T1 ,T2 , T3 are tensions, find T2?

enter image source here

1 Answer
Dec 24, 2017

See below.

Explanation:

T_3-T_2 = m_3 a_3
T_2-T_1 = m_2 a_2
T_1 = m_1 a_1

but if the link between the masses is non-extensible

a_1=a_2=a_3 and T_3 = F then solving

{(F-T_2 = m_3 a),(T_2-T_1 = m_2 a),(T_1 = m_1 a):}

for T_1,T_2,a we have

{(T_1 = F(m_1)/(m_1 + m_2 + m_3)),(T_2=F (m_1 + m_2)/(m_1 + m_2 + m_3)),(a=F1 /(m_1 + m_2 + m_3)):}

Here

F = 40 [N]
m_1 = 10 [Kg]
m_2 = 6 [Kg]
m_3 = 4 [Kg]