Have you ever climbed up a steep hill in Redwood city and wondered, “wouldn’t it be so much easier if this hill was just as tall but half as steep?” Well, I have, and so I began to wonder why moving things (including ourselves) up steeper inclines feels much harder.

Although a steep 20 foot hill and a flatter 10 foot hill in Redwood city require the same amount of force to climb, the less steep hill requires a lesser force over a longer distance, because of the smaller angle (finally, math!). This may sound complicated, but it’s much like running a slow jog around the track rather than sprinting it. Here is a more detailed explanation:

  

 

Using an advanced type of math called trigonometry, you can use triangle laws to calculate how the angle of the hill influences the actual distance of the hill, and the force you need to pull the item up the incline. A lower angle requires less effort over a long period of time, because the parallel force ( the vector difference of the weight and normal force) is less when the angle is not as steep!

This is a complicated concept, and do not fret if you do not understand it after this first exposure (because you will learn more about this in phsyics). for now, when you walk around Redwood City, remember to choose the less steep routes if you want a lesser parallel force to fight against!

For more math fun, visit Mathnasium of Palo Alto – Menlo Park