A rod of mass m and length L is hinged with a frictionless hinge at one end. The
ID: 1742760 • Letter: A
Question
A rod of mass m and length L is hinged with a frictionless hinge at one end. The moment of inertia about the center of mass is 1/12 mL2 Attached to the end of the rod opposite to the hinge there is a mass of magnitude 2m. The rod is released from rest in the horizontal position. What is the speed v2 of the mass 2m when the rod passes through the vertical po- sition? Consider the mass at the end of the rod to be a point particle.A rod of mass m and length L is hinged with a frictionless hinge at one end. The moment of inertia about the center of mass is 1/12 mL2 Attached to the end of the rod opposite to the hinge there is a mass of magnitude 2m. The rod is released from rest in the horizontal position. What is the speed v2 of the mass 2m when the rod passes through the vertical po- sition? Consider the mass at the end of the rod to be a point particle. 1. root 15gL/7 root 2gL root 2gL/5 root 2gl/3 root g/L root gL root 3gL/2 Root Gl/2
Explanation / Answer
Given that the mass of the rod is m Length of the rod is L mass of the attached body is 2m -------------------------------------------------------------------- Thecenter of mass of the rod and mass is = m(L/2) / (m+3m) = L/6 from the mass2m Applyconservation of energy at the horizontal and verticlepotion 3m *g*h = (1/2)I2 +3mg(L/6) 3m*g*L = (1/2)[ (1/12)mL2 + 2m*L2 ]2 + 3mg(L/6) 3m*g*L = (1/2)[ (1/12)mL2 + 2m*L2 ]2 + 3mg(L/6) 3m*g*L = (1/2)[ (25/12)mL2 ]2 + 3mg(L/6) 2 = (15/6)mgL /[ (25/24)mL2 ] = 12g/ 5L = ( 12g /5L)1/2 The speed of the mass 2mis v = L* =( 12gL /5)1/2Related Questions
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