Dimensional analysis also known as the factor-label method or unit-factor method is by far the most useful math trick you'll ever learn. Maybe you've learned some algebra, but will you use it? For many people the answer is, "not after the final exam.
Finally, after rockets decelerated it completely, the rover was lowered to the surface of Mars. Every step of this dance was carefully choreographed and rehearsed in many experiments here on Earth. But how could NASA engineers be sure that their designs would work on a totally different planet?
The answer is a problem-solving method called dimensional analysis. This video is part of the Problem Solving video series.
Problem-solving skills, in combination with an understanding of the natural and human-made world, are critical to the design and optimization of systems and processes.
Before watching this video, you should be familiar with unit analysis, and understand the difference between dependent and independent variables. Before we talk about dimensional analysis, we need to know what dimension is.
Dimensions and units are related, but different, concepts. Physical quantities are measured in units. The dimension of the physical quantity is independent of the particular units choosen. Both grams and kilograms are units, but they are units of mass.
There are 5 fundamental dimensions that we commonly deal with: All other dimensions are obtained by taking products and powers of these fundamental dimensions.
For example, no matter how you measure the physical quantity velocity, it has the dimension, which we denote with square brackets, of length divided by time, or length times time to the negative 1 power.
Pause the video here and determine the dimension of energy. Energy has dimension Mass times Length squared over Time squared. How is this useful? Part of the landing sequence calls for a parachute to slow the vehicle down. The terminal velocity of the Rover depends on the mass of the rover itself and its heat shield, and several different variables related to the parachute design: How do we predict the behavior of a parachute on Mars based on an Earth experiment?
And what variables do we need to consider in designing our experiment on Earth? This is where a problem solving method called dimensional analysis can help us.
Before we get started, we must first determine what the dependent and independent variables are in our system. The dependent variable is terminal velocity.What you are going to do is break the problem down into several small problems that you can solve.
Here's your first problem: 1. Ask You might remember this formula for a test, but don't expect to remember it when you need it. With dimensional analysis you can always think your way to the right answer.
write your answer to indicate a. Dimensional Analysis Worksheet Set up and solve the following using dimensional analysis. 1) 5, inches to miles 2) 16 weeks to seconds 3) 54 yards to mm 4) 36 cm/sec to mph 1 mile = 5, ft Write, and then solve your own dimensional analysis problem.
Be creative! Title. to cm 8 gcm to lbsft 9 32 ftsec to metersmin 10 write and then solve your own dimensional analysis problem6 a conversion factor? is a fraction obtained from an equality equality 1 in = cm? is written as a ratio with a numerator and denominator?
can be inverted to give two conversion. 5) g/mL to lbs/gal 6) 19 inches to feet 7) inches to cm 8) g/cm to lbs./ft 9) 32 ft/sec to meters/min 10) Write, and then solve your own dimensional analysis problem.
Problem Solving Dimensional Analysis LESSON 1. Worker bees travel up to 14 km to Write larger or smaller to show whether your answer will be a larger or smaller number of units. Solve the crossword puzzle. Across 4. There are meters in a.
7. Dimensional Analysis Worksheet Set up and solve the following using dimensional analysis. 1) 5, inches to miles 2) 16 weeks to seconds 3) 54 yards to mm 4) 36 cm/sec to mph 1 mile = 5, ft Write, and then solve your own dimensional analysis problem.
Be creative! Title.