First slide

Mechanical equilibrium force cases

Question

Two masses m and M are attached with strings as shown. For the system to be in equilibrium, we have

Moderate

A

$tanθ = 1 + \frac{2 M}{m}$
B

$tanθ = 1 + \frac{2 m}{M}$
C

$tanθ = 1 + \frac{M}{2 m}$
D

$tanθ = 1 + \frac{m}{2 M}$

Solution

$2 T_{1} \cos 45^{0} = m g$
$∴ T_{1} = \frac{m g}{\sqrt{2}}$
$T_{2} cosθ = \frac{T_{1}}{\sqrt{2}} = \frac{m g}{2}$
$T_{2} sinθ = M g + \frac{m g}{2}$
$tanθ = \frac{M g + \frac{m g}{2}}{\frac{m g}{2}} = 1 + \frac{2 M}{m}$

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