솔루션피아

$$ \begin{cases} N&=20\\ m&=5.0\times10^4\ut{kg}\\ f&=250v\\ v_1&=30\ut{km/h}=\frac{25}{3}\ut{m/s}\\ a_1&=0.20\ut{m/s^2} \end{cases} $$ $$\ab{a}$$ $$\Sigma \vec F = m\vec a,$$ $$F_T-Nf=Nm a $$ $$ \begin{aligned} F_T&=Nma+Nf\\ &=\frac{725000}{3}\ut{N}\\ &\approx 241666.66666666666\ut{N}\\ &\approx 2.4\times10^5\ut{N}\\ &\approx 0.24\ut{MN}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} \Sigma F..

$$ \begin{cases} R&=200\ut{m}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$\ab{a}$$ $$\Sigma \vec F = m\vec a,$$ $$ \begin{cases} \Sigma F_R &=\cfrac{mv^2}{R}\\ \Sigma F_y &= 0\\ \end{cases} $$ $$ \begin{cases} \cfrac{mv^2}{R} &=F_N\sin\theta+\mu_s F_N\cos\theta\\ 0 &= F_N\cos\theta-mg-\mu_s F_N\sin\theta\\ \end{cases} $$ $$ \begin{aligned} v_{\max}&=\sqrt{\frac{\mu_s+\tan\theta}{1-\mu_s\tan\theta}g ..

$$ \begin{cases} \theta&=35\degree\\ a&=0.80\ut{m/s^2}\\ \end{cases} $$ $$\Sigma \vec F = m\vec a,$$ $$ \begin{cases} \Sigma F_x &= m a\\ \Sigma F_y &= 0\\ \end{cases} $$ $$ \begin{cases} m a &= \mu F_N-mg\sin\theta\\ 0 &= F_N-mg\cos\theta\\ \end{cases} $$ $$ \begin{aligned} a &= \mu g\cos\theta-g\sin\theta\\ \mu&=\frac{g\sin\theta+a}{g\cos\theta}\\ &=\tan\theta+\frac{a}{g\cos\theta}\\ &\approx ..

$$ \begin{cases} m&=40\ut{kg}\\ F&=65\ut{N}\\ S&=1.4\ut{m}\\ v&=1.0\ut{m/s}\\g&=9.80665\ut{m/s^2} \end{cases} $$ $$2aS=v^2-{v_0}^2,$$ $$ \begin{aligned} a&=\frac{v^2-{0}^2}{2S}\\ &=\frac{5}{14}\ut{m/s^2} \end{aligned} $$ $$\Sigma \vec F = m\vec a,$$ $$ \begin{cases} \Sigma F_x &= m a_x\\ \Sigma F_y &= 0\\ \end{cases} $$ $$ \begin{cases} m a &= F-\mu F_N\\ 0 &= F_N-mg\\ \end{cases} $$ $$ \begin{a..

$$ \begin{cases} \theta&=35\degree\\ mg&=140\ut{N}\\ a&=0.86\ut{m/s^2}\\ \end{cases} $$ $$\ab{a}$$ $$\Sigma \vec F = m\vec a,$$ $$ \begin{cases} \Sigma F_x &= m a_x\\ \Sigma F_y &= 0\\ \end{cases} $$ $$ \begin{cases} m a &= mg\sin\theta-\mu_kF_N\\ 0 &=F_N-mg\cos\theta\\ \end{cases} $$ $$ \begin{aligned} a&= g\sin\theta-\mu_kg\cos\theta\\ \mu_k&=\frac{g\sin\theta-a}{g\cos\theta}\\ &=\tan\theta-\f..

(풀이자주:문제에 주어진 데이터가 부족해 운동마찰계수는 정확히 구할 수 없습니다. 경사로의 각도를 임의로 두고 풀었습니다.) $$ \begin{cases} S&=250\ut{m}\\ t_A&=62\ut{s}\\ t_B&=45\ut{s}\\ \end{cases} $$ $$\ab{a,b}$$ $$S=v_0t+\frac{1}{2}at^2,$$ $$ \begin{aligned} S&=(0)t+\frac{1}{2}at^2\\ a&=\frac{2S}{t^2}\\ \end{aligned} $$ $$\ab{a}$$ $$ \begin{aligned} a_A&=\frac{2S}{{t_A}^2}\\ &=\frac{125}{961}\ut{m/s^2}\\ &\approx 0.13007284079084286\ut{m/s^2}\\..

$$ \begin{cases} v&=70\ut{km/h}=\frac{175}{9}\ut{m/s}\\ R&=170\ut{m}\\ g&=9.80665\ut{m/s^2} \end{cases} $$ $$\ab{a}$$ $$ \begin{cases} \Sigma F_R&=\cfrac{mv^2}{R}\\ \Sigma F_y&=0 \end{cases} $$ $$ \begin{cases} \cfrac{mv^2}{R}&=F_N\sin\theta\\ 0&=F_N\cos\theta-mg \end{cases} $$ $$ \begin{aligned} \theta&=\tan^{-1}\frac{v^2}{gR}\\ &\approx 0.22301633395178838\ut{rad}\\ &\approx 0.22\ut{rad}\\ \en..

$$ \begin{cases} \theta&=35.0\degree\\ \mu_{s1}&=0.710\\ \end{cases} $$ $$ \begin{cases} \Sigma F_x&=0\\ \Sigma F_y&=0\\ \end{cases} $$ $$ \begin{cases} mg\sin\theta-\mu_{s2}F_N&=0\\ F_N-mg\cos\theta&=0 \end{cases} $$ $$\mu_{s2}=\tan\theta,$$ $$ \begin{aligned} \Ans&=1-\frac{\mu_{s2}}{\mu_{s1}}\\ &\approx 0.0137921997046343\\ &\approx 1.38\% \end{aligned} $$

$$ \begin{cases} R&=32.0\ut{m}\\ v&=6.50\ut{m/s}\\ m&=85.0\ut{kg} \end{cases} $$ $$\ab{a,b}$$ $$ \begin{aligned} \Sigma F_R&=f=\frac{mv^2}{R}\\ &=\frac{14365}{128}\ut{N}\\ &=112.2265625\ut{N}\\ &\approx 1.12\times10^2\ut{N}\\ \end{aligned} $$

$$ \begin{cases} mg&=22\ut{N}\\ F_N&=70\ut{N}\\ \mu_s&=0.60\\ \mu_k&=0.40\\ \end{cases} $$ $$ \begin{aligned} f_s&=\mu_sF_N\\ &=42\ut{N} \end{aligned} $$ $$ \begin{aligned} f_k&=\mu_kF_N\\ &=28\ut{N} \end{aligned} $$ $$\ab{a}$$ $$P=+34\ut{N}$$ $$ \begin{aligned} \abs{\Sigma F_y}&=\abs{P-mg}\\ &=\abs{12\ut{N}}\lt f_s=42\ut{N},\\ f&=\Sigma F_y=-12\ut{N},\text{Down} \end{aligned} $$ $$\ab{b}$$ $$P=..