Category: Part 1: Mechanics

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: A particle of mass $m$ starts from rest at $x=0$ under force $F = F_0(1-e^{-\alpha x})$. Find the velocity as a function of position. Mass: $m$, force: $F=F_0(1-e^{-\alpha x})$, starts from rest at $x=0$ Since force depends on position,…

Problem Statement A particle of mass $m$ is thrown vertically upward with initial speed $v_0$ in a medium with linear drag $\alpha v$. Find the maximum height $h$ and time $t_{\rm top}$ to reach it. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section)…

Problem Statement Solve the kinematics problem: Solve the kinematics problem: A boat of mass $m$ initially moving at speed $v_0$ decelerates due to quadratic water resistance $F = \beta v^2$. Find the velocity as a function of time $v(t)$. Initial speed: $v_0$, drag: $F = \beta v^2$, mass: $m$ Unlike the spatial form (Problem 1.94),…

Problem Statement A particle of mass $m$ moves horizontally with initial speed $v_0$ against quadratic drag $F = \beta v^2$. Find velocity as a function of position $v(x)$ and the distance to halve the speed. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section)…

Problem Statement Solve the kinematics problem: Solve the kinematics problem: A particle of mass $m$ falls through a viscous medium with linear drag $F_{\rm drag} = \alpha v$. Starting from rest, find (a) the terminal velocity $v_T$, (b) velocity $v(t)$, (c) distance traveled to reach speed $v_T/2$. Mass: $m$, drag coefficient: $\alpha$, starts f Given…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: A block of mass $m$ is pressed against a vertical wall by a horizontal force $F$. The wall has static friction coefficient $\mu$. What is the minimum $F$ to prevent the block sliding down? Mass: $m$, static friction: $\mu$,…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: A force $F$ is applied at angle $\alpha$ above horizontal to a block of mass $m$ on a rough horizontal surface (static friction $\mu$). Find the minimum force required to start the block moving and the optimal angle $\alpha$.…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: Find the force $F$ required to move a block of mass $m$ at constant velocity up an inclined plane (angle $\theta$, kinetic friction $\mu$) when the force is applied (a) parallel to the incline, (b) horizontally. Mass: $m$, angle:…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: A bar of mass $m$ rests on a frictionless wedge (angle $\alpha$, mass $M$) which itself slides on a frictionless floor. Find the acceleration $W$ of the wedge and the normal force $N$ between bar and wedge. Bar mass:…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: Two masses $m_1 > m_2$ are connected by a string over a massless frictionless pulley (Atwood machine). Find the acceleration and tension. $m_1 > m_2$, massless frictionless pulley The heavier mass accelerates downward, the lighter mass upward, both with…