솔루션피아

$$ \begin{cases} mg&=556\ut{N}\\ \mu_s&=0.68\\ \mu_k&=0.56\\ \end{cases} $$ $$ \begin{aligned} f_s&=\mu_sF_N=\mu_smg\\ &=\frac{9452}{25}\ut{N}\\ &=378.08\ut{N}\\ \end{aligned} $$ $$ \begin{aligned} f_k&=\mu_kF_N=\mu_kmg\\ &=\frac{7784}{25}\ut{N}\\ &=311.36\ut{N}\\ \end{aligned} $$ $$\ab{a}$$ $$ \begin{aligned} F_a&=250\ut{N}\lt f_s,\\ &\therefore \text{Stop}\\ f&=F_a=250\ut{N}\\ \end{aligned} $$..

$$\ab{a}$$ $$\Sigma \vec F = 0 \Harr \Delta \vec v=0,$$ $$ \begin{cases} \Sigma F_x &= 0\\ \Sigma F_y &= 0\\ \end{cases} $$ $$ \begin{cases} 0&=F\sin\theta-f_k\\ 0&=F_N-mg-F\cos\theta \\ f_k&=\mu_kF_N \end{cases} $$ $$ \begin{aligned} F&=\frac{\mu_k \text{mg}}{\sin\theta-\mu_k \cos\theta} \end{aligned} $$ $$\ab{b}$$ $$\Sigma \vec F = 0 \Harr \Delta \vec v=0,$$ $$ \begin{cases} \Sigma F_x &= 0\\ ..

$$ \begin{cases} \theta&=35\degree\\ a&=0.10\ut{m/s^2}\\ \end{cases} $$ $$\Sigma \vec F = m\vec a,$$ $$ \begin{cases} \Sigma F_x &= m a_x\\ \Sigma F_y &= 0\\ \end{cases} $$ $$ \begin{cases} \mu_kF_N-mg\sin\theta &= m a\\ F_N-mg\cos\theta &= 0\\ \end{cases} $$ $$ \begin{aligned} m a&= \mu_kmg\cos\theta-mg\sin\theta \\ \mu_k&= \frac{a }{g\cos\theta}+\tan \theta\\ &\approx 0.7126559746152249\\ &\ap..

$$ \begin{cases} m&=630\ut{kg}\\ S&=90.0\ut{m}\\ \theta&=10.2\degree\\ f_1&=62.0\ut{N}\\ v_0&=6.20\ut{m/s}\\ f_2&=50.0\ut{N}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$\Sigma \vec F = m\vec a,$$ $$ \begin{aligned} m a&=mg\sin\theta-f \\ a&=g\sin\theta-\frac{f}{m} \end{aligned} $$ $$S=v_0t+\frac{1}{2}at^2,$$ $$\ab{a}$$ $$ \begin{aligned} t_1&=\frac{m v_0-\sqrt{2 m^2g S \sin\theta+m^2 {v_0}^2-2 mf_1 ..

$$ \begin{cases} m_1&=2.00\ut{kg}\\ m_2&=3.80\ut{kg}\\ \theta&=25.0\degree\\ \mu_1&=0.226\\ \mu_2&=0.113\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$\Sigma \vec F = m\vec a,$$ $$ \begin{cases} \Sigma F_{1x} &= m_1 a\\ \Sigma F_{2x} &= m_2 a\\ \Sigma F_{1y} &= 0\\ \Sigma F_{2y} &= 0\\ \end{cases} $$ $$ \begin{cases} m_1 a &= m_1g\sin\theta+F_T-\mu_1F_{N1}\\ m_2 a &= m_2g\sin\theta-F_T-\mu_2F_{N2}\\ 0..

$$ \begin{cases} m&=62\ut{kg}\\ \mu_f&=1.2\\ \mu_b&=0.80\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$\ab{a}$$ $$\ab{b}$$ $$ \begin{cases} \Sigma F_x&=F_{Nf}-F_{Nb}=0\\ \Sigma F_y&=\mu_fF_{Nf}+\mu_bF_{Nb}-mg=0\\ \end{cases} $$ $$F_{Nf}=F_{Nb}=F_N$$ $$ \begin{aligned} F_N&=\frac{mg}{\mu_f+\mu_b}\\ &=31g\\ &=304.00615\ut{N}\\ &\approx 3.0\times10^2\ut{N}\\ \end{aligned} $$ $$\ab{c}$$ $$ \begin{aligned}..

$$ \begin{cases} \theta&=35\degree\\ S&=2.1\ut{m}\\ t&=4.0\ut{s}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{cases} \Sigma F_x &= 0\\ \Sigma F_y &= 0\\ \end{cases} $$ $$ \begin{cases} \mu_sF_N-mg\sin\theta &= 0\\ F_N-mg\cos\theta &= 0\\ \end{cases} $$ $$\mu_smg\cos\theta-mg\sin\theta=0$$ $$ \begin{aligned} \mu_s&=\tan\theta\\ &=\tan35\degree\\ &\approx 0.7002075382097097\\ &\approx 0.70\\ \end{aligned..

$$ \begin{cases} m&=0.060\ut{kg}\\ L&=0.90\ut{m}\\ 2\pi R&=0.50\ut{m}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$R=\frac{0.5}{2\pi}=\frac{1}{4\pi}$$ $$ \begin{aligned} h&=\sqrt{L^2-R^2}\\ &=\sqrt{\frac{81}{100}-\frac{1}{16 \pi ^2}} \end{aligned} $$ $$$$ $$ \begin{cases} \sin\theta=\cfrac{R}{L}\\ \cos\theta=\cfrac{h}{L} \end{cases} $$ $$ \begin{cases} \Sigma F_y&=F_T\sin\theta-mg=0\\ \Sigma F_R&=F_T..

$$ \begin{cases} m&=110\ut{g}\\ S&=17\ut{m}\\ v_0&=5.0\ut{m/s}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$2aS=v^2-{v_0}^2,$$ $$ \begin{aligned} \vec a&=\frac{0^2-{v_0}^2}{2S}\\ &=-\frac{{v_0}^2}{2S}\\ a&=\frac{25}{34}\ut{m/s^2} \end{aligned} $$ $$\ab{a}$$ $$ \begin{aligned} f&=ma\\ &=\frac{11}{136}\ut{N}\\ &\approx 0.08088235294117647\ut{N}\\ &\approx 0.081\ut{N}\\ &\approx 81\ut{mN}\\ \end{aligned..

$$ \begin{cases} \theta&=40\degree\\ x&=\theta-\phi\\ \mu_s&=0.60\\ \end{cases} $$ $$ \begin{aligned} \Sigma F_y&=F_N-mg\cos x=0\\ F_N&=mg\cos x \end{aligned} $$ $$ \begin{aligned} \Sigma F_x&=\mu_sF_N - mg\sin x=0\\ &=\mu_smg\cos x- mg\sin x\\ \end{aligned} $$ $$\mu_s=\tan x$$ $$ \begin{aligned} \phi&=40\degree-\tan^{-1}\(\frac{3}{5}\)\\ &\approx 0.15771220052714763\ut{rad}\\ &\approx 0.16\ut{r..