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 L1 and the Force F1 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 F1
  • 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 F1

  • 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 F1L1 and F2L2 however we have made a variable pivot so the Torques are F1(L1 - O) and F2(L2 - 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.

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