Category: Part 1: Mechanics

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: Two bars of masses $m_1$ (lower) and $m_2$ (upper) are connected by a weightless string on a rough inclined plane (angle $\theta$). Friction coefficients are $\mu_1$ and $\mu_2$ respectively, with $\mu_1 > \mu_2$. Find the acceleration $a$ and string…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: A bar of mass $m$ slides down an inclined plane (angle $\theta$, coefficient of kinetic friction $\mu$). Find the force that the inclined plane exerts on the bar. Mass: $m$ Incline angle: $\theta$ Kinetic friction coefficient: $\mu$ The inclined…

Problem Statement Solve the kinematics problem: A point traversed half the distance with velocity $v_0$. The remaining part of the distance was covered with velocity $v_1$ for half the time and with velocity $v_2$ for the other half. Find the mean velocity averaged over the whole trip. Let total distance $= 2s$. Time for first…

Problem Statement A car starts from rest, accelerates at $w = 5.0\, ext{m/s}^2$, then moves uniformly, then decelerates at the same rate $w$ to rest. Total time $ au = 25\, ext{s}$, mean velocity $\langle v angle = 72\, ext{km/h}$. How long does it move uniformly? Given Information $w = 5.0\, ext$ $ au =…

Problem Statement Solve the momentum/collision problem: A bullet of mass $m = 10\,\text{g}$ moving at $v_0 = 800\,\text{m/s}$ embeds in a wooden block of mass $M = 990\,\text{g}$. Find the velocity after collision and the fraction of KE lost. Conservation of momentum: $$mv_0 = (m+M)V$$ $$V = \frac{mv_0}{m+M} = \frac{0.010\times800}{1.000} = \boxed{8.0\,\ Given Information $m…

Problem Statement Solve the momentum/collision problem: A bomb of mass $M$ at rest explodes into two fragments of masses $m_1 = 1.0\,\text{kg}$ and $m_2 = 3.0\,\text{kg}$. Fragment 1 has speed $v_1 = 120\,\text{m/s}$. Find $v_2$ and the total kinetic energy released. Conservation of momentum (initial $p = 0$): $$m_1 v_1 – m_2 v_2 = 0…

Problem Statement Solve the momentum/collision problem: A ball of mass $m_1 = 2\,\text{kg}$ moving at $v_0 = 6\,\text{m/s}$ makes a head-on elastic collision with $m_2 = 1\,\text{kg}$ at rest. Find the velocities after collision. For elastic collision — conservation of momentum and KE give: $$v_1 = \frac{m_1-m_2}{m_1+m_2}v_0 = \frac{2-1}{2+1}\times6 = \f Given Information $m_1 =…

Problem Statement A rocket ejects mass at rate $\mu = 50\,\text{kg/s}$ with exhaust speed $u = 3000\,\text{m/s}$ relative to the rocket. Find the thrust force. Given Information $\mu = 50\,\text{kg/s}$ $u = 3000\,\text{m/s}$ Physical Concepts & Formulas The Tsiolkovsky rocket equation describes the motion of a rocket as it expels propellant. As the rocket ejects…

Problem Statement Solve the Newton’s Laws / mechanics problem: A water jet of diameter $d = 3\,\text{cm}$ hits a wall at speed $v = 20\,\text{m/s}$ and stops (fully absorbed). Find the force on the wall. Mass flow rate: $$\dot m = \rho A v = 1000\times\frac{\pi(0.03)^2}{4}\times20 = 1000\times7.07\times10^{-4}\times20 = 14.1\,\text{kg/s}$$ Force (momentum per s Given…

Problem Statement A rocket ejects mass at rate $\mu = 50\,\text{kg/s}$ with exhaust speed $u = 3000\,\text{m/s}$ relative to the rocket. Find the thrust force. Given Information $\mu = 50\,\text{kg/s}$ $u = 3000\,\text{m/s}$ Physical Concepts & Formulas The Tsiolkovsky rocket equation describes the motion of a rocket as it expels propellant. As the rocket ejects…