Banked Turns for Bikes

This summer, my family and I went to California (same trip as the rope swing picture) and when my parents were done paddling we visited some colleges. These two pictures are of the campus as UC Davis. On the right, you can see that there are tons of bikes on campus and this picture was taken in the summer so classes weren't even in session, so during the regular year there would be even more. The picture on the right is a walkway/bike path that winds through campus and you can see that the path is banked as it curves down the hill. Banked curves allow for greater speeds, because on a banked curve centripetal force is made up of a combination of normal force and the x-direction component of friction. On level ground, centripetal force just comes from normal force, so on a banked curve, there is more centripetal force than on level ground. This added centripetal force allows bikers to travel at greater speeds without losing grip and flying off tangent to the curve. This banked path is especially important on a college campus because there are tons of bikers, all of whom are in a hurry and probably hyped up on caffeine :)

Rope Swing!

This summer, my cousin Malcolm and I went to California with my parents. My mom and her crew were paddling in the World Sprints races in Sacramento and Malcolm and I had gone with them to check out colleges. Malcolm and I had a lot of time on our hands because we had to hang out at the lake where the races were for an entire week, one day when we were out paddling we found a rope swing and so we spent a lot of time playing on it. We had a waterproof camera, so this is a picture of me on the rope swing. This picture is an example of circular motion. Circular motion is when an object is rotating about an axis that is outside of the object. Although you cannot see it, the end of the rope is connected to a tree branch, so the axis of my motion is the tree branch. When I let go of the rope, I will become a projectile and no longer have circular motion. This picture also shows kinetic and potential energy. At the moment of this picture, I have both KE and PE because I am in motion and I am above the water, which is my reference point. When I let go of the rope and start to fall toward the water, my KE will increase as my PE decreases. Just in this one picture there is so much physics going on! I never stopped to think this summer that something so entertaining and fun would have so much physics involved. 

The Physics of Ice Skating

In February my friends and I went to the ice palace. In this picture we are skating together with our arms linked and playing the game where you spin in a circular motion with the person on the inside as our axis. The person on the outside of the line gets swung around and when they let go they go really fast. When our arms are all linked, we are generally moving in a uniform circular motion with the centripetal force coming from friction. When the person on the outside lets go, they move in a straight line, instead of continuing in a circle, because inertia causes us to resist change in motion and direction. When we whip the outside person around, we are exerting a torque. Torque = force x lever arm. The force comes from our bodies as we use our arms to push the outside person forward and the lever arm is measured from the axis (the inside person) to the force (which comes from the person next to the outside person), they the torque exerted on the outside person will be larger if you have more people in your line, because then the lever arm is longer.

Tree Bridges & Energy

This is a picture of my friend Sarah and I standing on a fallen tree that we found when we were hiking in Nuuanu. The tree was about fifteen feet off the ground and knowing this information would could have calculated our potential energy by using the equation PE = mv. Our potential energy while standing on top of the tree equals our kinetic energy at the ground if we had fallen off. So we could have figured out the velocity we would have been moving at when we hit the ground at if we had fallen by using the equation PE = KE, mv =(1/2)(m)(v)(v). Knowing our velocity at ground level, we could use the momentum formula, P = mv, to figure out what our momentum would be at the bottom of the fall. Impulse (J) is a force that acts for a certain amount of time and it represents change in momentum, J = (F)(t)= change in P= mv. So we know that the impulse exerted on us when we hit the ground is equal to mv. Luckily, we both have sick balancing skills and neither of us fell, which considering that the impulse would be rather large would have hurt a lot, but it is interesting to know that you can basically calculate how much a fall will hurt with only a very small amount of starting information (mass and height). 

Brothers & Energy

A couple summers ago, my brothers, their friends, and I went out to the Mokolua Islands in Lanikai and jumped off the rocks at Shark's Cove. In this picture, my brother Ian is in the air and my brother Haakon is standing up on the rocks waiting to jump. Ian has both potential and kinetic energy. Ian's potential energy is with respect to the water, as soon as he jumped off the rock, his potential energy started to transfer to kinetic energy, and as he gets closer to the water his potential energy will get smaller and smaller. Potential energy can be negative or positive, depending of the reference level, and because my reference level is the water, Ian will have negative potential energy once he hits the water and goes under. The equation for potential energy is PE=mgh. Haakon is not in motion, so his velocity is zero, so his kinetic energy is zero, because KE=1/2mv2. All of Haakon's energy is potential. However, once Haakon jumps off the rock his potential energy will begin to transfer to kinetic energy, just as Ian's did. In a closed system, total energy is always constant and TE=PE + KE. PE can be negative or positive, depending on your reference point, but KE is always positive. An object only has KE if it is in motion. 

Riding the Physics Wave

This is a picture of my brother Haakon surfing (because I couldn't find any good pictures of myself surfing). My impression of this course so far has kind of been like surfing. When you get out into the lineup for the first time in a day you don't really know what to expect, but you hope its going to be good. I wasn't really sure how I would like physics, but everyone said that if I liked biology then I would probably like physics too, and they were right. I worked hard at the beginning of the year, kind of like paddling to get on a wave, and the first couple of days were a little crazy, like dropping into a wave that is bigger than you thought, but for now I feel like I've gotten on the wave and my main job is to keep my balance and work out the kinks. I guess my only worry would be coming to a topic that I totally don't get, but that would just be like going back to chemistry, and I've learned that you can always get help and figure it would well enough to get by. I have been working hard and focusing and I think that my performance generally reflects that. I actually really like physics right now and I am kind of just riding the wave, trying to enjoy it, and hoping ti doesn't end too abruptly.

Inertia in Kayaking, Newton's 1st Law

This is a picture of the start of a kayaking race, all of the kayakers go from a position at rest to that of movement, meaning that they are providing a net force to overcome their inertia. The foot-wells of our kayaks have holes in them so that if water gets in them it can drain out as we kayak, however when we are at rest eh foot-wells just fill up with water because of the holes. I have always found it irritating that when we start kayaking too quickly from a rest position all of the water in the foot-wells rushes back into the seat area, rather than going out the holes in the foot-wells as it is designed to do. However at kayaking on Wednesday we were doing a workout that included starts, meaning that we had to go from a complete standstill to accelerating as fast as we would, and so of course every time we did a start all of the water from the foot-wells sloshed into our seats. It was at this moment that I suddenly realized it was inertia causing this to happen. Inertia describes the fact that an object at rest will remain at rest and an object in motion will remain in motion, unless acted on by a net force (Newton's 1st Law of Motion). When I am stopped in the kayak, my body, the kayak, and the water in the foot-wells are all at rest. However, when I abruptly start kayaking, I am applying a new force of the outside water, which in turn propels the boat and my body forward. Unfortunately, this net force does not act on the water in my foot-wells and so it stays at rest while the boat and myself move forward. Thus, it is not that the water rushes back into my seat when I start kayaking, but rather that my seat rushes forward to scoop up the water that is still at rest. When this realization suddenly hit me during practice I was pretty excited and I turned to my friend yelling, "its inertia!", but of course she had no idea what I was talking about or referencing.