The Art of Approximation

Problem Solving

Summary

This video leads students through an approximation technique to compute the fuel efficiency of a car moving at highway speeds. This is accomplished by using dimensional analysis and a simple experiment to identify the exponents in a formula for the drag force on a car.

Learning Objectives

After watching this video students will be able to:

Model drag to predict terminal velocities.
Determine the fuel efficiency of a car.

Funding provided by the Singapore University of Technology and Design (SUTD)

Developed by the Teaching and Learning Laboratory (TLL) at MIT for SUTD

It is highly recommended that the video is paused when prompted so that students are able to attempt the activities on their own and then check their solutions against the video.

During the video, students will:

Predict the ratio of fall speeds for two cones, one with twice the diameter of the other.
Test their prediction with a simple experiment.
Use dimensional analysis to find exponents in an expression for drag.
Determine the drag force ratio between two cones of equal size, but different mass.
Check the dimensions of an expression for fuel efficiency.