Question

a light rope connects two blocks with mass of 5kgs and 10kgs as shown. find the acceleration of the system and the tensions in the cable.

Answer 1

Solution.

$m_1=5kg;$

$m_2=10kg;$

$m_1a=T-m_1g;$

$m_2a=m_2g-T;$

$m_1a+m_2a=m_2g-m_1g;$

$a(m_1+m_2)=m_2g-m_1g;$

$a=\dfrac{m_2g-m_1g}{m_1+m_2};$

$a=\dfrac{10\sdot9.8-5\sdot9.8}{5+10}=3.27m/s^2;$

$T=m_1a+m_1g;$

$T=5\sdot9.8+5\sdot3.27=65.35N;$

Answer: $a=3.27m/s^2; T=65.35N.$