솔루션피아

(풀이자 주:곡선아래의 면적으로 어림해서 구하라는 의도인지는 모르겠으나, 그래프만 제시하고 적분으로 구하겠습니다. 애초에 적분자체가 곡선아래의 면적을 구하는 행위입니다.) $$\put \exp(x)=\e^x,$$ $$ \begin{cases} \vec F&=10\exp\(-\cfrac{x\ut{m}}{2.0}\)\i\ut{N} \\ x_0&=0\\ x_2&=2\ut{m}\\ \end{cases} $$ $$\ab{a}$$ $$\ab{b}$$ $$W_{i\rarr f}=\int_{i}^{f} \vec F \cdot \dd \vec S,$$ $$ \begin{aligned} W_{0\rarr 2}&=\int_{0}^{2} 10\exp\(-\frac{x}{2}\) \cdot \dd x\\ &=\[-20 \exp..

$$ \begin{cases} m&= 72\ut{kg}\\ S&=1.5\ut{m}\\ h&=0.85\ut{m}\\ \end{cases} $$ $$\Sigma \vec F = 0 \Harr \Delta \vec v=0,$$ $$ \begin{cases} \Sigma F_x &= 0\\ \Sigma F_y &= 0\\ \end{cases} $$ $$ \begin{cases} 0&=F-mg\sin\theta \\ 0&=N-mg\cos\theta \\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \sin\theta&=\frac{h}{S}\\ &=\frac{17}{30}\\ \end{aligned} $$ $$ \begin{aligned} F&=mg\sin\theta\\ &=\f..

$$ \begin{cases} \vec F_0&=-7.00\i+7.00\j+5.00\k\ut{N}\\ v_0&=5.00\ut{m/s}\\ m&=2.80\ut{kg}\\ \Delta \vec d&=4.00\i+4.00\j+7.00\k\ut{m} \end{cases} $$ $$W=\vec F \cdot \vec S=\Delta K,$$ $$K=\frac{1}{2}mv^2,$$ $$ \begin{aligned} K_1&=K_0+\vec F \cdot \vec S\\ \frac{1}{2}m{v_1}^2&= \frac{1}{2}m{v_0}^2+\vec F \cdot \vec S\\ {v_1}^2&= {v_0}^2+\frac{2\vec F \cdot \vec S}{m}\\ \end{aligned} $$ $$ \be..

$$ \begin{cases} \vec d_i&=3.00\i-2.00\j+5.00\k\ut{m}\\ \vec d_f&=-5.00\i+4.00\j+7.00\k\ut{m}\\ m&=2.00\ut{kg}\\ \vec F &= 4.50\i+8.50\j+6.00\k\ut{N}\\ t&= 4.00\ut{s} \end{cases} $$ $$ \begin{aligned} \vec S &= \vec d_f-\vec d_i\\ &=-8\i+6\j+2\k\ut{m} \end{aligned} $$ $$\ab{a}$$ $$W=\vec F \cdot \vec S,$$ $$ \begin{aligned} W&=4.5\cdot(-8)+8.5\cdot6+6\cdot2\\ &=27\ut{J}\\ &=27.0\ut{J}\\ \end{ali..

$$ \begin{cases} \vec F_a&=102\ut{N}\\ m&=3.00\ut{kg}\\ \phi &= 53.0\degree\\ h&= 0.230\ut{m} \end{cases} $$ $$\put \begin{cases} \theta : \text{경사각}\\ \vec N : \text{수직항력}\\ \vec S : \text{변위} \end{cases} $$ $$\sin\theta = \frac{h}{S},$$ $$\vec S = \frac{h}{\tan\theta}\i+h\j$$ $$\Sigma \vec F = 0 \Harr \Delta \vec v=0,$$ $$ \begin{cases} \Sigma F_x &= 0\\ \Sigma F_y &= 0\\ \end{cases} $$ $$ \be..

$$ \begin{cases} \vec S&=-1.80\ut{m}\\ F_1&=6.00\ut{N}\\ F_2&=9.00\ut{N}\\ F_3&=14.00\ut{N}\\ \theta &=60.0\degree\\ \end{cases} $$ $$\ab{a}$$ $$\Sigma \vec F = 0 \Harr \Delta \vec v=0,$$ $$\Sigma F_y=0$$ $$ \begin{aligned} \Sigma F_x &= -F_1 +F_2\cos\theta\\ &=\frac{3}{2}\ut{N}\\ \end{aligned} $$ $$ \begin{aligned} W&=\Sigma F_x \cdot \vec S\\ &= \frac{3}{2}\cdot (-1.8)\\ &= -\frac{27}{10}\ut{J..

$$ \begin{cases} A&:(3.0,4.0)\ut{m}\\ F&=5.0\ut{N},\theta_F=100\degree\\ \end{cases} $$ $$W=\vec F \cdot \vec S,$$ $$ \begin{aligned} W&=(5\cos100\degree\i+5\sin100\degree) \cdot (3\i+4\j)\\ &=5\cos100\degree \cdot 3+5\sin100\degree\cdot4\\ &\approx 17.091432395240204\ut{J}\\ &\approx 17\ut{J}\\ \end{aligned} $$

$$ \begin{cases} m&=6.0\ut{kg}\\ v(0\ut{m})&=4.0\ut{m/s} \end{cases} $$ $$ F(x)=\begin{cases} 8-8x&:(0\le x \le2)\\ -8&:(2\le x \le8) \end{cases} $$ $$W_{i\rarr f}=\int_{i}^{f} \vec F \cdot \dd \vec S,$$ $$ \begin{aligned} W_{0\rarr (2+s)}&=\int_{0}^{2+s} F \cdot \dd x\\ &=\int_{0}^{2} F \cdot \dd x+\int_{2}^{2+s} F \cdot \dd s\\ &=0+(-8\cdot s)\\ &=-8s \end{aligned} $$ $$ \begin{aligned} K(2+s)..

$$ \begin{cases} m&=3.05\ut{kg}\\ F&=50.0\ut{N}\\ F_N&=14.97\ut{N}\\ S&=1.85\ut{m}\\ g&=9.80665\ut{m/s^2}\\ \end{cases} $$ $$ \begin{cases} \Sigma F_x &= F-mg\sin\theta\\ \Sigma F_y &= F_N-mg\cos\theta=0 \end{cases} $$ $$ \begin{aligned} \cos\theta &= \frac{F_N}{mg},\\ \sin\theta &=\sqrt{1-\(\frac{F_N}{mg}\)^2} \end{aligned} $$ $$ \begin{aligned} \Sigma F_x&=F-mg\sqrt{1-\(\frac{F_N}{mg}\)^2}\\ &..

(풀이자주:그래프로 주어진 데이터가 정확한 값을 읽기가 힘듭니다. 풀이자가 임의로 데이터를 읽었습니다. 구체적 데이터가 달라지면 답은 달라질 수 있습니다. ) $$ \begin{cases} m&=2.0\ut{kg}\\ \vec v_0&=v_0\i\\ \vec F&=-F\i\\ \end{cases} $$ $$ \begin{cases} x(0\ut{s})&=0\ut{m}\\ x(5\ut{s})&=2.5\ut{m}\\ x(5\ut{s})&=\max(x) \rarr v(5)=0 \end{cases} $$ $$ \begin{cases} v=v_0+at\\ S=v_0t+\frac{1}{2}at^2 \end{cases} $$ $$ \begin{cases} 0&=v_0+a(5)\\ 2.5&=v_0(5)+\frac{1}..