# Torque

### Purpose: To balance the torque applied on a beam.

Simulation Used: Balancing Act from the PhET collection at the University of Colorado.
• Theory

• When a force F is applied at a distance r from an axis, and the angle between the two is given as θ, the torque is defined as:

$\tau = r F \sin \theta$

By convention, the counterclockwise (CCW) torque is considered positive and the clockwise (CW) torque is considered negative.
When an object is at equilibrium, both the net force and torque must be zero:

$\sum F=0; \sum \tau = 0$
In other words, the CCW torque and CW torque must be equal in absolute value.

• Preliminary Settings.
• Open the simulation Balancing Act.
• Select "Balance Lab" tab from the top
• In the "Show" window to the right of the simulation, select "Mass Labels", "Ruler", and "Forces from Objects".

• Activity 1: Two Bricks
• From the brick window, click and drag one 20-kg brick (Brick 1) at 1.0 m to the left of the pivot point (location x1 = -1.0 m)
• Find the location x2 of a second brick (Brick 2) in order for the beam to be balnced. You can check whether the beam is balanced by clicking on the "Remove Supports" button at the bottom.
• Calculate the corresponding torques, Torque 1 and Torque 2.
• Repeat for all the selected bricks and locations given in the table below. Record the location of Brick 2 with its correct sign: "plus" for locations to the right, and "minus" for locations to the left of the pivot point.
• Data and Results: Record your results in the table below. Follow the example (row 1)

 Brick 1 (kg) location x1(m) Brick 2 (kg) location x2(m) Torque τ1 (m.N) Torque τ2 (m.N) 20 - 1.0 10 20 kg - 0.75 m 10 kg 5.0 kg - 1.5 m 15 kg 15 kg - 1.0 m 10 kg

• Activity 2: Three And More Bricks.
• Click and drag two bricks to the locations given in the table below. Determine the location of a third brick so that the beam is balanced.
• Calculate the corresponding torques, as well as the net clockwise and counterclockwise Torque.
• Data and Results: Record your results in the table below following the example done in row 1.

 m1 (kg) x1 (m) τ1 (m.N) m2 (kg) x2 (m) τ2 (m.N) m3 (kg) x3 (m) τ3 (m.N) CCW Torque (m.N) CW Torque (m.N) 10 - 1.5 5 -1.0 20 10 - 1.5 5 +1.0 20 10 - 1.75 15 +0.75 5 20 +0.25 10 +1.75 15

• Activity 3: Determine the mass of an object
• In the Bricks window, use the right and left arrows to navigate to the mystery objects: A, B, C, and D.
• Place object A on the beam, balance the beam by placing bricks or humans. Determine the mass of A in kg.
• Repeat for objects B, C, and D.
• Data and Results: Record your results in the following table.

 Object mass (kg) A B C D

Acknowledgements.
• The Java Applet comes from the PhET Interactive Simulations at the University of Colorado, Boulder.
• Some activities are based on the "Laboratory Manual, Physics 231 - 232" by Walter Wimbush, Northern Virginia Community College, 2008.

Created: Sat Jul 07 14:32:17 Eastern Daylight Time 2012 Last modified: Sun Jul 8 23:06:58 EDT 2012