## Monday, September 28, 2015

### Are there any F1 drivers in the room?

When I was working through HW 3, the last question caught my attention. What forces must a car overcome to prevent sliding out while cornering?
The clear answer is the radial acceleration of the turn. If the car lost traction and could no longer exert acceleration in the radial direction, it would continue on at the current speed in the tangential direction at the instant it lost traction.
Alas, the complete answer is quite a bit more complicated. As you can see below, a wheel utilizes its static friction, even while in motion. At a given moment, the point on the wheel in contact with the ground is not moving in the direction of the wheel's movement with respect to the ground.
If the car loses traction, then the kinetic friction comes into play. If the wheel is simply spinning independent of the ground, its friction is much lower - in all directions. Once the wheels are spinning, the car is only accelerating at a rate proportional to the kinetic friction, which won't be very much. Watch an example here :
A BMW M5 should be able to accelerate quite a bit more rapidly, but in order to do so, it must utilize all of the static friction of the wheels. Once the wheels start spinning, not enough force can be transferred onto the road surface to accelerate the car much more than if he had been riding a tricycle.
The question now becomes more complicated. To what extent does a loss of friction in the tangential direction of the wheels translate into decreased friction in the lateral direction of the vehicle? Once the wheels are spinning, if the car were to slide laterally, there is a certain kinetic component to the friction applied by the tires. Over a given lateral distance, the starting and ending rotation of the wheels is not the same, even independent of the forward motion of the car. It follows then, that if a driver accelerates or brakes so rapidly going into a corner that the wheels lose traction, they are even more subject to the radial acceleration because of lower friction applied by the wheels in every direction.
But at the moment in the original problem, the driver has not lost traction with his forward acceleration. When friction isn't lost, what forces act on the car, and how should a driver approach a corner?
In fact, there are multiple approaches to this question. Many feel that all braking our acceleration should be done before and after the actual turn, so that all "available" friction is applied against the lateral g's to which the car is exposed. Intuitively, this makes sense, and it makes sense with regard to the overall system and the risk of loss of traction that we described above.
Others argue that you should accelerate through a turn. Given the equation for radial acceleration's reliance of tangential velocity, the though is that by increasing velocity through a curve, the magnitude of the acceleration in the radial direction increases, so the combined vector over time starts to point in the direction of the curve, rather than tangentially. This is an interesting thought problem, but doesn't seem to affect the instantaneous forces acting on the car.
Still other make a good point that braking in a curve can be helpful as well. Rather than addressing any of the points above, this has to do with the weight distribution of the car. You can imagine, that on it's suspension, the car's weight "shifts" rearwards during acceleration, and forwards during braking. Since only the front wheels of a car actually turn, the argument is that shifting the weight of the car onto the front wheels will increase their contact with the road as well as the downwards force on them, allowing them greater friction and therefore to withstand greater lateral force without slipping. Since they are the wheels that are causing the change of direction, this is supposed to help support that change of direction. On the other hand, if the rear wheels have insufficient friction and begin to slide laterally, the car will spin out, which seems even worse than just drifting off on the car's tangent when all wheels lose friction simultaneously. This phenomenon is called oversteer, because the car will try to spin out in the direction of the turn.
Considering the weight distribution in acceleration, the weight moves onto the rear wheels, and our steering front wheels have less weight and less contact area. This can result in what is called understeer, as the front wheels slip laterally because they have insufficient friction to change the direction of the car's travel to the direction of the wheel's orientation.
If you've made it this far, it's time to ask: if the stakes were high, and you had all the time to think about it, would you accelerate, brake, or stay constant through a turn? What factors would guide your decision in different circumstances?

## Sunday, September 27, 2015

### Dangerous playground rides

After class when we discussed the dangerous, yet ever amusing, playground merry-go-round, I decided to look up the physics behind it and some videos of people "experimenting" with them. I found that when a person is using one of these merry-go-rounds and they achieve a high rotational velocity there is a tendency to send bodies flying in all directions. From what I have found, it appears that this happens when the riders lean back away from the center. The person is no longer only accelerating toward the center of rotation, they are now accelerating outward because they are moving away from the center of rotation. This is coupled with the velocity, which is tangential to the centripetal acceleration, and the rider is sent flying through the air. This happens because there is a large force outward at this point because F=ma and the person is accelerating outward so the force (which is directly proportional) is now outward and the person goes soaring.

Here is a video, demonstrating this effect in a real life scenario:

Please do not try this at home.

## Wednesday, September 23, 2015

### Lyrical Physics

Today, I’d suddenly noticed physics in a song I’d heard dozens of times. “First” by the Cold War Kids is rock ballad invigorated with a commanding beat and emotional melody which summates to express confusion behind a failing relationship. While earlier, I’d loved this song for its intensity, now I have a new reason to love it: the mention of physics! Listening to the words today I hear the lines:

“Flying like a cannonball, falling to the earth, / heavy as a feather when you hit the dirt.”

And suddenly the song takes on a whole new meaning as real world use of projectiles and gravity as means to cope with a disappointing relationship. On the surface, these lyrics express the struggle of feeling like you are lost in a freefall when someone is not the person you thought. Once hearing these lyrics though, I had to use our physics skills to unearth what the artist was actually trying to say. Based on the lyrics, the artist is comparing the similarities between a cannon and a feather in a free fall. The first concept to address is the force gravity. The force of gravity is acting on both the cannon and the feather. If we disregard air resistance, these objects would fall at the same acceleration, -9.8 m/s2. In the context of the song this means that metaphorically, both a cannon and feather can experience the same relationship struggles. The interesting part of the lyrics though is the last line of “heavy as a feather when you hit the dirt.” Cannons and feathers obviously have different masses. This means that they have different weights because Fg=m*g. Therefore, the cannon could not be “heavy as a feather” at the end of a freefall because the mass is not changing. Since the mass of the cannon is not changing, it should have the same force of gravity acting on it at the top and bottom of its freefall. In order for the second part of the line to be true, the mass of the falling object would need to change over the course of the freefall in order for the falling object to be as “heavy as a feather.” If this were the case, in a deep way, maybe the artist saying that the freefall of this relationship as caused him to loose a piece of himself (some mass) so that he is now experiencing the same force of gravity as a feather by the time the relationship is through.

In all, understanding this concept of physics has immensity increased my appreciation of this song. Who’d of thought that metaphors involving physics could access a new perspective of relationships, allowing them to seem even more beautiful and tragic than before.

## Friday, September 18, 2015

### The Physics of Aqua Jogging Compared to Running

A large problem with running is the stress that is placed on the runner’s body due to the constant motion and pounding of hitting the ground—it is estimated that up to 85% of runners have been injured at some point. A way that many runners are combatting that are by integrating aqua jogging into their routine as a cross training exercise. The question is how this compares to the physics of running, and how effective it can be as a training technique. The technique is growing in popularity with many collegiate runners training in this way, and even some NCAA champions have used this method. So is it really effective or is it just a fad?

The biggest differences between normal running and aqua jogging are the forces of gravity and resistance. In regular running, the full effect of gravity is felt. The runner is feeling the acceleration of -9.8 m/s2 in the y direction when coming down from each step. This brings in the importance of the runner’s general center of mass, which must be well balanced in order to prevent compensation in other areas of the body and to create minimal impact. When running on land, it is important to have good posture in order to prevent over striding (which offsets the balance of the enter of mass). Injury occurs when the runner is in the support phase of a stride, the time when the runner is on the ground (as opposed to the flight phase when the runner is in the air). So if a runner has certain weaknesses that are made worse by poor posture and a stride that keeps them on the ground for long periods of time, there is a high likelihood for injury. The goal is to run with legs underneath the general center of mass in order to make running as impact free as possible (accelerating without too much effect of gravity). The air resistance in the x direction in regular running is about 1N on a wind-free day.

Aqua jogging provides an option that can reduce body weight up to 90%, thus reducing the normal force that is placed on the runner (because they are not on a surface). Water also provides a more resistive force because it is 800 times denser than air. Thus, aqua jogging replaces the force of gravity with the force of resistance in the x direction, which the body (in lower leg injuries) is better able to cope with. Studies have shown that baseline heart rates are similar when comparing aqua jogging and regular running, it is just hard to get the maximum heart rate when running equivalent to that when swimming. Thus it can act as a good way to maintain fitness, but aqua jogging is not a good method to improve on pacing and speed training for specific races. Aqua jogging reduces the need to balance the general center of mass (since the mass is greatly reduced by the reduction of the normal force). Thus, there is less stress in the y direction of acceleration, which helps the runner to stay injury free.

With these ideas in mind, aqua jogging is presented as a useful technique for combatting injury. It provides a way to continue training without losing fitness during an injury, and for those who are not injured, it provides a way to maintain fitness without adding an additional day of impact.

## Thursday, September 17, 2015

### Sedentary Shoes

The topics learned in the first few weeks of Physics 111 conjured up a funny memory that I have from my childhood. My dad, a NYC fireman, was on his way to work and was dropping me off at school on the way. We had traveled a few blocks from home when we stopped at a red light, and a woman gave us a very funny glance, pointed at the roof of our car, and then motioned for us to pull our windows down. She then exclaimed to us, "There's a pair of boots on your roof!" Pulling over, my dad realized that he had forgotten to place his work boots back inside the car: carrying multiple things in his hands, he had temporarily placed them on the roof so that he could unlock the car and put his coffee in the cup holder. Being in a rush he had forgotten about them and left them up there. We both laughed about how we could have driven without them falling off. Now, I can understand that physics played an instrumental role in keeping his shoes stationed at the top of our car.

Newton's laws of motion played a role in allowing the shoes to stay stationary. Specifically, Newton's second law of motion, which states that “the acceleration of an object is directly proportional to the net force acting on it, and inversely proportional to its mass. The direction of acceleration is in the direction of the net force acting on the object” (Class notes).
Î£F = ma

I have made the following free body diagram to consider the forces acting on the car and the boots.

It is important to note that the force of friction acting on the boots is in the same direction as the car's travel. This is due to the fact that, lying on top of the car, the boots would have been jerked backwards if they had ever begun to move. Because friction is a resistive force, it is thus acting in the +x direction.

The question to consider, then, is why didn't the boots fall off of the car as the car accelerated and traveled during its route to school? The important factors in answering this question are friction and acceleration. It is clear that the car accelerated when it went from rest, in our driveway, to driving through my neighborhood. Because the boots were stationed on top of the car, the acceleration of the car is the same acceleration of the boots. However, while the car was accelerating, the boots must have been carried along on top of the car in order for them to stay secured to the car during travel. This stationary aspect is thus a result of the force of friction between the car roof and the boots.

Considering Newton's second law, it is apparent that the boots will not move (accelerate) without a force acting on it to cause this motion. The only force acting on the boots in the x direction is the force of friction, thus the equation for the boots becomes:

FFr = mbootsacar

Because the boots never slid, the relevant friction force is static friction:
The static friction coefficient depends on the surfaces of the situation: in this case the boots and the roof. If a force was applied that was greater than this force of static friction, the boots would have started moving, transitioning into the realm of kinetic friction. Even though the boots were in motion as the car moved (they were carried along on the top), the part of the boots in contact with the roof were stationary relative to the roof, so it was static rather than kinetic friction.

Summing all of these pieces of information together: for the boots to stay on the roof, the force of static friction was equal to the force of acceleration acting on the boots (the acceleration of the car).  In other words, the total force applied when the car began to move was not enough to move the boots, thus "canceling out" the effect of the car's movement. If the force of the car's acceleration would have increased dramatically, the static friction would have increased until the maximum possible static friction was achieved: it would then transition to kinetic friction, be able to overcome the force of the car's acceleration, and also move. For all of this to be true, I assume that the acceleration of the car must not have been very large: if there was a very large acceleration it would have most likely surpassed the force of static friction and enabled the boots to move. This is reasonable because we were driving slowly through my neighborhood, with no major roads or highways: the speed of the car was relatively slow and there were no major changes in speed which would have tossed the boots off. Additionally, there may (or may not) have also been a large coefficient of static friction (allowing the boots to stay stationary), for the rubber soles of the boots on the roof- since the boots were textured and had grooves in them, despite the smoother roof. A larger coefficient would mean that the acceleration could have been larger and still been equal to a force of friction that lies in the static range: thus, the boots would not move. Despite these assumptions, it is certain that the acceleration was equal to the force of friction, sparing my dad the issue of being shoe-less at work.

## Monday, September 14, 2015

### World Rowing Championships

Competitive rowing races take place over 2,000 meters, and in eight man shells at the professional level, are completed in around five and a half minutes. Clearly, these boats are moving quickly and the rowers are applying quite a bit of force. But just how hard are the rowers working (we will use force applied as a proxy for exertion)? The winning British crew completed the race in 5:36.19, attaining their terminal velocity of at 500m, and passing this point in 1:20. This crew (the rowers, oars, and boat) had mass of 932.9 kg. So, using kinematics, the boat accelerated at 0.156 m/s^2 and using Newton's Second Law the rowers applied 145.53 N, with each rower applying 18.19 N. This however, is just the x-component of the force applied, as a rower presses against a footplate that is at a 45 degree angle. Using some trigonometry, each rower applied 25.73 N.

Rowing involves many more forces than just that applied by the athletes' legs. The buoyant force, and minute forces applied to the boat by the athletes by their movement in the shell all contribute (since boats need to be balanced, the resultant of these small movements must equate to zero). Additionally, air resistance opposes the movement of the crew, which explains why the British did not continually accelerate throughout the race. This cursory consideration of rowing hints at how comprehensive a lesson in physics rowing can be. Click the link to watch the race from earlier this month!

http://www.worldrowing.com/photos-videos/racevideos/

## Sunday, September 13, 2015

### Trying to Throw the Trash Out

Last night, I was making dinner in my Birch kitchen. I tried to slide some cucumber peels off the edge of my counter into the trashcan, but (sadly) I missed. I realized that, using kinematics, I could easily figure out why I missed, assuming the trashcan is 0.5 m away from the counter edge, and 0.5m lower than the counter. From the calculation below, it's pretty obvious why I missed. Then I thought, I shouldn't let this happen again. Doing a simple calculation, I then realized I should have pushed the cucumber peels off at a velocity of 1.6 m/s instead of 3.0 m/s. Lesson learned: less velocity means a cleaner kitchen.

## Friday, September 11, 2015

Cliff Jumping

This summer I went on a hiking trip to Colorado. While in Aspen, we visited a place called "Devil's Punchbowl", which is famous for its cliff jumping. Despite my excitement to jump, I ended up chickening out. This trip got me thinking about how intricate Cliff Jumping actually is. Although normally considered fun, some people take cliff jumping to the extreme. Laso Schaller jumped 59 meters this summer in Switzerland. Although the video doesn't show any math or physics, Schaller's jump was completely controlled by the kinematics we've been learning about. We know during his fall he accelerated 9.8 m/s^2 downward and his displacement was also 56 meters down. This information is very important because it can help us calculate the speed he will impact the water, which is important for breaking the surface of water. The video actually tells us this information, 123 km/hr, but we could use the total time of his fall 3.28 seconds to calculate this as well. Also, using kinematics, we can find out how deep he will travel below the surface to make sure he will never hit the ground. We would do this by using is velocity upon breaking the surface (123 km/hr) as his initial velocity, final velocity of zero, acceleration, and the time it took him to stop. Overall, this demonstrates how kinematics are involved in everyday life that most people dont know. Also it shows that some things that may seem harmless are actually more intricate than you think.