Engineering Mechanics

Present friction as resistance to relative motion between contacting surfaces, define static and kinetic friction, introduce normal force and the coefficient of friction, and explain the static-to-kinetic transition.

Analyze frictional equilibrium on a wedge at angle alpha using a rotated free-body diagram (normal force, friction, weight) and derive minimum P/Q condition from sin alpha minus mu cos alpha.

Analyzes equilibrium of a two-direction friction surface for case B larger than Q, using a FBD with X along the wedge and Y along normal, deriving the limiting friction condition.

Compute the minimum force B to initiate motion in a two-block system with mu 0.3, using free-body diagrams and a 3-4-5 triangle; the required B is about 388–400 N.

Analyze a wedge with equal weights to determine the impending slip condition under friction using the angle alpha, with free-body diagrams and friction forces F1 and F2.

Study pin joints, weightless trusses that carry loads at joints. Use the method of joints to determine tension and compression in each member with free-body diagrams.

Master trusses through the method of joints in a first numerical problem with six equal-length members, using free-body diagrams to enforce equilibrium and identify zero-force members and member forces.

Engineering mechanics lecture uses the method of joints on a ten-member truss to determine axial forces and classify members as tension or compression, revealing zero‑force members.

Set up support reactions and construct joint free body diagrams to identify zero-force members, then use equilibrium to show that the force in the target member equals the applied load.

Apply the method of joints to a nine-member truss to determine tension and compression in members, using free-body diagrams, reactions, and moment equations in a 60-degree equilateral-triangle geometry.

Learn how to determine axial forces in truss members using the method of sections, by calculating reactions, cutting a section, and applying equilibrium and moment equations.

Apply the method of sections to a truss: draw a free-body diagram, take moments about strategic points, and solve for member forces S1, S2, and S3.

Use the method of sections on a truss to solve for member forces S1 and S4 by moments about E and B, selecting the cut section to simplify the problem.

Apply the method of sections to a fixed truss, draw a free-body diagram, and determine the member forces S1, S2, and S3 using moment equations.

Apply the method of sections to a weightless truss to determine axial force in a member by cutting the section and using a free body diagram with moment equilibrium.

Explore solving a truss problem using both the method of joints and the method of sections, including free-body diagrams, equilibrium equations, and a side-by-side comparison of approaches.

Explore the center of gravity as the resultant of all gravity forces and its relation to the centroid, locating it via moments for lines, surfaces, and solids.

Explore how to locate the centroid of semicircular and quarter circular arcs using numerical integration, symmetry about the line y = x, and the relation x^2 + y^2 = R^2.

Practice centroid calculations for a semicircular arc using a numerical approach, leveraging symmetry about y equals x and integration to determine the centroid distance.

Learn to find the centroid of a parabolic spandrel by modeling the region with tiny rectangular elements, applying moments of area, and integrating to locate the centroid coordinates.

Learn to find the centroid of a composite figure by combining centroids of a square, a right triangle, a semicircle, and a rectangle, using signed areas for subtraction.

Explore the area moment of inertia and its central, parallel, and perpendicular axis theorems, applied to beam cross-sections to assess bending resistance and buckling tendencies.

Compute the area moment of inertia of a rectangle about its centroid and central axes, using the parallel and perpendicular axis theorems and the polar moment of inertia.

Compute the area moment of inertia of a triangle about the x axis and the central axis using the parallel axis theorem, focusing on base, height, and centroid.

Compute the area moment of inertia about the central axis for an I-beam by decomposing it into rectangles and applying the parallel axis theorem to combine contributions.

Explore equilibrium in single rigid bodies and interconnected systems of rigid bodies. Apply the principle of virtual work to solve hazy equilibria in interconnected systems.

Explore virtual work in rigid-body mechanics through numerical examples, compare moment equations and the principle of virtual work with equilibrium methods, and assess potential advantages.

Apply the principle of virtual work to solve equilibrium of an interconnected system of rigid bodies, drawing free-body diagrams and using virtual displacements and geometry to relate theta to forces.

Apply virtual work principle to a force at the top left of a triangular frame. Derive the compression using angles, base, height, and B, H, X from the line diagram.

Explore how dynamics extends statics with unbalanced forces causing acceleration, and learn three dynamic problem-solving approaches—Newton's laws with kinematics, energy methods, and impulse–momentum—focused on particle kinetics.

Explores kinematics of a rod sliding along a frictionless wall, deriving displacement, velocity, and acceleration profiles via a right triangle relation and differentiation, then signals a move to kinetics.

Compute the acceleration along the incline using Newton's laws with friction, then apply kinematics to find the travel time from A to B and the bottom velocity.

Apply Newton's second law with kinematics to a skier on a 40-degree incline; compute acceleration from 20 m in 2.5 s and determine the coefficient of friction.

Model the airplane as a particle and apply Newton's law with three engines to determine the takeoff distance at 61 m/s on a 0.5-degree incline with no friction.

Analyze an accelerating card with a pendulum, derive the equilibrium angle theta as a function of acceleration and gravity, and determine the force required to sustain this configuration.

Explore particle kinetics and the work-energy theorem, linking the net work of forces to changes in kinetic energy, and compare this approach with Newton's laws and kinematics.

Use the work-energy theorem on a vertically fired ball with zero air resistance to find maximum height from initial kinetic energy, equating gravity's work to the kinetic energy change.

Apply the work-energy theorem to a 50 kg block on a 15-degree wedge with mu 0.3. Compute final velocity vb ≈ 3.15 m/s, showing energy losses due to friction.

Apply the work-energy theorem to a block moved by spring and string forces from rest, compute the spring and string work, and determine the velocity at point B.

Explore impulse momentum theory by linking force over time to changes in momentum, and apply conservation of momentum to elastic collisions and impulse-driven impacts.

Apply the impulse momentum theorem to a fighter plane by calculating its final velocity after a 3-minute thrust of 20 kN, using the initial speed and mass with unit conversions.

Apply impulse momentum and conservation of linear momentum to a bullet embedded in a block scenario. Compute the final velocity of the combined mass as about 0.898 m/s.

Apply impulse–momentum principles to determine the golf stick’s impact force on a golf ball, using mass, final velocity, and a brief contact time.