vector - a definition
Vectors are a mathematical tool used a lot in physics to represent physical quantities with a direction and a magnitude (from Lat. magnus - great, meaning the size). Vectors are drawn to scale to be able to campare the physical quantities involved.
adding two vectors in 2-dimensional space
Here, an example for calculating the sum of forces in different directions.
Move one of the vectors so that the tip and the end meet (keeping the direction). The distance from the end of the first to the tip of the second vector gives you the direction of the resultant (green vector) and the magnitude to scale.
components
Any vector can be seperated into two directions. Here the directions are the x-axis and y-axis. This doesn’t have to always be the case.
Note: showing the correct signs indicating the direction + or - still needs fixing.
inclined plane - geneigte (schiefe) Ebene
For example, on an inclined plane the Weight (W or FG) due to gravity points towards the centre of the Earth and one component is parallel (Hangabtriebskraft - FH) to plane while the other component is perpendicular (or normal or orthogonal - Normalkraft FN) to the plane.
geogebra app
The force due to the weight of the ball (die Gewichtskraft) is split into two components, one downhill (die Hangabtriebskraft) and one perpendicular to the surface (die Normalkraft).
Drag the point H to change the weight. Drag C to change the angle (inclination) of the plane.
TASK
- observe how the forces
$F_H$and$F_N$change. - what happens to
$F_H$when the angle is 0°? 90°?
using Pythagoras and trigonometry
exercise
Find the force in the wire using trigonometry.
Find the force in the wire using trigonometry.
lamp hanging from the wall - bird on wire
Adjust the weight $F_G$ to the correct value. You can adjust the angles as well.