Question

Version 3 Part B (Mechanical Encrgy and Conservation of Energy) Problem B1: Two blocks with masses m,-Skg and mz= 10kg hang on either side of a pulley as shown in figure below. Block m, is on an incline 0 30° and is attached to a spring whose constant is k 40N/m. The system is released from rest with the spring at is natural length. m2 Use the conservation of mechanical energy to find: 1) The maximum extension of the spring. 2) The speed of m, when the extension of the is 0.5m. Ignore friction and the mass of the pulley.

Answer 1

Given: 5kg 30 PART-1 Marimum ntension of he i observed at bun d's eguillibim positcon (ater release of system) DIAGRAM FREE BODY 0f (at equellb Yium) mass m2

Hen ce 7 - FREE BODY DIAGRAM Mass fosprng fre At guhι6γαm Z Fx' fs 7- m,q Smp sin&t fs But fs maximum extension af sprng mi9sme t k x -(i')

from (i) kr 3 Sx9.8 x S /0 x 9.8 73.5 73.S /.8375 7 Marimum eatension of Spring PART-2 dsme smoH Jo blck represents positon Red block at later stage of

initial heught f blaek mass,m Hught o mass, m, at later stage mitial heught of bloek HI 2 H2 of mass later heght mass, m2 _ from geornetry: Now applying methance al Initral enengy osystem potentral energy 7sprng tblck Lonservation enengy system potentral nengy +lock spreng + kimetre energy ot blocks

"gн тдHz rd' mgn т9 H gttmagth = kdl mg mg(h-sme 2 -m,gd smp ) Sim m2 (mit m2 m2-m 2 (lo-9.8x0. sin30 2(sh)v d o.5 m) given 0. 9666 0.98 Speed of m2 when entension is asm