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

Determine the single force which is equivalent to a force and a couple.

Replace two forces with a equivalent force-couple system at a specified point.

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

Replace two parallel forces with an equivalent single force

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

Find the sum of two couples in a plane.

Calculate the moment of a force about three points using the definition of a Moment.  All forces and points are in the same plane.

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.

MECE3930U: Heat Transfer Bonus Assignment (Transient Heat Conduction).

Please follow the Numbas guidance first if you did not attend the Numbas session.

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

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

This question uses a Geogebra applet to solve a linear program with two variables using the graphical method. It contains three steps:

1. Construct the feasible area (polygon) by adding the constraints one by one. The students can see what happens when the constraints are added.
2. Add the objective function, and the level set of the objective value is shown, as well as its (normalised) gradient.
3. Compute the optimal solution by moving the level set of the objective around.

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

End of chapter exercises for Engineering Statics: Open and Interactive 

End of chapter exercises for Engineering Statics: Open and Interactive 

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.

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

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