Answer to Question #259489 in Mechanics | Relativity for Karthi

Question

Two blocks of weight 50 N and 200 N connected by a cord rest on two inclined planes asshown in figure. Determine the maximum tension in the cord when limiting friction conditions develop for both blocks.W 200NW-SON2012STO - 111=50NW2=200NAngle at A is 450Angle at B is 30°Co-efficient of Friction at W1 is 0.25Co-efficient of friction at W2 is 0.12

Answer 1

for weight 200 N:

$m_1a=200sin30\degree-200\cdot 0.25cos30\degree-T=56.7-T$

for weight 50 N:

$m_2a=-50sin45\degree-50\cdot 0.12cos45\degree+T=T-39.6$

acceleration:

$a=(56.7-39.6)/(m_1+m_2)=9.8(56.7-39.6)/(200+50)=0.67$ m/s²

tension:

$T=\frac{56.7-m_1a+m_2a+39.6}{2}=48.15-7.65a=48.15-7.65\cdot0.67=43.02$ N