📘 mechanics

1. **State the problem:** Find the speed of the particle when it reaches the level AB after being pulled down 0.55 m from its equilibrium position and released.

1. **State the problem:** We need to find the maximum compressive stress a square column can support given a downward force of 281,500 N and a side length of 7 inches. 2. **Formula

1. **Problem statement:** We need to find (d) the time between the two collisions of balls P and Q, and (e) the ratio $d_1 : d_2$ given the setup and previous results.

1. **Problem 1: Determine the magnitude of the reactions on the beam at A and B (Fig. 1). Given: By = 586 N; FA = 413 N.** 2. The beam is in equilibrium, so the sum of forces and m

1. **Problem Statement:** A wedge is jointed and subjected to forces. We need to find the force and tension by taking moments.

1. **Problem Statement:** Given a composite area consisting of a semicircle and a rectangle, find:

1. **Problem statement:** A body weighing $12\sqrt{3}$ gm.wt is on a smooth inclined plane at angle $\theta$ to the horizontal. It is held in equilibrium by a force of magnitude 12

1. **Problem statement:** Two particles A and B of masses $3m$ and $m$ respectively are connected by a light inextensible string over a smooth pulley at the top of a wedge. Each pa

1. **State the problem:** Given the speed of pulley A as 600 r.p.m. and diameters of pulleys A, B, C, and D as 2, 4, 1, and 5 inches respectively, find the speeds of pulleys B, C,

1. **Nyatakan masalah:** Sebuah balok kantilever dengan panjang $L=500$ m menerima gaya terpusat $F=600$ N pada ujung bebasnya. Kekuatan lentur maksimum balok adalah $\sigma_b=50$

1. **Problem statement:** Replace the given system of forces and couple on bent rod ABC by an equivalent force-couple system at point C. 2. **Given data:**

1. **Problem statement:** ABCDEF is a regular hexagon with side length $a$. Forces $p$, $2p$, $3p$, $kp$, and $3p$ act along directions $AB$, $CB$, $DC$, $DE$, and $AF$ respectivel

1. **Problem Statement:** Determine the reaction forces at points A, B, C, and D for two identical cylindrical rollers each of mass 10 kg and diameter 100 mm placed in a box with s

1. **Problem Statement:** Two identical cylindrical rollers each of mass 10 kg and diameter 100 mm (radius 50 mm) are placed in a box. The rollers touch the box at points A, B, and

1. **Nyatakan masalah:** Diberi pendulum yang terdiri daripada cakera dengan jisim 6 kg dan rod nipis CD dengan jisim 20 kg/m. Rod CD mempunyai panjang $L$ yang tidak diketahui.

1. **Problem statement:** A light elastic string of natural length $a$ and modulus of elasticity $kmg$ is fixed at point $A$. A particle $P$ of mass $4m$ hangs in equilibrium a dis

1. **Stating the problem:** We want to derive the equation of motion for a Timoshenko cantilever beam using Newton-Euler principles. 2. **Background:** The Timoshenko beam theory a

1. **Problem Statement:** Calculate the forces and analyze the mechanical system with lever A of length 1 m inclined at 30° to the horizontal, connected to a spring at point B, wit

1. **Problem Statement:** A horizontal beam of length $L$ is supported at two points: a fixed support at $A$ (left) and a roller support at $B$ (right). The beam carries a uniforml

1. **Problem Statement:** Prove that Hart's inversor mechanism produces a straight line movement. 2. **Background:** Hart's inversor is a mechanical linkage designed to convert rot

1. **Problem Statement:** Given a linkage with two guided blocks at points A and B moving in fixed slots, point A moves downward with velocity $v_A = 2$ m/s. At the instant when $\