M-K6: Projection of a Vector to obtain a Component

PIRA: 1A40.15

Equipment: Dowel rod equipped with head to represent vector, arc lantern (or other projection lantern, such as a Cenco lamp without the lens), rotatable hub with two attached vectors. Set 6, Cabinet 2, Shelf 5 contains the vectors.

Procedure: "Oftentimes the component of a vector is described in terms of the projection of the vector. A demonstration of what is meant by projection is far superior to a lengthy description of the process. Orthogonal projection should be the limit of your demonstration or you will have a lot of explaining to do.

"I think the best arrangement places the projection lantern in front of the audience and at the extreme right (or left) with the projection screen (or wall) the same distance in front of the audience but at the extreme left (or right). If possible, adjust the lantern for a relatively small projected spot on the screen and the screen so that its plane is perpendicular to the axis of the beamfrom the lantern. Make sure that the front of the screen can be seen by all in the audience. Room lights may be dimmed, but should not be turned off. Stand near the screen so that the shadow will be sharp and shadow enlargement by any divergence of the beam will be quite small. Hold the vector in a vertical plane which is parallel to the axis of the beam. Its shadow on the screen will then be vertical and the students' line of sight will be near enough to perpendicular to the length of the vector that their interpretation of position and orientation will probably be correct. (Not all people have good 3-dimensional depth perception.) Stepped rotation of the vector in the vertical plane demonstrates well in the shadow the value of the vector's vertical component for each position.

"A hub capable of holding two vectors and another vector which can be attached to one of these can be used to demonstrate that the sum of the components in a given direction is the component of the sum in the same direction. The equipment is also excellent for displaying the instantaneous values as related to phasor diagrams in both AC and in optics." ¾Percy Carr (1970)