Question

A 2.5-lb collar is attached to a spring and slides without friction along a circular rod in a vertical plane. The spring has an undeformed length of 4 in and a constant k = 20 lb/ft. Knowing that the collar is at rest at C and is given a slight push to get it moving, determine (a) the velocity of the collar as it passes through point A, and (b) the force exerted by the rod on the collar as it passes through point A. (30)

Answer 1

we ure energy conservation 3 A 4 energy at @ = energy att B spring Ni k x? > 5-4 c length at ce 7-3 7-3. hinch extension=' 4-4=0 (be) energy of Spring ake a Ž K (o)=0J Spring length at A - Tatu? Jan16 5 inch extension ?), inch at Ac } 20 ) ossa 0006944 lb-ft Spring length at B Bo 7 inch extension 7-423 spring energy at Ba ļ zo ½ 20 ( 1 ) SPB z) 0.625 lb-ft 2 Spring energy 2 SPA 2) 2

وفى Now apply E. = E PEAT FEA+ SPA +55 こ PEx + FBC (PEC-PEX). 2 2 į mu? (2.5x32:247) = KEA+SP mg (R) +0.06.944 1 (C205) v? +0.06944 5. + (02.5)v?+0.06944 VA= 6.124 ft/sec 46.958 Now E c = EB PEC + Effet spe PFE - PEB) - PEBTHER & SPB { my ² + 0.625 mg (2R) 2 mv²t0.625 9 3.916 : 1 (205) 8² +0.625 VB = 8.639 Ft/m 2

o' SP Sposo OL Sp- Spring force こ r os Tan' (12/4) 23.1985 N=mus (spcose) (20x 1 ) cos 23.148. (+) N = 160 12-14531 N = 159: 188 1b Normal force..on yodl N= .2.5 (6.124) at a