I Can Be More Powerful Than You!

A photo of me sitting at the top of the Koko Head stairs hike.

NOTE: To keep things simple, I neglected air resistance and friction in all of my calculations and explanations.

Looking up from the bottom of the Koko Head stairs.

My dad and I often hike the Koko Head stairs during free time on the weekends. For the past few weekends, I have been able to complete the 805 meter long hike in about 15 minutes (V=0.89m/s) while my dad has been able to complete it in about 20 minutes (V=0.67m/s). At the top of the hike, our total work done can be calculated by W=KE+PE. Given our velocities, masses of 59kg and 82kg for me and my dad, respectively, and that the height of the mountain is 368m, our total work at the top is as follows:

My Work:

W=(0.5)(59kg)(0.89m/s)^2 + (59kg)(9.8m/s^2)(368m)

W=212800.967 J

My Dad’s Work:

W=(0.5)(82kg)(0.67m/s)^2 + (82kg)(9.8m/s^2)(368m)

W=295743.205 J

How embarrassing… My 55 year old dad does more work up a mountain than I do! Really though, this isn’t surprising. Since my dad weighs significantly more than I do, his work is going to be greater than mine at the top of the mountain because his PE will always be greater. KE, in this case, will not affect total work by much at all.

Surely, because my dad does the most work up the mountain, he has the most power too, right? Not necessarily. In this case, however, his power is actually greater than mine. Given our times of 15 minutes and 20 minutes for me and my dad, respectively, we can calculate power as P=Work/Time.

A view from the top of the Koko Head stairs.

My Power:

P=212800.967 J / 900s

P=236.45 W

My Dad’s Power:

P=295743.205 J / 1200s

P=246.45 W

As a cross country runner, I don’t know if I’m going to be able to let my dad beat me in terms of power for much longer. After all, I am only 10 watts behind him! If I were able to cut down my time the next few times I hike Koko Head stairs, I will probably be able to soon beat him in terms of power. Although his total work will be significantly larger than mine, I can, with a fast enough time, become more powerful than my dad. Who knew that hiking up Koko Head could become so technical and competitive?! Ah, the life of an athletic physics nerd.

Why Can’t I Get Down?!

A photo of the Area 51 ride at the 50th State Fair.

As Jordan and I were walking through the 50th State Fair trying to find a ride to go on this past summer, she turned to me and said, “We should go on that Area 51 ride! It is completely physics based and it’s supposed to be really fun.” Curious as to how the ride worked, I asked Jordan for an explanation. Not having taken AP Physics B at the time, however, most of her explanation went over my head. Now that I have been enlightened by the beauty of circular motion, however, I can easily explain the phenomenon of the Area 51 ride.

Before the ride begins, everyone stands up against a circular wall with seemingly no safety measures like seat-belts or straps in place. At first a bit worried about how safe the ride was, Jordan assured me that the laws of physics behind circular motion would be the only safety measures needed to keep us safe.

A photo of me and Jordan inside the Area 51 ride. She is trying to assure me that, because of centripetal force, I am not going to die on the ride.

The ride starts to spin at a slow angular velocity but then increases its angular velocity as time goes on. Given that the distance of any person from the center of rotation to the wall (the radius) is constant, using the relationship v=ωr we see that the linear velocity increases as angular velocity increases. Furthermore, given that friction is directed upwards and weight is directed downward, we find that our resultant, centripetal force (Fc=mv^2/r) is directed inward toward the center of rotation. As the centripetal force, also the normal force, increases with an increase in linear velocity, friction increases as well because f=(Fn)(μs). Eventually, the ride is going so fast that friction is greater than weight directed downward, which makes the rider feel as if they are stuck to the wall unable to easily move or get down.

Not having any understanding of circular motion at the time, I was confused as to why I was stuck on the middle of a spinning wall unable to get down. Now, with a thorough understanding of circular motion, the fact that I can be stuck to a spinning wall is not surprising, it’s just physics! How phun!