Swimming (and other floating activities)

During this Thanksgiving weekend, I was relaxing and floating on my back in a swimming pool. But, physics soon invaded my thoughts and I started thinking about physics and Archimedes' principle. According to Archimedes' principle, the buoyant force keeping me afloat was equal to the weight of the water I displaced. I realized that I was able to float because the density of the pool water was greater than my density (m/v). The upward buoyant force was enough to counter the downward force of my weight. (Ok, so sorry I don't have any picture for this part.)

This is a picture of a cruise ship on the other side of Glacier Bay (Alaska) when I went on a cruise this past summer. Although the ship seems large and heavy, it floats because its density is less than the density of the water it is sitting in. All of these cruise ships could not possibly exist without buoyant forces!

Doors

My door, the gateway to the wonderful place where I get to do my endless amounts of homework and sleep every now and then...I realized that this door I use everyday demonstrates torque and rotational motion. When I turn the doorknob to open the door, my hand exerts a torque on the doorknob, causing it to move in a circular path. When I push the door open, the door is moving in a circular path with the axis of rotation going vertically through the two hinges. This circular motion is due to the torque I exerted on the door, which is equal to rFsintheta. Therefore, if the doorknob was closer to the axis of rotation, the radius would be shorter, so the door would be harder to open because the torque exerted on the door would be less even if I pushed on the door with the same amount of force. This idea is demonstrated at Forever 21 because the doors of the dressing rooms each have a huge doorknob right in the middle of the door. I found that these doorknobs are not very effective because in addition to the fact that they don't turn, it is harder to open the door when pushing on these huge doorknobs instead of just pushing on the edge of the door opposite of the hinges. Such impractical, physics-ignorant decorations...

Dance Concert

Yesterday, I went to the Castle High School Dance Concert. The contemporary dances were pretty cool. In many of the numbers, the dancers leaped as they moved across the stage. The motion as the dancers leaped and fell back to the floor is an example of projectile motion. In order to move across the stage instead of jumping in place, the dancers had to leap with a certain x-velocity. Also, another basic move that was repeated was turning. The dancers doing single and double turns showed rotational motion. Eventually, the dancers would stop turning after a turn or two because of the torques opposing the rotational motion. There was a torque of friction acting on the foot spinning on the floor and there was also a torque of air resistance on the dancer's body. The dancers had to put in enough initial angular velocity to create a large enough torque to overcome the opposing torques of friction and air resistance to complete the turns.

Fan

After I turned on my fan, I realized that the fan showed uniform circular motion because the blades moved in a circular path at a constant speed. The period of the blades in the fan (the time it takes for the blades to make 1 complete turn) is equal to 2πr/v. The centripetal force on the blades is equal to mvv/r and the centripetal acceleration is equal to vv/r. Because the air was too strong at first, I turned the knob on the side of the fan to reduce the fan speed. The blades slowed down, so the speed was not constant anymore and the motion became just regular rotational motion. This essentially reduced the angular acceleration of the blades, which would be equal to change in angular velocity/ change in time. Well, I guess I can't ever run away from physics...it's everywhere...can't even turn on my fan without thinking about physics concepts and equations...

Reducing the Impulse of a Juice Can

The other day, my friend tossed me a can of juice. Before I could mention that throwing the can was not the best idea considering my slightly incompetent catching skills, she threw the can towards me in a projectile motion. In order to prevent any injury to myself, I caught the can before it hit me and cradled it towards my body. Since J=force*time, cradling the can increased the time of the impulse, and therefore decreased the force felt by my hand to stop the can. If I had held out my hands stiffly or caught the can after it hit my body, I would have felt a stronger force upon impact (ouch). If I knew the mass of the can, speed of the can before it hit my hand, and the time of the impulse, I could calculate the force I felt using the equation J=change in p=force*time. I realized that this situation was similar to the egg catching game because both involved cradling an object to reduce the force of impulse.