Question

calculate the weight of horizontal force P required to start wedge in motion and raise the block. The coefficient of friction for all contact surfaces is 0.2

Answer 1

$\Sigma F_x=0\\\Rightarrow-N_1sin15\degree-0.2N_1cos15\degree+N_2cos60\degree+0.2N_2sin60\degree=0$

$\Rightarrow N_1=\dfrac{N_2(cos60\degree+0.2sin60\degree)}{sin15\degree+0.2cos15\degree}\\\Rightarrow N_1=1.489N_2\space\space\space\space\space\space\space\space\space\space\space\space(1)$

$\Sigma F_y=0\\\Rightarrow N_1cos15\degree-0.2N_1sin15\degree+N_2sin60\degree-0.2N_2sin60\degree=1000$

$\Rightarrow2.127N_2=1000\space\space\space\space\space\space\space\space\space\space\space\space\space from(1)$

$\Rightarrow N_2=470.14\space N \\N_1=700.03\space N$

$\Sigma F_y=0\\\Rightarrow -N_1cos15\degree+0.2N_1sin15\degree-N=0\\\Rightarrow N=639.9\approx640\space N$

$\Sigma F_x=0\\\Rightarrow-P+0.2N+N_1sin15\degree+0.2N_1cos15\degree=0\\\Rightarrow P=444.41\space N$