Tension in a String/Resolution of Forces

Brief Description

This physics demonstration illustrates how a single vertical load is distributed into components of tension when supported by a string at an angle. When a mass is hung from the center of a horizontal string, the downward force of gravity (F_g =mg) must be balanced by the vertical components of the tension in each segment of the string. As the string is pulled tighter and the angle θ relative to the horizontal decreases, the tension T required to support the weight increases dramatically according to the relationship 2Tsin(θ)=mg. This effectively demonstrates vector resolution, showing that as the string approaches a perfectly horizontal line (θ→0), the tension approaches infinity, explaining why a string will always sag or eventually snap regardless of how much force is applied to straighten it.

Materials Needed

Two table clamps, four rods with a length of over a meter, two 90° rod clamps, two variable angle clamps, after mass of 1 kg, two PASCO tension protractors, two chalk tray spacers, and fishing line.

Setting Up and Performing the Demo

The set-up shown in the photos are on one of the metal rolling carts from the demo room.  The support structure is built on the cart. Using the table clams and chalk tray spacers attached the vertical rods. Using the 90° rod clamps attached a horizontal rod to the vertical ones. Using the variable angle clamps and the final rod to add a cross bar between the two vertical rods.  Attached the tension protractors to the horizontal rod. Tie the fishing line between the two tension protractors and add the mass some where in the middle of the fishing line making sure the angles formed read either 30° and 60° or 45° on both protractors to make the math easier to do (the 30° and 60° is what is shown in the photos). Make sure that the students cannot see the scales as they will be asked to calculate the forces each protector reads. After the students are done calculating rotating the cart around to see if their calculation matches the results.

Alternate Setups

This demo can be set-up using the normal demo table and the students can be asked to calculate the forces given a certain weight and given the angles that the forces are applied. After the calculations are made add the mass to the system and compare the results.