Force systems

Part of the Statics course offered by the Division of Applied Mechanics, School of Engineering and the Engineering and Technology Portal

Lecture

Force systems are the starting point of engineering analysis.

Force Vectors

A force vector is a force defined in two or more dimensions with a coponent vector in each dimension which may all be summed to equal the force vector.

<math>\vec F(x,y,z) = F_x + F_y + F_z</math>

or

<math>\vec F(x,y,z) = \hat{i} + \hat{j}+ \hat{k}</math>

Moment

For a system wherein a rigid body experiences a force at a distance from a fixed point, the moment is the quantity (oddly enough of the same units as energy) defined by the force multiplied by the length of distance between the fixed point and the point where the force is applied.

<math> M \ = F * L </math>

In the event that a force impacts the rigid body at an angle other than a right angle <math>\vec F = F\angle\alpha = F_x + F_y</math>, the moment is determined by the component of the force vector <math>\vec F</math> that is orthogonal to the length L.

Example:

M = Force * Length = 100 Newtons * 10 Meters = 1,000 Newton-meters (N-m)

Example: Force F is incident on the end of a rigid body of length L at an angle A degrees from the central axis of the body x.

<math>F_y \ = \vec F \sin (A)</math>

<math>M \ = F_y \ * L </math>

Assignments

Activities:

1. Create an activity

Readings:

1. Peruse the appropriate sections of Wikibooks:Statics

Study guide:

1. Wikipedia article:Force System
2. Wikipedia article:Vector
3. Wikipedia article:Force Vector
4. Wikipedia article:Moment
5. Wikipedia article:Couple
6. Wikipedia article:Resultant