using System; using L=Science.Physics.GeneralPhysics; namespace Serway.Chapter07 { /// /// Example09: Block Pulled on a Rough Surface /// A 6.0 kg block initially at rest is pulled to the right /// along a horizontal surface by a constant horizontal /// force of 12 N. /// (A) Find the speed of the block after it has moved 3.0 m /// if the surfaces in contact have a coefficient of kinetic /// friction of 0.15. (This is Example 7.7, modified so that /// the surface is no longer frictionless) /// v_f = 1.8 m/s /// (B) Suppose the force F is applied at an angle \theta as /// shown in Figure 7.18b. At what angle should the force be /// applied to achieve the largest possible speed after the /// block has moved 3.0 m to the right? /// \theta = 8.5^{\circle} /// public class Example09 { public Example09() { } private string result; public string Result { get{return result;} } public void Compute() { L.Mass m = new L.Mass(); m.kg = 6.0; //(A) L.Force f = new L.Force(); f.X = 12.0; L.Displacement d = new L.Displacement(); d.X = 3.0; L.Force friction = new L.Force(); friction.X = - 0.15*m.kg*L.Constant.AccelerationOfGravity; L.Work[] W = new L.Work[2]; W[0] = new L.Work(f,d); W[1] = new L.Work(friction,d); L.KineticEnergy ki = new L.KineticEnergy(); ki.J = 0.0; L.KineticEnergy kf = new L.KineticEnergy(); kf.VariableQ = true; L.FundamentalLaw.WorkEnergyTheorem(ki,W,kf); L.Velocity vf = new L.Velocity(m,kf); result += Convert.ToString(vf.Norm)+"\r\n"; //(B) double theta = 0.0; for(int step = 0; step < 100; step++) { theta = 0.1*(double)step; L.Force fB = new L.Force(); fB.X = 12.0*Math.Cos(theta/180.0*Math.PI); fB.Y = 12.0*Math.Sin(theta/180.0*Math.PI); L.Force frictionB = new L.Force(); frictionB.X = - 0.15 *(m.kg*L.Constant.AccelerationOfGravity-fB.Y); L.Work[] WB = new L.Work[2]; WB[0] = new L.Work(fB,d); WB[1] = new L.Work(frictionB,d); L.KineticEnergy kfB = new L.KineticEnergy(); kfB.VariableQ = true; L.FundamentalLaw.WorkEnergyTheorem(ki,WB,kfB); L.Velocity vfB = new L.Velocity(m,kfB); result += Convert.ToString(theta)+" " +Convert.ToString(vfB.Norm)+"\r\n"; } } } } /* 1.7832554500127 0 1.7832554500127 0.1 1.78413096885236 0.2 1.78499581636509 0.3 1.78585000542198 0.4 1.78669354870976 0.5 1.78752645873205 0.6 1.7883487478105 0.7 1.789160428086 0.8 1.78996151151976 0.9 1.7907520098945 1 1.79153193481551 1.1 1.79230129771174 1.2 1.79306010983686 1.3 1.79380838227035 1.4 1.79454612591847 1.5 1.79527335151527 1.6 1.79599006962363 1.7 1.79669629063618 1.8 1.79739202477629 1.9 1.79807728209897 2 1.79875207249183 2.1 1.79941640567593 2.2 1.8000702912067 2.3 1.80071373847482 2.4 1.80134675670701 2.5 1.80196935496692 2.6 1.80258154215592 2.7 1.80318332701392 2.8 1.80377471812012 2.9 1.8043557238938 3 1.80492635259508 3.1 1.80548661232565 3.2 1.80603651102946 3.3 1.80657605649349 3.4 1.80710525634837 3.5 1.80762411806912 3.6 1.80813264897574 3.7 1.80863085623393 3.8 1.80911874685566 3.9 1.80959632769983 4 1.81006360547283 4.1 1.81052058672918 4.2 1.81096727787203 4.3 1.8114036851538 4.4 1.81182981467668 4.5 1.81224567239314 4.6 1.8126512641065 4.7 1.81304659547142 4.8 1.81343167199435 4.9 1.81380649903404 5 1.81417108180203 5.1 1.81452542536301 5.2 1.81486953463538 5.3 1.81520341439157 5.4 1.81552706925848 5.5 1.81584050371792 5.6 1.81614372210694 5.7 1.81643672861822 5.8 1.81671952730045 5.9 1.81699212205863 6 1.81725451665447 6.1 1.81750671470663 6.2 1.8177487196911 6.3 1.81798053494146 6.4 1.81820216364917 6.5 1.81841360886386 6.6 1.81861487349354 6.7 1.8188059603049 6.8 1.81898687192353 6.9 1.81915761083412 7 1.81931817938071 7.1 1.81946857976684 7.2 1.81960881405578 7.3 1.81973888417069 7.4 1.81985879189477 7.5 1.81996853887143 7.6 1.82006812660442 7.7 1.82015755645795 7.8 1.82023682965681 7.9 1.82030594728649 8 1.82036491029325 8.1 1.82041371948421 8.2 1.82045237552741 8.3 1.82048087895187 8.4 1.82049923014765 8.5 1.82050742936586 8.6 1.82050547671869 8.7 1.82049337217942 8.8 1.82047111558242 8.9 1.82043870662313 9 1.82039614485805 9.1 1.82034342970468 9.2 1.82028056044148 9.3 1.82020753620782 9.4 1.82012435600388 9.5 1.82003101869061 9.6 1.81992752298959 9.7 1.81981386748295 9.8 1.81969005061322 9.9 1.81955607068324 */