Question

What is the value of 'P' in the system shown in Fig to cause the motion to impend? Assume the pulley is smooth and coefficient of friction between the other contact surfaces is 0.2. Figure:5.​

Answer 1

The value p in the system in $630.239N$.

Explanation:

FBD for 500N weight:

∑$F_{x}=0$

T+ µ  $R_{2}-Pcos 30=0$

$T+0.22R_{2}-Pcos30=0--->(1)$

∑$F_{y}=0$

$R_{2}+Psin30-500=0$

$R_{2}=500-Psin30--->(2)$

sub equation (1),

$T+0.22(500-Psin30)-Pcos30=0$

$T+110-0.5P-0.866P=0$

$T+110-1.366P=0--->(3)$

FBD for 750N weight:

∑$F_{x}=0$

T + µ $R_{1}$ –$750sin60=0$

$T-0.22R_{1}-649.52=0--->(4)$

∑$F_{y}=0$

$R_{1}+750cos60=0\\R_{1}=750cos60$

$R_{1}=375N$

sub (4) equation,

$T=0.22*375+649.52$

$T=732N$

sub (3) equation,

$732+110-1.336=0$

$P=630.239N$