Calculate reactions and shear and bending moment at a point for an overhanging beam with a constant or uniformly varying distributed load.

Determine the forces in the pistons of a hydraulicly operated excavator.

Determine expressions for internal shear and bending moment as a function of $x$ for a beam with two vertical loads.

Find the area, first moment of area, and coordinates of a general spandrel.  The area may be above or below the function.

Find the centroid of a shape made up of a rectangle and two triangles.

Find the centroid of a shape made from a rectangle, triangle, and circle.

Equilibrium of a rigid body.  Find tension to raise a pole.

Determine the reactions supporting a cantilever beam carrying concentrated forces and moments.

Replace three tangential forces with an equivalent force-couple system acting at the center of a circle.

Find the tension required to hold a pole at a specified angle.

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant.

Calculate the moment of a force about three points using Verignon' theorem.  All forces and points are in the same plane.

Find the sum of two couples in a plane.

Find the moment of a couple formed by two equal and opposite forces.

Equilibrium of two interacting particles.

Solve a random oblique triangle for sides and angles.

Rigid body equilibrium problem.  Easiest to solve by replacing forces on the perimiter of the pulley with equivalent forces at the axle.

Find the tension in a rope necessary to prevent a bracket from rotating by applying $\Sigma M = 0$.

Find the force required to balance a see-saw.

Determine the moment of a force about a point by using $M= F d_\perp$ or $M = F_\perp d$.

Calculate the moment of a force.  Must calculate perpendicular distance based on simple geometry, and recognize direction.

Pulley supported by a cable, so the tension in the rope is constant.    Advice is a youtube video showing how to solve the problem.

Find the tensions in two ropes supporting a weight.

Three random forces act on a particle.  Determine the force required for equilibirum.

Find forces required to hold a particle in equilibrium when subjected to a downward load.  Directions of the reactions are given.  

Determine the resultant of three random 2-D vectors.  

Use the parallelogram rule to solve a force triangle.