Saturday, January 6, 2018

Physics of karate

Even though I have never done karate myself, in the past I have seen many karate videos of people breaking concrete bricks and wooden boards with their bare hands. Looking at a basic principle of physics helps to understand how people can pull off these impressive moves.
Since F=ma and Momentum = mass x velocity, force and mass are positively related. When trying to break a board, force needs to be transferred as fast as possible and the person also has to use as much of his or her body mass in the motion as possible.
In addition, the extension of a person’s arm is crucial to breaking the board. Since momentum and velocity are also positively related, the extension point at which the person’s hand hits the board must maximize velocity. Therefore, his or her arm must not be fully extended. Rather, it should be at a point of extension in which the hand has a positive or zero acceleration.
Finally, the person must attempt to exert as much force per square inch on the board as possible in order to break it. That is why hitting the board with the side of the hand is much more effective than hitting it with the palm.
By using the side of the hand, learning to efficiently channel body mass, and finding the optimal point of arm extension, one can plausibly break a board with lots of practice.

Friday, January 5, 2018

Ice vs. Field Hockey

Having played field hockey for much of my life, I never really thought about why field hockey sticks are so stiff compared to ice hockey sticks and what implication this has on shooting in both sports. The fundamentals of physics suggest that the ball velocity of a field hockey shot is created slightly differently than the puck velocity of an ice hockey shot.
Since field hockey sticks are so hard and stiff, the stick is minimally flexed before it makes contact with the ball. When hit, a field hockey ball gains its velocity predominantly by the kinetic energy created as the player accelerates the stick. A large force is exerted on the ball and momentum is transferred from the stick to the ball.
However, in ice hockey, the puck velocity on a shot is created through kinetic energy and elastic potential energy. While the puck gains velocity through kinetic energy in a similar mechanism as a field hockey ball, a puck gains additional velocity through the release of potential energy that is stored when the hockey stick is flexed against the ice. The momentum created by the velocity of the moving hockey stick and the release of the stick flex is transferred from the stick to the puck and determines the velocity of an ice hockey shot.
Another reason why ice hockey is a much faster paced sport is because of the friction involved. Field hockey is commonly played on grass turf, which, compared to ice, is much rougher. Assuming hockey pucks and field hockey balls are made of the same type of plastic, the coefficient of friction for the between the turf and ball is much greater than that between the ice and puck. Thus, if one was the apply the same amount of force to both the puck and ball, the puck would travel much farther. This is why the field hockey turf is watered at the beginning of the game and a halftime, as water helps to reduce the friction between the ball and turf.

Wednesday, December 13, 2017

Thermal Equilibrium

After seeing this picture, my friend texted me asking if we could try this, so we set up our own using hot coffee, a glass of ice water, and straws.
The principle it's based upon is thermal equilibrium, but I didn't think the ice water would be enough to actually cool the coffee a significant amount since it moved so quickly through the strawIt did actually work.

Theoretically, the calculations for the thermal equilibrium equation would be as follows:

Assuming there is approximately one straw full of coffee in the ice water, and the average drinking straw has a length of around 8 inches and a diameter of 0.21 inches, the volume of the coffee inside the straw will be 4.541x10(^-6) m³. Since coffee is very similar to water, we can use the conversion 1 m³ of water = 1000.0 kg of water, giving us a mass of .0045 kg of coffee in the straw. Since we got the coffee fresh, and most coffee is served at about 180°F, we convert that to 82.2°C. 

The straw only takes up 4.541x10(^-6) m³ in the water, so it won't interact with the entirety of the cup of water. Using double the volume of water displaced by the straw, to represent the volume surrounding the straw that might have a chance of interacting with the coffee in the straw in such a short amount of time, gives us .009 kg in the cup at freezing

So Qʷᵃᵗᵉʳ+Qᶜᵒᶠᶠᵉᵉ = 0J
Because we use water for both of them, specific heat (c) can be cancelled out.

(.0045kg)(cwater)(Tᶠ - 82.2) + (.009kg)(cwater)(Tᶠ - 0) = 0J
.0045Tᶠ - .3699 + .009Tᶠ = 0J
.0135Tᶠ = .3699
Tᶠ = 27.4°C

Ice cream heat transfer

The other day, I set out a gallon of ice cream so it could thaw enough for me to actually be able to scoop some out with a plastic fork, because I am a lazy college student who doesn't want to do the dishes. In considering what this melting entails, I thought about heat transfer.

In order for the ice cream to melt, heat is is absorbed. Enough heat needs to be absorbed to first melt the ice cream, Lf for ice cream, and then heat continues to absorb so that the ice cream can reach thermal equilibrium with its surroundings. Obviously, no one wants to eat room temperature ice cream. Therefore, the ideal situation is to scoop the ice cream before it can absorb enough heat to completely melt. The energy being transferred to melt the ice cream comes from the surroundings such as the counter or air. It also explains why people will run an ice cream scooper under hot water prior to scooping. The warm scooper provides energy necessary to melt the ice cream, and make it easier to scoop. Therefore, it's unfortunate I am a broke college student and don't own an ice cream scooper.

Unfortunately, I didn't have a scale to weigh the half empty ice cream container, but the heat of fusion for vanilla ice cream is about 204kj/kg, meaning it's okay if you forget about the ice cream for a few minutes, as it takes quite a bit of energy to melt. According to the internet, it takes more energy to melt vanilla ice cream than chocolate or strawberry. I don't really have an explanation for this, but just thought it was an interesting reasoning for next time your friend's chocolate ice cream is melting faster than your vanilla.


If you’ve been keeping up on your Physics 111 blog post readings, you’d know that Emily Schweitzer is the fearless leader of Colgate’s Curling team. I, although not nearly as skilled, am also a curler, and am fascinated by the physics that makes curling work (like nearly perfect elastic collisions, angular motion, etc.). If you need a basic introduction to the sport as a whole, as it’s important for my post, here’s a wonderful crash course:

There has recently been significant strife in the curling community about certain synthetic fabrics that have been used to make the broom heads for sweeping. These new broom heads have different properties such as less waterproofing, artificial textures/hairs, and different kinds of padding, all which have the ability to melt and carve into the pebbles on the ice much more effectively than the standard broom heads. The concern here is that this new technology allows for cheating and lessening the skill required to curl well, as rocks can be manipulated much more when the brooms are much more effective at changing the ice in its path.

The main logic as to why the sweeping helps the stone travel farther is that by momentarily raising the temperature of the ice, but not melting it, you reduce the kinetic coefficient of friction, slowing the stone down less. You do not want to melt the pebbles on the ice, because then you are increasing the amount of surface area the stone has in contact with the ice, increasing the frictional force on the stone. 

I wanted to more thoroughly understand why these different types of broom heads change the ice in different ways. The standard broom head is padded and made of nylon coated in a waterproof material, and in this example I will examine what would happen if you swapped the fabric out for something that creates more friction with less padding, as done in the newly popular icePad broom head (which is banned in some levels of competition). This is supposed to increase the overall power of the sweep by reducing the surface area wasted on the unpebbled ice, allowing all of the frictional force to be concentrated on the pebbles. This change in fabric is also shown to create more friction between the broom and the ice to heat up the ice more, causing less friction between the stone and the ice. These two manipulations allows a sweeper to exert far less energy to manipulate the stone much more effectively.

If you're looking to read more on this, here’s a few articles that discuss this issue more in depth:

As for now, the verdict on new broom technology is as follows: use a standard broom, and there’ll be good curling!

I was foam rolling the other day and wondered if it mattered whether or not you had both legs on the roller at once when rolling out you quads. Logically it makes sense that you are doubling the weight and doubling the area on which that force is acting. But this can also be thought of in terms of pressure, or force/surface area. Because putting a second leg under the foam roller while the force remains the same (as body weight and gravity are not changing) changes the surface area, the total amount of pressure felt is less.

Here is an example with rough estimates:

Surface area of one leg (the amount of thigh that would be of the roller) about 20 cm2 or 0.002m2

Force of thigh on roller: The thigh is estimated to be 12% of body weight in females (10.5% in males). We will assume the person weighs 130 pounds. 130 x 0.12 = 15.6 pounds or 0.45 kg

P= F/A = (0.45kg)(9.8 m/s2)/0.002m2
 = 2205 Pa

Both legs:
            P = 2(.45kg)(9.8 m/s2)/(0.002m2)2
            = 2205 Pa

Through these calculations, you can see that the same amount of pressure is felt regardless of having one or both legs on the roller.

The Physics of Salting Roads

Winter is a harsh season here in Colgate and usually, it snows heavily and makes it hard to walk or drive on the road. The recent snow up to now has not caused large congestion on the road because there are almost no snow or ice on the road. It is because a certain substance is pulled onto the road and lower the freezing point of ice, and it turns out to be very safe in the winter! Usually people add saltwater and it turns out to be very useful!

According to National Snow & Ice Data Center, saltwater has a relatively lower freezing point than freshwater, which freezes at 0 degree Celsius. And for saltwater,  its freezing point decreases by 0.28 degree Celsius for every 5 ppt increase in salinity. 

The graph above shows the freezing point of salt with respect to its salinity. By adding certain portion of salt into fresh water, the freezing point continuously decreases till around -21 degree Celsius when the salinity is around 290g/kg. After this point the freezing point begins to increase as the salinity increases.