Engineering Mechanics - College Level -Statics Part I

Begin your engineering mechanics journey with the warm up, familiarizing yourself with the work style and methods, while noting part one’s simplicity compared to parts two and three.

Explore the fundamentals of forces, Newton's laws, and gravitational attraction, comparing imperial and SI measurement systems to understand weight in engineering mechanics.

Explore mechanics as a subbranch of physics, describing nature with mathematics through forces and displacement at macroscopic scales. Ground your study in classical mechanics and rigid bodies as the foundation.

Examine how Newtonian mechanics treats rigid bodies as idealizations, noting real materials deform under load; begin with statics, then move to dynamics as acceleration changes.

Explore the origins and definitions of SI base units—meter, kilogram, and second—along with prefixes and imperial differences, to understand universal, practical measurement in engineering mechanics.

Explore how to describe force with vectors, derive Newton's first, second, and third laws, and connect mass, acceleration, and the newton unit through gravity and water weight.

Explore Newton's law of gravitational attraction, showing how two masses interact via inverse-square distance and the gravitational constant, with Earth tides and scales versus balances implications.

Explore the meaning of Newton's laws, gravitational attraction, density and the specific weight of water, and master unit conversion, four significant figures, and homework formatting via a training assignment.

Apply trigonometric laws to 2d force systems, using cosine and sine laws, vector addition and decomposition, and parallelogram methods to determine the planar resultant and its angle.

Identify vectors by direction and magnitude with arrowheads, distinguish them from scalars, and decompose into i-hat and j-hat components with magnitude and angle.

Apply vector decomposition to compute resultant force on hooks, determine its x and y components, magnitude, and the angle relative to the positive x axis using 3-4-5 and 5-12-13 triangles.

Master trigonometric laws, 2d vector operations, and vector decomposition to solve force problems, balance forces, and prepare for homework in engineering mechanics.

Learn to analyze 3D forces by establishing a right-handed Cartesian system, describing vectors as A = a_x i_hat + a_y j_hat + a_z k_hat, and using directional cosines alpha, beta, gamma.

Learn to describe 3D forces with Cartesian vectors, use directional cosines alpha, beta, gamma, and project onto axes to determine components and the resultant in engineering mechanics.

Develop proficiency with 3D vectors by mastering right-handed coordinate systems and directional cosines. Apply alpha, beta, gamma components to analyze force vectors and related homework problems.

Explore the scalar (dot) product to determine the angle between vectors and the magnitudes of parallel force components in engineering mechanics, using unit vectors and cosine of the angle.

Use the scalar dot product to find the angle between two position vectors and project one vector onto another using a unit vector, yielding parallel and axis components in 3D.

Explore scalar product to project a force onto a member, determine the parallel force component along AB using AB hat, and distinguish parallel and perpendicular components in vector decomposition.

Explore how the scalar (dot) product projects vectors to reveal parallel components using unit vectors and magnitude. Relate formulas, physical interpretation, and 3D angle problems to homework on projections.

Explore the equilibrium of particles in two dimensions, applying free body diagrams and Newton's third law to calculate tensile forces in simple cable structures.

Master free body diagrams by including all known and unknown forces with clear naming and directed components. Use 2D or 3D components and a coordinate system to analyze equilibrium.

Learn to draw the free body diagram for Node A, apply two-equation equilibrium to solve the tensile forces in cables AB and AC, and verify the results.

Learn to apply free body diagrams and equilibrium conditions to solve for forces in particle and truss problems, including tensile forces in cables and real-world applications.

Apply free body diagrams and equilibrium to solve advanced cable structures with springs, finding cable forces and spring stretches using F = Kx and angle components.

Solve a two-dimensional cable system with two weights, including a 4-pound weight and a 15-degree angle, by applying free-body diagrams and node equilibrium to determine all cable tensions.

Apply Hooke's law and spring constants to analyze equilibrium and displacement in cable and spring systems, solve 2d problems, and prepare for 3d structures with springs.

Extend 2D equilibrium to 3D by applying sum of forces in x, y, and z equals zero, express components, and solve three unknowns with three equations using a free-body diagram.

Solve three-dimensional cable structures by free-body diagrams, resolving cable forces, and using symmetry to balance weight; determine spring extension with F = k s.

Form 3d equilibrium equations for a box with a 10-pound vertical load, resolve forces in cables AB, AC, and AD, and solve via a matrix method.

Extend equilibrium from 2D to 3D and solve cable forces in simple 3D structures using symmetry and three equations in three unknowns.

Learn how moments, or torque, arise from force times lever arm, expressed as a scalar for in-plane systems, indicating tendency to rotate about a point with clockwise or counterclockwise.

Examine 2d and 3d moments from forces and lever arms, defining moments about x, y, and z axes and how the line of action and perpendicular distance determine the moment.

Learn to compute moments by decomposing a force into perpendicular components and its lever arm, then sum the moments about the z-axis with counterclockwise positive.

Compute moments about a point by summing force times perpendicular distance, with counterclockwise as positive, as shown in three example problems with lever arms and rotation signs.

Master moment concepts—force, lever arm, perpendicular components, and the right-hand rule—applied relative to a reference point, then solve 2D homework with proper components and signs.

Explore moments in three dimensions by using the vector product to compute x, y, and z components from a force and lever arm, guided by the right-hand rule.

Calculate 3d moments about a point p using the determinant form of r cross f. Resolve into cartesian components Mx, My, Mz and determine magnitude and direction.

Explore moments in three dimensions by computing R cross F with vector components, determinants, and unit vectors, and interpret the moment magnitude and direction.

Extend 2d concepts to 3d by treating moments as vector products (torque) and interpreting magnitude, components, and direction for 3d problems, including lever arms and plane projections.