# Optional Practical: Balanced beam (Geogebra)

Introduction

In this exercise you will construct a GeoGebra simulation to show when the torques on a beam are balanced. First we will consider the simple case of a beam with no mass.

#### Drawing the beam

- Use the polygon tool to draw a rectangle from -3 to +3 with a width of 0. Don't worry about drawing this exactly, you can adjust the corners afterwards.

#### Placing the pivot

To enable the pivot to be moved you need to define its position with a slider

- Add a slider named O from -3 to +3 with increment 0.1
- Add a point close to the origin and redefine its coordinates as (O, 0.1).
- Changing the value of O will now move the pivot along the beam.

#### Adding forces

The forces will be displayed as vectors but before these can be added you must define the beginning and end with points.

- Add sliders for The distance to the point of application L
_{1}and the Force F_{1}from -3 to +3 with increment 0.1. (To get subscript type L_1) - Add a point on the beam and redefine its coordinates as (L_1,0.1), this is the point of application of F
_{1} - To define the length of the vector add a second point and redefine its coordinates as (L_1,F_1+0.1)
- Draw a vector between the points
- Hide all the labels.

Use the same method to add a second force.

#### Displaying the size of the forces

The size of the two forces is given by the sliders but to make it easier you can add labels to the vectors.

- Add text box and choose F_1 from objects
- Right click the text in properties define the position of the text as the top point of vector F
_{1}

- Add a label for the other Force in the same way.

#### Equation for equilibrium

The next stage is to write the equation for equilibrium that will be used to display text indicating if the beam is balanced or not. Torque = Force x perpendicular distance to pivot, if the pivot was in the center than torques would be simply F_{1}L_{1} and F_{2}L_{2} however we have made a variable pivot so the Torques are F_{1}(L_{1} - O) and F_{2}(L_{2} - O)

- In the input line type Torque = F_1*(L_1 - O) + F_2*(L_2 - O)

#### Balanced condition

The last step is to display "balanced" text when the resultant torque = 0

- Add text "balanced"
- Right click the text and choose properties.
- Under the "advanced" tab enter Torque=0 in the "condition to show object" box

#### Further development.

Now you have the basic simulation but you can make a more advanced version with a beam that has weight. You can also add arrows to show the distances.