📘 statics

1. **State the problem:** We have a vertical truss with forces applied at joints D (23 kN upward), F (20 kN right), and G (20 kN right). Supports are at A (left fixed) and A (right

1. **Stating the problem:** We have a right triangle with a vertical side of 1.2 m, a horizontal base of 2.3 m, and a hypotenuse with a distributed load of 5 kN/m acting downward.

1. **State the problem:** We have a right triangle with base $2.3$ m and height $1.2$ m, fixed support on the left, pinned support on the right, a horizontal force of $6$ kN to the

1. **State the problem:** We have a beam with a distributed load of 30 N/m over 40 cm on the left side and a point force of 10 N acting to the left at the left end. The beam length

1. **State the problem:** We need to find the length of cord AC so that an 8-kg lamp is suspended in equilibrium at point A. The spring AB has an undeformed length $l_{AB} = 0.4$ m

1. **State the problem:** We have two pipes weighing 43 kg and 28 kg supported at points A and B by two cords AB and AD and a spring CB. The system is in equilibrium with angles \(

1. **Problem statement:** A light ladder leans against a smooth vertical wall at an angle of 30° to the horizontal. A load of 800 N is placed three-quarters of the way up the ladde

1. **State the problem:** We have a beam AB of length 10 ft with a trapezoidal distributed load starting at 120 lb/ft at A and increasing linearly to 280 lb/ft at B. We need to fin

1. **Problem 28: Replace the loading with an equivalent resultant force.** Given multiple load values, the equivalent resultant force is the vector sum of all loads. Since the opti

1. **Calcul du câble avec poulies** : On a une masse $m=500$ kg suspendue.

1. **Problem statement:** Determine the forces in cables AC and AB needed to hold a 20-kg ball D in equilibrium with given parameters $F = 300$ N and $d \approx 1$ m. Then, for a 2

1. Problem No.1: Given forces on a bracket, find magnitude $F$ and direction $\theta$ such that the resultant force $\vec{R}$ is 750 N along positive x-axis. 2. Identify given forc

1. **Problem No.1**: Given the resultant force $R = 750$ N along the positive x-axis, find magnitude $F$ and direction $\theta$ of force $F$. 2. Forces given:

1. The problem asks to explain two terms and prove a trigonometric identity involving the resultant of two equal forces. 2. First, explain the terms: