http://politics.sgforums.com/forums/2297/topics/309959 en-US 60 <p>if the answer for the last question is dimensionally correct, apparently it will produce these 2 answers:</p> <p>&nbsp;</p> <p>&nbsp;</p> <p>L=0.64 m and Kmax=0.031 J</p> Sat, 08 Mar 2008 19:47:51 +0800 politics.sgforums.com:2297:309959:7915456 WoAiMeiMei http://politics.sgforums.com/forums/2297/topics/309959 <blockquote> <p>3) A thin uniform rod with mass m swings about an axis that passes through one end of the rod and is perpendicular to the plane of the swing. The rod swings with a period T and an angular amplitude of φm (assume this angle is sufficiently small to allow for the use of the equations in this chapter). (a) What is the length of the rod? (b) What is the maximum kinetic energy of the rod as it swings? State your answers in terms of the given variables, using g and π when applicable.</p> </blockquote> <p>a) cannot remember if it is done like that...</p> <p>let length be 2L, so CG of rod is at length L from the pivot</p> <p>T = 2π sqrt (L/g)<br /> Hence, L = (T/2π)^2 * g</p> <p>Length of rod = 2L = 2 * (T/2π)^2 * g</p> <p>&nbsp;</p> <p>b) At amplitude, vertical distance of CG from pivot = L cos φm<br /> Hence, PE gained from rest point = mgL (1 - cos φm)<br /> KE = 0 at this point</p> <p>At max KE, PE = 0<br /> By conservation of energy, max KE = mgL (1 - cos φm)</p> Fri, 07 Mar 2008 21:03:06 +0800 politics.sgforums.com:2297:309959:7913559 eagle http://politics.sgforums.com/forums/2297/topics/309959 <p>2) At t=0</p> <p>x = x<em>_m</em>cos(π/9)<br /> PE = 1/2 k x^2 = 1/2 k [ <em>x_m</em>cos(π/9) ]^2</p> <p>v = dx/dt = -ω<em>x_m</em>sin(ωt + φ) = -ω<em>x_m</em>sin(π/9)<br /> KE = 1/2 m v^2 = 1/2 m [ω<em>x_m</em>sin(π/9)] ^2<br /> But ω = 2π / T and T = 2<span>π sqrt (m/k)<br /> hence,</span> ω^2 = k/m</p> <p>Thus, KE =1/2 k [ <em>x_m</em>sin(π/9)] ^2</p> <p>So, KE/PE = cos(π/9)^2 / sin(π/9)^2 = [ tan(π/9) ]^2</p> <p>Ans: 0.132</p> Fri, 07 Mar 2008 20:56:03 +0800 politics.sgforums.com:2297:309959:7913543 eagle http://politics.sgforums.com/forums/2297/topics/309959 <p>hmm correction for q2 is:</p> <p>&nbsp;</p> <p>If the phase angle for a block-spring system in SHM is π/9 rad and the block's position is given by <em>x</em> = <em>x_m</em>cos(ωt + φ), what is the ratio of the kinetic energy to the potential energy at time <em>t</em> = 0?</p> <p>&nbsp;</p> <p>change: π/9 rad</p> Fri, 07 Mar 2008 13:50:27 +0800 politics.sgforums.com:2297:309959:7912881 WoAiMeiMei http://politics.sgforums.com/forums/2297/topics/309959 <p>yeah sorry i dont have answers ey...</p> Fri, 07 Mar 2008 13:19:56 +0800 politics.sgforums.com:2297:309959:7912806 WoAiMeiMei http://politics.sgforums.com/forums/2297/topics/309959 <p>Please post the answers if you have them (Homework Forum guidelines)</p> <p>Either someone will help you, or I find some time tonight to do the rest... The first question is to help you get started....</p> Fri, 07 Mar 2008 13:16:26 +0800 politics.sgforums.com:2297:309959:7912800 eagle http://politics.sgforums.com/forums/2297/topics/309959 <p>yay thanks eagle.. the first one is correct.</p> <p>&nbsp;</p> <p>the last one is the hardest apparently &gt;.&lt;</p> Fri, 07 Mar 2008 13:14:21 +0800 politics.sgforums.com:2297:309959:7912796 WoAiMeiMei http://politics.sgforums.com/forums/2297/topics/309959 <p>I think:</p> <p>1) a)</p> <p>Equation: a = -<span style="">ω2x</span></p> <p>So <span style="">ω2 = -a / x = 1382.857</span></p> <p><span style="">Thus ω = 2</span><span style="">πf = 37.186787</span></p> <p>f = 5.92 Hz</p> <p>&nbsp;</p> <p>b) T = 2<span style="">π sqrt (m/k)</span></p> <p>But T (period) = 1/f</p> <p>m = 0.332 kg (3 sf)</p> <p>&nbsp;</p> <p>c) <span style="font-family: arial,helvetica;">x = Acos(wt+f) -- (1)<br /> v = dx/dt = -wAsin(wt+f) =&gt;</span> <span style= "font-family: arial,helvetica;">Asin(wt+f) = -V /</span> <span style="font-family: arial,helvetica;">w -- (2)<br /></span></p> <p>(1) ^2 + (2) ^2 = A^2&nbsp; = x^2 + (-V/<span style= "font-family: arial,helvetica;">w )</span>^<span style= "font-family: arial,helvetica;">2</span></p> <p>So using the instant where x = 0.0875 and V = -17.5</p> <p>A = 0.479 m</p> <p>&nbsp;</p> <p>Someone confirm for me because no answer was posted...<br /> And lazy to do Q2 and Q3 right now.</p> <p>&nbsp;</p> Fri, 07 Mar 2008 12:58:31 +0800 politics.sgforums.com:2297:309959:7912749 eagle http://politics.sgforums.com/forums/2297/topics/309959 <p>actually i need help &gt;.&lt;</p> <p>&nbsp;</p> <p>&nbsp;</p> <p><br /> 1) An oscillator consists of a block attached to a spring (k = 460 N/m). At some time t, the position (measured from the system's equilibrium location), velocity, and acceleration of the block are x = 0.0875 m, v = -17.5 m/s, and a = -121 m/s2. Calculate (a) the frequency (in Hz) of oscillation, (b) the mass of the block, and (c) the amplitude of the motion.<br /> <br /> <br /> <br /> 2) If the phase angle for a block-spring system in SHM is π/9 rad and the block's position is given by x = xmcos(ωt + φ), what is the ratio of the kinetic energy to the potential energy at time t = 0?<br /> <br /> <br /> <br /> 3) A thin uniform rod with mass m swings about an axis that passes through one end of the rod and is perpendicular to the plane of the swing. The rod swings with a period T and an angular amplitude of φm (assume this angle is sufficiently small to allow for the use of the equations in this chapter). (a) What is the length of the rod? (b) What is the maximum kinetic energy of the rod as it swings? State your answers in terms of the given variables, using g and π when applicable.</p> Thu, 06 Mar 2008 18:16:54 +0800 politics.sgforums.com:2297:309959:7910418 WoAiMeiMei http://politics.sgforums.com/forums/2297/topics/309959