솔루션피아

$$\begin{cases} m_1&=4.00\ut{kg}\\ m_2&=3.00\ut{kg}\\ \theta_1&=25.0\degree\\ \theta_2&=65.0\degree\\ \end{cases}$$ $$\Sigma \vec F = m\vec a,$$ $$\begin{cases} \Sigma F_1 &= m_1 a\\ \Sigma F_2 &= m_2 a\\ \end{cases}$$ $$\begin{cases} T-m_1g\sin\theta_1 &= m_1 a\\ m_2g\sin\theta_2-T &= m_2 a\\ \end{cases}$$ $$ \begin{aligned} T&= m_1 g(\sin\theta _1+ \sin \theta _2)\\ &\approx 52.129250544..

$$\begin{cases} m_A&=13\ut{kg}\\ m_B&=20\ut{kg} \end{cases}$$ $$\ab{a}$$ $$\Sigma \vec F = m\vec a,$$ $$\begin{cases} \Sigma F_A &= m_A a_A\\ \Sigma F_B &\ge0\\ \end{cases}$$ $$\begin{cases} T-m_Ag &= m_A a_A\\ T &\gt m_Bg\\ \end{cases}$$ $$\begin{aligned} a&\ge\frac{7}{13}g\\ &~~~~\approx5.280503846153846\ut{m/s^2}\\ &~~~~\approx5.3\ut{m/s^2}\\ \end{aligned}$$ $$\ab{b}$$ $$\Sigma \vec F..

$$\begin{cases} N_a&=20.0\ut{N}\\ N_b&=10.0\ut{N}\\ \Sigma m&=15.0\ut{kg} \end{cases}$$ $$\Sigma \vec F = m\vec a,$$ $$\begin{cases} \Sigma F_{aA} &= m_{aA} a_{aA}\\ \Sigma F_{aB} &= m_{aB} a_{aB}\\ \Sigma F_{bB} &= m_{bB} a_{bB}\\ \Sigma F_{bA} &= m_{bA} a_{bA}\\ \end{cases}$$ $$ \begin{cases} \Sigma F_{aA} &= m_{A} a_{a}\\ \Sigma F_{aB} &= m_{B} a_{a}\\ \Sigma F_{bB} &= m_{B} a_{b}\\ \Sigm..

$$\begin{cases} T_3&=95.0\ut{N}\\ m_1&=10.0\ut{kg}\\ m_2&=14.0\ut{kg}\\ m_3&=23.0\ut{kg} \end{cases}$$ $$\Sigma \vec F = m\vec a,$$ $$\begin{cases} \Sigma F_1 &= m_1 a\\ \Sigma F_2 &= m_2 a\\ \Sigma F_3 &= m_3 a\\ \end{cases}$$ $$\begin{cases} T_1 &= m_1 a\\ T_2-T_1 &= m_2 a\\ T_3-T_2 &= m_3 a\\ \end{cases}$$ $$\ab{a}$$ $$ \begin{aligned} a&=\frac{95}{47}\ut{m/s^2}\\ &\approx 2.02127659574..

$$\begin{cases} m&=67\ut{kg}\\ T&\le400\ut{N}\\ g&=9.80665\ut{m/s^2} \end{cases}$$ $$\ab{a}$$ $$\begin{aligned} mg&=657.04555\ut{N}\\ &\approx 6.6\times10^2\ut{N}\gt400\\ \end{aligned}$$ $$\text{Lope Broken}$$ $$\ab{b}$$ $$\Sigma \vec F = m\vec a,$$ $$ \begin{aligned} a&=\frac{\Sigma \vec F}{m}\\ &=\frac{T-mg}{m}\\ &=\frac{400-67g}{67}\\ &\approx -3.8365007462686567\ut{m/s^2}\\ &\approx -3.8..

$$\begin{cases} F_1&=4500\ut{N}\\ a_1&=0\\ \end{cases}$$ $$\begin{cases} F_2&=2600\ut{N}\\ a_2&=-0.39\ut{m/s^2}\\ \end{cases}$$ $$\ab{a}$$ $$\Sigma \vec F = 0 \Harr \Delta \vec v=0,$$ $$\begin{aligned} \Sigma F_1 &= 0\\ F_1-mg &= 0\\ mg&=F_1\\ &=4500\ut{N} \end{aligned}$$ $$\ab{b}$$ $$\Sigma \vec F = m\vec a,$$ $$\begin{aligned} \Sigma F_2 &= m a_2\\ F_2-mg &= m a_2\\ \end{aligned}$$ $$ ..

$$\begin{cases} m&=4.0\ut{kg}\\ \vec x(t\ut{s})&=3.0+4.0t+ct^2-3t^3\ut{m}\\ \vec F(2.0\ut{s})&=-48\ut{N} \end{cases}$$ $$\begin{aligned} \vec a&=\dxtt{\vec x}\\ &=\dtt(3.0+4.0t+ct^2-3t^3)\\ &=2c-18t\\ \end{aligned}$$ $$\begin{aligned} F&=ma\\ &=8(c-9t)\\ F(2)&=8 (c-18)=-48,\\ c&=12\ut{m/s^2} \end{aligned}$$

$$\begin{cases} m&=0.600\ut{kg}\\ x(t\ut{s})&=-15.00+3.00t-2.00t^3\ut{m}\\ y(t\ut{s})&=25.00+7.00t-7.00t^2\ut{m}\\ t&=1.20\ut{s}\\ \end{cases}$$ $$\vec r=(-15+3t-2t^3)\i+(25+7t-7t^2)\j,$$\\ $$\begin{aligned} \vec v&=\dxt{\vec r}\\ &=\dt\bra{(-15+3t-2t^3)\i+(25+7t-7t^2)\j}\\ &=(3-6t^2)\i+(7-14t)\j\ut{m/s} \end{aligned}$$ $$ \begin{aligned} \vec a&=\dxt{\vec v}\\ &=\dt\bra{(3-6t^2)\i+(7-14t)\j..

$$\begin{cases} a_1&=10.0\ut{m/s^2}\\ a_2&=6.20\ut{m/s^2}\\ \end{cases}$$ $$\ab{a}$$ $$\begin{cases} m_1&=\cfrac{F}{a_1}\\ m_2&=\cfrac{F}{a_2}\\ \end{cases}$$ $$\begin{aligned} a_a&=\frac{F}{m_2-m_1}\\ &=\frac{F}{\frac{F}{a_2}-\frac{F}{a_1}}\\ &=\frac{1}{\frac{1}{a_2}-\frac{1}{a_1}}\\ &=\frac{310}{19}\ut{m/s^2}\\ &= 16.3158\ut{m/s^2}\\ &\approx 16.3\ut{m/s^2}\\ \end{aligned}$$ $$\ab{b}$$ $..

$$\begin{cases} T_0&=43\ut{N}\\ v_a&=5.3\ut{m/s}\\ a_b&=1.2\ut{m/s^2}\\ v_b&=7.6\ut{m/s^2}\\ g&=9.80665\ut{m/s^2} \end{cases}$$ $$\ab{a}$$ $$\Sigma \vec F = 0 \Harr \Delta \vec v=0,$$ $$T_a=43\ut{N}$$ $$\ab{b}$$ $$\Sigma \vec F = m\vec a,$$ $$\begin{cases} T_a-mg&=0\\ T_b-mg&=m(-a_b) \end{cases}$$ $$\begin{aligned} T_b&=43-\frac{258}{5g}\\ &=37.7383\ut{N}\\ &\approx 38\ut{N} \end{aligned}$$