📘 mechanics

1. **Problem Statement:** Determine the magnitude and direction of the normal force exerted on the disc by the bar (part a), and solve for the angular acceleration of the bar (part

1. **Problem Statement:** Given a mechanism with a linear actuator attached at a fixed point O, and a sliding block A moving with velocity $\vec{v}_A = 5$ mm/s horizontally, we nee

1. **Planteamiento del problema:** Se tiene una caja con peso $P=400$ lb sostenida en equilibrio por dos cables $AB$ y $AC$ y una fuerza $F$. Se debe encontrar la magnitud de las f

1. Problem statement: A 5 m uniform wooden beam of weight 300 N is supported at both ends.

1. **Stating the problem:** Determine the reaction forces at the supports of the first beam structure and then draw the diagrams of Normal force (N), Shear force (T), and Bending m

1. **Problem statement:** Two particles A and B with masses 0.8 kg and 1.2 kg lie on inclined planes at angles 30° and 60° respectively, connected by a light inextensible string ov

1. **Problem Statement:** Determine the elongation of wire DE when an 80-kg man sits on seat C. The wire has a diameter of 5 mm and is made from A-36 steel.

1. **Problem Statement:** Determine for rods AB and CD made of steel with failure stress $\sigma_{fail} = 510$ MPa and factor of safety $F.S.=1.75$:

1. **State the problem:** We are given the equation for total deformation $\delta$ as the sum of three parts: $$\delta = \delta_{AB} + \delta_{BC} + \delta_d$$

1. **Problem Statement:** Calculate the polar moment of inertia $J$ for a hollow circular tube with outer diameter $D_o = 2$ in, inner diameter $D_i = 1.5$ in.

1. **Problem statement:** We have two blocks connected by a string over a pulley. Block P (mass $2m$) is on a rough inclined plane at angle $\alpha$ where $\tan \alpha = \frac{5}{1

1. **Problem Statement:** Determine the angular velocities of bars ABC and CD given that the solenoid plunger at point A moves left with velocity $v_A = 3.0$ in/s.

1. **Problem statement:** We have two forces and one couple (moment) acting on a 3D block. We want to replace these by an equivalent force-couple system at point A and find the wre

1. **State the problem:** A steel rod with diameter 10 mm and length 2 m is subjected to a tensile load of 15 N. We need to calculate the stress, strain, and elongation given Young

1. **Problem statement:** A steel rod with diameter 10 mm and length 2 m is subjected to a tensile load of 15 N. We need to calculate the stress, strain, and elongation. 2. **Given

1. **Problem Statement:** Determine the position of the centre of gravity (centroid) of a composite body made of a titanium plate with a circular lead-filled hole.

1. **Problem Statement:** Draw the free-body diagrams (FBDs) for the system with blocks A, B, and C connected by ropes and pulleys.

1. **Problem statement:** We need to find the minimum diameter of a steel rod that can hold a tensile force of 30000 N (30 kN) without elongating more than 0.005 m (5 mm). The rod

1. **State the problem:** We have a smooth ring R of mass 0.8 kg threaded on a string fixed at points A and B, with A vertically above B. The string sections AR and BR make angles

1. **Problem statement:** We have a system with a 5 kg particle on a rough horizontal table connected by strings over pulleys to 4 kg and 6 kg hanging masses. The 6 kg mass is 0.5

1. **State the problem:** We have three blocks P, Q, and R with masses 25 kg, 20 kg, and m kg respectively, held in equilibrium by strings OP, OQ, and OR passing over pulleys A and