Category: Part 1: Mechanics

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: A block of mass $m_1$ rests on a frictionless horizontal table, connected by a massless string over a frictionless pulley to a hanging block of mass $m_2$. Find the acceleration $a$ and string tension $T$. Table mass: $m_1$, hanging…

Problem Statement A particle of mass $m$ rests at the center of a smooth horizontal tube of length $2l$ rotating at constant angular velocity $\omega$ about its midpoint. The particle is released from rest (relative to tube). Find its speed relative to the tube when it reaches the end. Given Information All quantities, constants, and…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: Two equal masses $m$ are connected by a string of total length $2l$ lying on a smooth horizontal table, rotating about the string’s midpoint with angular velocity $\omega$. Find the tension in the string. Mass of each particle: $m$,…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: A car rounds a bend of radius $R$ on a road banked at angle $\phi$. Find the speed $v_0$ at which no lateral friction is needed, and the normal force from the road at that speed. Radius: $R$, bank…

Problem Statement A particle of mass $m$ moves in horizontal circles inside a smooth spherical bowl of radius $R$. The string from the particle to the center makes angle $\theta$ with the vertical. Find the speed $v$ and the normal force $N$. Given Information All quantities, constants, and constraints stated in the problem above Physical…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: A ball of mass $m$ on a string of length $R$ moves in a vertical circle. Find the minimum speed at the top of the circle for the string to remain taut, and the tension at the bottom of…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: A conical pendulum consists of a mass $m$ on a string of length $l$ making angle $\theta$ with the vertical. Find the tension $F$ in the string and the period of revolution $T$. String length: $l$, mass: $m$, half-angle:…

Problem Statement A simple pendulum of length $l$ is in a lift. Find the period when the lift (a) accelerates upward with $w$, (b) accelerates downward with $w$, (c) falls freely. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas…

Problem Statement A body rests on a rough cone with vertical axis and half-angle $\alpha$. The cone rotates with angular velocity $\omega$. Coefficient of friction $\mu$. Find the range of $\omega$ for the body to remain stationary at distance $r$ from axis. Given Information All quantities, constants, and constraints stated in the problem above Physical…

Problem Statement A block of mass $m$ sits at distance $R$ from the axis of a rotating horizontal platform. Coefficient of static friction is $\mu$. Find the maximum angular velocity $\omega_{\max}$ before the block slides. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section)…