 #1
Crystal037
 165
 7
 Homework Statement
 Three blocks of masses m1, m2 and m3 are connected as shown in the figure. All the surfaces are frictionless and the string and pulleys are light. Find the acceleration of the block of mass m1.
 Relevant Equations

2T=m1a1
m3gT=m3a3
Tm2g=m2a2
a2+a3=2a1
Since 2nd pulley accelerates downward with the same acceleration of m1, and because the string around pulley has a constant length, it must be that a2=−a1+ar and a3=−a1−ar, where ar is the relative acceleration between the pulley and m2.
From the above 4 equations, we are supposed to determine the effective mass pulling on m1 by comparing to the case where the 2nd pulley system is replaced with a single hanging mass. In my opinion the effective mass should be m2+m3 but it is given as
m(eff)= 4m2m3/(m2+m3)
I know that
m(eff)*g  2T=m(eff)a1
[m(eff) + m1]a1 = m(eff) *g
But how to find m(eff)
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