To begin, the mass of the IOLab was measured. an IOLab is a device with an accelerometer and mounting points for lanyards. The readings from the accelerometer were compared to the calculated tension force.
A rope was tied to the IOLab and fed through a tube, anchored at the end. This apparatus allowed a constant radius to be maintained, and it also reduced error from the rope having to pass over the uneven surface of the human hand.
To help maintain a constant period of motion, a metronome was used. Stopwatches were used to measure the period of each rotation. Because the act of swinging a mass in the air is extremely rapid, data from 60 rotations was collected. The data from the stopwatches and the acceleration data from the IOLab was used to determine an average force of tension.
The objective of this experiment is to swing a mass over one’s head and figure out what the tension in the string is based on the mass of the mass and period of its rotation.
Materials
PocketLab One String Ruler A mass Cowboy hats (optional but highly encouraged) Stopwatch
Introduction
Kenneth, Rohit and Erfan grew up watching western movies, but being children of Eastern descent, one can easily infer the complications associated with their dreams to be cowboys. Additionally, having grown up in the 21st century, there are much cooler and arguably easier jobs to be had, such as being a jazz musician.
To understand the forces at play, check out this free-body diagram of the swinging mass
Where Fg is the force due to gravity and FT is the tensile force from the string on the mass
We can isolate FT with this formula:
where r is the length of the string between the test subject’s hand and the mass, m is the mass of the object, and T is the period of the rotation. Check out this link to see how we derived this formula.
To get a consistent period, we can swing the mass to the beat of our favourite songs. We’d pick anything with a tempo between moderato and allegro (100 – 150 bpm). See table for some recommendations.
Song
Tempo (bpm)
Period (s)
Moanin’ – Art Blakey
120
0.5
Die MF Die – Dope
130
0.462
Girl From Ipanema (Getz version)
130
0.462
Arise – Flyleaf
140
0.429
Dark Thoughts – Josh A
160
0.375
Work Song – Nat Adderley
160
0.375
From a Cage – Envoi
170
0.353
Ocean Avenue – Yellowcard
175
0.343
KARATE – BABYMETAL
180
0.333
Theme from Black Orpheus (Paul Desmond version)
190
0.316
Giant Steps – John Coltrane
300
0.2
Procedure
Record the mass of the mass and the PocketLab
Measure a length of a string, and attach it to the pocketlab.
Put on your cowboy hat
Have a partner record the amount of time it takes for the mass to complete a full circle around you. This is the period of the revolution. To reduce error, count ten revolutions and divide the recorded time by ten.
Repeat Step 4 ten more times to determine a mean period and the standard deviation. These will be used to determine the tensile force in the string.
Time permitting, try different lengths of string, or swing the mass faster or slower.
Rather than swinging the mass in a circle parallel to the ground, we could try swinging the mass perpendicular to the ground (a yoyo trick entitled “around the world”) and see how the tension changes at different parts of the orbit.
