William Haynes

An A-frame structure supporting a force and a moment. The feet are at the same vertical position, so taking moments at one foot yields the y component of the reaction at the other.

Solve Truss by the method of joints.  The solution is simplified by recognizing symmetry.

Classic machine problem.  Find the mechanical advantage of a pair of pliers and the force on the hinge pin.

Find the centroidal moment of inertia of a sideways T shape. This requires first locating the centroid, then applying the parallel axis theorem.

Solve for the internal force in three members of a truss.

Find the rectangular (scalar) components of a force for two coordinates systems.

Friction

Student estimates, then calculates exactly and symbolically the value of $k$ for a parabola $y = k x^2$ which passes through a given point.

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

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.

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

Shows how to switch to the 3D graphics view of a geogebra applet using an extension function.

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.

This demonstrates how to set xmin, ymin, xmax and ymax for an embedded geogebra diagram.

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

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

Two dimensional particle equilibrium problem.  Advice shows how to use how to use slope triangles to find sines and cosines, rather than finding the angle and using that.

Shows different ways to load a geogebra applet.

Different methods of loading a geogebra applet.

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

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

Student is given two points defined symbolically, and must find the equation of the line they define, then use integration to find an equation for the area under the line, bounded by the x-axis and vertical lines through the two points.   

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

Determine frictional force acting on a block on an incline.  Coefficients of friction, weight and a horizontal force are given

Friction

Friction

Friction

Replace two parallel forces with an equivalent single force

Friction

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