Engineering Statics

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.

Given three vectors, arrange them in a tip to tail arrangement using geogebra, then estimate the magnitude and direction of their resultant.

Determine the oblique components of a vector.

Given the specifications of two vectors, draw the parallelogram representing their sum, then estimate length of the diagonal. 

Given three vectors with integer components, find the corresponding magnitude and direction.

Find the magnitude and direction of a force given its scalar components.

Equilibrium of two interacting particles.

Find the tensions is a system of cables supporting two loads.

3D equilibrium of a particle problem.  Rectangular steel plate supported by three cables, dimensions and density given.

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.  

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

Solve for an angle which will result in equilibrium for a triangle subjected to three couples.   A trial and error solution is recommended.

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.

Two known forces, and a third with known magnitude act on a rigid body.  Apply $\Sigma M = 0$ about a pin restraint to determine the direction of the third force.  The problem has two valid answers.

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

Find the reactions of a rigid body (a triangular plate) at a pin and roller, using the three-force body principle.

Find the reactions of a rigid body (a triangular plate) at a pin and roller.  The load is at an angle.

Find the reactions of a rigid body (a truss) at a pin and roller.  All loads are either horizontal or vertical.

Two forces act on a bell crank. This problem has two unknown magnitudes and an unknown direction which makes it tricky to solve by the equilibrium equation method.  

The solution is much simpler if three force body principle is used.

A hand truck on wheels.  Easiest to solve by rotating coordinate system.

Classic problem of a vehicle parked on an incline.  Best solved by rotating the coordinate system.

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

Find the force required to produce a given moment, or vice-versa.

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