Answer
path 1: -100 J; path 2: -47 J; path 3: -66 J
Work Step by Step
We can find the required work done as follows:
For path 1
$W_1=-\mu_k mg(d_1+d_2+d_3+d_4+d_5)$
We plug in the known values to obtain:
$W_1=-0.026(3.7)(9.81)(11.0)=-100J$
For path 2
$W_2=-\mu_k mg(d_6+d_7+d_8)$
We plug in the known values to obtain:
$W_2=-(0.26)(3.7)(9.81)(2.0+2.0+1.0)=-47m$
For path 3
$W_3=-\mu_k mg(d_9+d_{10}+d_{11})$
We plug in the known values to obtain:
$W_3=-(0.21)(2.3)(9.81)(1.0+3.0+3.0)$
$W_3=-66J$
