what will be the relationship between the acceleration of the
masses shown in the figure?
Accn. of upper m = -8 times accn. of lower m
can you show proof?
Each movable pulley contributes factor of 2. So 2 x 2 x 2.
let acceleration of topmost mass 'm' be a1 and acceleration of pulleys viz. 2nd,3rd,4th from the first pulley be a2,a3,&a4 respectively.
applying contraint relation-
eqn 1-for pulley 2nd
a1-a2-a2=0
→a1=2a2
eqn 2- for pulley 3rd
-a3-a3+a2=0
→a2=2a3
eqn 3- for pulley 4th
a3-a4-a4=0
→a3=2a4
solving eqns 1,2 &3 ,we get
a1=2×2×2×a4=8a4
therefore,acceneration of topmost mass is 8 times the lowest mass.
Haroon you should first of all remember that "where ever tension doubles acc. becomes half"
So the upper mass has Tension=T
=> its acc. let be a
The lower mass has tension=8T
=>its acc will be a/8 times of the first mass.
Thats it!!!