of unknown mass M is at rest on but not attached to the same frictionless surface, as shown at right. The block slides up the ramp after reaching it. 1) The block rises to a maximum height h = 0.125 m on the ramp. What is the velocity of the block at the instant it is at that maximum vertical height? 2) What is the velocity of the block at the instant the block loses contact with the ramp?
Self-test 1B.1 Derive the expression for (v²) in eqn 1B.7 by evaluating the integral in eqn 1B.6 with n = 2.
Problem 4.4 The uniform, horizontal beam shown in Fig. 4.51 is hinged to the wall at point A and supported by a cable attached to the beam at point C. Point C also represents the center of gravity of the beam. At the other end, the cable is attached to the wall so that it makes an angle 0 = 68° with the horizontal. If the length of the beam is 1= 4 m and the weight of the beam is W = 400 N, calculate the tension T in the cable and components of the reaction force on the beam at point A. レ B Answers: T = 431 N RAX = 162 N (→) RAy = 0 Fig. 4.51 Problem 4.4
Problem 12.15 Part A At what altitude above the Earth's surface is the acceleration due to gravity equal to g/6? h = Γ' Ε, αβ, ΔΣ, Submit My Answers Give Up reset shortcuts ? help m
Practice Problem 3.4.6: Determine the resultant of the three forces if (a) e = 30•; and 500 N (b) e = 45 degrees. %3D 300 mm 500 N 500 N
7.2 please answer part d, previous parts are answered. In order to answer part d, you need to use the expression from part c.
Exercise b. Hard spin glasses.Physicists use a model called an Ising spin glass to study magnetic materials. We havea graph G = (V, E) and a function J : E → Z, where J(u, v) is the interaction strengthof edge {u, v} ∈ E. A state is a function s : V → {−1, +1}.1 The energy of a states is H(s) = −P{u,v}∈EJ(u, v) · s(u) · s(v).2 An edge {u, v} is called ferromagnetic ifJ(u, v) > 0, and antiferromagnetic if J(u, v) < 0. Ferromagnetic edges “pressure” uand v to be the same spin, and antiferromagnetic edges “pressure” them to be different.We wish to find the ground state, i.e., values of s(u) for each u ∈ V that minimize theenergy. Phrased as a decision problem, we ask whether a state exists below a certainenergy threshold:Spin-GlassInput: a graph G = (V, E), interaction strengths J : E → Z, and a threshold hˆ ∈ ZQuestion: is there a state s : V → {−1, +1} with H(s) ≤ hˆ?Show that Spin-Glass is NP-complete.1Each s(u) is called the spin of u; if u is a magnetic domain, think of s(u) as…
Problem 4.19 A bead slides down a wire. You want to determine the shape the wire must have for the bead to slide from its initial position to its final position in the least amount of time. (This is called the "brachistochrone" problem.) Note that the quantity to be minimized is the time and that dt = ds/v where the velocity v is given by conservation of energy. I do not expect you to actually solve this problem; it will be sufficient if you write the functional that describes the system.12