# Amazing Weight Loss Program

### Model Description

This is a simple and rapid demonstration of the perpendicular and parallel components of a force vector on an inclined plane.  By weighing a student or instructor first on the floor and then at some inclination, a “loss of weight” is observed.  This demonstration should take 5-8 minutes.

### Engineering Principle

Spring scales are designed to measure the force acting perpendicular to their surface, and are deliberately insensitive to shear forces.  Thus, the scale will read different weights for the same person if the inclination of the scale is changed. One can show the trigonometric relationship between the angle of inclination and the triangle formed by the weight vector and its components in as much detail as desired. If the angle of inclination is taken from the horizontal, the equations given hold true, and the “weight loss” is observed as the difference between the weight measured on a flat floor versus the normal component at the inclination.

$w_{\bot} = w \cos (\theta)$

$w_{\parallel} = w \sin (\theta)$

### What You Need

Item Quantity Description/Clarification
Scale 1 An old-style spring bathroom scale works best.  Standard laboratory scales can also be utilized with a book instead of people if necessary. Can probably find an appropriate scale for approximately \$20.
Ramp 1 Any stable inclined surface.

### How It’s Done

Before Class: Pre-position the title “Amazing weight loss program” somewhere in the classroom with the scale positioned nearby to get students curious.

In Class: To begin, have a student read off your weight while standing with the scale flat on the floor (see figure, top left). Then, place the scale on the ramp and have the student read your weight again (see figure, bottom left). Everyone will applaud your ingenious weight loss program (see figure, right). Depending on your student population and how long the summer/winter break has been, students can struggle with how the angle of inclination relates to the triangle formed by the weight vector.  Be ready to work through the derivation.

The use of the scale and ramp to demonstrate force vectors.

Additional Application: Prior to the scale demo, emphasize that statics is a subject in which you’ll be touching, measuring, and investigating the world around you.  As a warm up and trigonometry review, state that a sloppy design partner left one dimension off the ramp.  Using only a protractor, challenge the student to find the missing dimension.  Inevitably, students struggle with where to put the protractor and some need the refresher on basic trigonometry.

### Cite this work as:

Tom Messervey and John Richards (2018), "Amazing Weight Loss Program," http://www.handsonmechanics.org/statics/352.