## Physics (10th Edition)

$\mu_k=0.128$
From the given information, $v_0=0$, $v_f=2m/s$ and $m_{sled}=16kg$. Using these, we can calculate the kinetic energies: $KE_0=\frac{1}{2}mv_0^2=0$ $KE_f=\frac{1}{2}mv_f^2=32J$ According to the work-energy theorem, $W=KE_f-KE_0=32J$ We have $$W=(\sum F\cos\theta)s=(F-f_k)\cos\theta\times s$$ We know $s=8m$ and $\sum F$ is parallel with displacement, so $\theta=0$. Therefore, $$F-f_k=\frac{W}{s}=4N$$ $$f_k=F-4=24-4=20N$$ We have $f_k=\mu_kF_N$. Since there is no vertical acceleration, $F_N=mg=16\times9.8=156.8N$ $$156.8\mu_k=20$$ $$\mu_k=0.128$$