Question: A two-step pulley supports two weights A=40N & B=60N as shown. Find the downward acceleration of A if radius of bigger pulley is double that of the smaller one. Neglect friction & inertia of pulley.
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Mumbai University > FE > Sem 1 > Engineering Mechanics

Marks : 04

Years : DEC 2015

 modified 2.9 years ago  • written 2.9 years ago by Aksh_31 • 680
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Let length of strings associated with A & B be l1 & l2 respectively.

As $2r2 = r1 \\ 2l2 = l1$

Now, as total length of string remains constant

$2l2 - l1 = c$_____[as l2 is increasing & l1 is decreasing]

Differentiating w.r.t. t

$2v2 = v1$ _____(i)

Differentiating w.r.t. t

$2a2 = a1$ _____(ii)

Now, considering block B

Applying newton's second law

$\sum Fy= may \\ T - 60 = (60/9.81)*a2 \\ T - 6.17a2 = 60$ _____(iii)

Considering block A

$\sum Fy= may \\ 40 - T = (40/9.81)*a1 \\ T + 4.08a1 = 40$ _____(iv)

Using equations (ii),(iii) & (iv)

We get, $a1= -2.79 m/s2 , a2 = 1.395 m/s2$ &$T=51.39 N$

Downward acceleration of A is -2 .79 m/s2