Running on Ice vs Concrete without slipping

https://www.runnersworld.com/training/a20822715/running-on-snow-and-ice/

Before taking PHYS 111, I had never thought that the force of friction would be the forward force allowing us to move forward when we walk and run. Instinctually around this time of the year, one would dive deeper into the topic of force of friction by asking: "Would it be easier to run on land or ice?". Logically, we would slip when running on ice. This happens when we push back for a step because the force we apply works in the opposite direction. For our purposes, the interaction of ice and the soles of our shoe is non-slipping.


Figure 1: Image of forces in effect while runninghttps://forces-in-running.weebly.com/how-do-forces-affect-running.html

To focus on the variables and components of friction we use:
 uFn= Ffr

Since normal force, when running on flat land, is equal to our mass times the gravity constant (mg), we can see that the Fn is a constant when running on flat land. This would allow u, the coefficient of friction, to be the deciding factor as to whether or not a person is moving faster with the same amount of applied force in the opposite direction (Fapp).  The kinetic friction of concrete is 0.8, according to https://hypertextbook.com/facts/2006/MatthewMichaels.shtml. The kinetic friction of ice is around 0.4 according to hypertextbook.com. This would mean the Force of friction would be greater for a person theoretically applying the same amount of force when running on concrete than on ice. Thus, although it may seem that ice would allow us to run with less force if we weren't slipping all the time on it, concrete would still be the feasible choice for running.

Physics of a Falling Christmas Tree

My family celebrates Christmas, and our tree goes up the day after Thanksgiving to get maximum holiday cheer out of the season. Every year, we tie the tree to the wall in order to prevent it from tipping.

But what if it were to fall? Why are trees easy to tip over and what are some physics concepts involved in the tipping of the tree?

First, a tree is basically an uneven pole with its center of mass more towards the bottom due to the general cone shape of the branches and trunk. One might think this would make the tree stable. However, despite the wide sweeping base of the branches, the trunk is very narrow so one only needs to tip the tree over the edge of its trunk in order to get the tree to fall.

Second, there are many physics concepts involved with the tipping of the tree. For our purposes, the tree can be called the lever arm with the base of the tree acting as the pivot point. Now if a cat were to begin climbing up the trunk of the tree, it would not start tipping until the cat climbed farther from that point. The farther away from the pivot point, the more likely the tree will fall due to the force of the cat acting farther away. This relates to torque, or the rotational equivalent of linear force. 

Fig. 1. Diagram of Christmas tree with an ornament demonstrating the force of gravity and arrows demonstrating the place where a cat climbs and the relative amount of force required to generate enough torque to tip the tree. The cat would have changed the force of gravity applied at the point due to the mass change.  The torque would be greater farther away from the pivot point (bigger r), and the tree will be easier to tip.

Once the tree starts tipping (which is quite easy as discussed above), the tree can be said to have rotational motion. If considering the tree as an uneven pole, we can say that the tip of the tree will have a much greater linear velocity at the tip than at the base when each hit the ground. Their angular velocities will be the same.

But a Christmas tree also has branches which can provide cushioning so much so that the tip of the tree may not even hit the ground.

But lest you think your ornaments can be saved at the top, they will likely fall off due to the force of gravity acting on a different side of the ornament, and they will hit the ground with the linear velocity that the tip of the tree would have felt.

Physics and Braces

Physics and Braces

You might be wondering, how the heck does braces work? All they are doing is just sticking two wires in my mouth for about two years and then out of nowhere, boom, straight teeth. Don't worry, they aren't using black magic or anything strange. All the orthodontists are using are laws physics, particularly, Newton's laws. In this case, when the wire is bent, the two tension forces create a vector force towards the back of the mouth. These continuous forces signal for the teeth to encourage the movement. But, if there is an interruption in the force, the teeth will not be signaled to move. Osteoclasts are released which signal for some bone to be removed in order for the teeth to move around. The constant force being applied is crucial for braces to work. So the science behind physics lies in the forces exerted by the wire!

https://www.renickortho.com/orthodontic-care-treatment/orthodontics-the-science-of-moving-teeth/

Do You Want to Build a Snowman? - The Physics Behind the Ideal Snowman

In light of the winter storm hitting Colgate and the recent release of Frozen 2, I decided to provide you with some tips on how to build the perfect snowman by using physics. 

Tip #1: The snowball must be firm. 

To achieve this, you need to pack the snow well by exerting a fair amount of pressure on the snow on your hands. Because pressure is equal to force over area, the more force you apply, the more pressure is exerted. Additionally, because pressure is directly proportional to force (P = F/A), one way to increase the pressure is to increase the force applied. This can be done by increasing the weight applied by having more people put their weight on the snowball. Moral of the story - make sure to make your snowmen with friends, the more the merrier! 

Tip #2: Don’t stray from the traditional sphere shape. 

The sphere is the best shape for a snowman. This is because as the snowballs are packed into a sphere, the snow exerts pressure on the ice crystals so that some crystals melt while the ball is being formed. This way, the melted ice can then recrystallize in the cold temperature and bind the snowball together. Also, because spheres have a small surface area to volume ratio, they’ll melt slower than other shapes when exposed to the sunlight. 

Tip #3: Avoid making the snowballs too big!

This is because as the size of the sphere snowball grows, so too does it’s total surface area. Therefore, because pressure is inversely proportional to area, an increase in area with a constant applied force is associated with a decrease in pressure. Since pressure is directly proportional to force, more force is needed to apply the same amount of pressure to a larger snowball as the smaller snowball. Thus, it becomes increasingly difficult to apply enough pressure to pack larger snowballs - it requires more force to achieve the same pressure. 

Tip #4: Don’t stack too high! 

The height of your snowman is really important. This is because as you increase the height of the snowman, the center of mass becomes higher above the ground. The lower the center of mass is to the ground, the better and more stable the snowman is.  

Tip #5: Stick with the standard snowman structure! 

The standard structure of 3 snowballs - a large base, a medium middle, and a small head - is the best design. The base snowball needs to be the largest to be able support the downward force of the above snowballs without collapsing (by applying an equal and opposite upward force, according to Newton’s Third Law) so that they remain at rest. 

Downward force of medium and small snowballs = (m-medium + m-small) * g 

Upward force of large snowball = m-large * g

m-large * g = (m-medium + m-small) * g 

An inverted snowman (small base, medium middle, and large head) would not be ideal since the force of the combined upper snowballs would likely be too great for the small bottom snowball. This is because force is directly proportional to mass - the mass of the combined snowballs would be much greater than the mass of the bottom snowball. So, although the inverted design is possible, it isn’t sustainable. 

m-small < (m-large + m-medium)

m-small * g < (m-large + m-medium) * g 

Tip #6: Where you build your snowman also matters. 

Make sure to build your snowman on level ground. This is because on flat ground, the upward normal force of the ground on the bottom snowball and the force of gravity on the bottom snowball both only have y-components that directly cancel each other out. Therefore, the snowman is likely to remain at rest and not topple over, according to Newton’s First and Third Laws. 

If you build your snowman on the side of a hill, the force of gravity on the bottom snowball now has an x- and a y-component. This means that the force in the x-direction is not equal and opposite the normal force of the ground acting in the y-direction. So, there is a net force that could cause the snowman to slide or fall over. 

Take Elsa and Anna’s word for it - they know what they’re doing! 

So, make sure to keep these tips in mind if you decide to spend your snow day outside building snowmen! 

References:

https://www.smithsonianmag.com/science-nature/do-you-want-build-snowman-physics-180954024/

https://qz.com/153318/the-science-behind-the-art-of-building-a-snowman/

https://offspring.lifehacker.com/how-to-build-the-best-snowman-according-to-science-1832051410

https://www.inverse.com/article/61304-sixth-mass-extinction-neanderthals

Underwater Camera

This past year, my sister got an underwater camera for her birthday. She got a Panasonic Lumix waterproof digital camera that is designed to be waterproof up to 23 ft. Every summer, we go up to my uncle’s lake house on Lake George for a week. This past summer, we brought the camera and took some underwater pictures of fish, rocks, and our family. We didn’t pay much attention to the depth of the water because we only used it to a depth of about 4 ft.  I want to calculate the difference in pressure that the camera experiences when used at our average depth of 4 ft, vs. its maximum depth of 23 ft.

Pressure is equal to F / A which is also equal to phg where p is density, h is depth, and g is gravity. The density of freshwater is 1000 kg/m2. The total pressure is equal to PO + phg where PO is equal to atmospheric pressure. The formula for change in pressure is ΔP = Pf - Pi.

Pressure at 4 ft.

Pi = PO + pgh

Pi = (1.01 X 105 N/m2) + (1000 kg/m2)(4 ft)(9.8m/s2)(1m / 3.281 ft)

= 1.1 X 105  Pa

Pressure at 23 ft.

Pf = PO + pgh

Pf = (1.01 X 105 N/m2) + (1000 kg/m2)(23 ft)(9.8m/s2)(1m / 3.281 ft)

= 1.7 X 105  Pa

Change in Pressure

ΔP = Pf - Pi

 ΔP = 1.7 X 105  Pa - 1.1 X 105  Pa

= 60,000 Pa = 60 kPa

To put this into perspective, the world record for free-diving is 700 ft. This equates to around 2.2 X 106  Pa, almost 13 times more than what the camera can withstand.

Sources: https://www.nationalgeographic.com/news/2014/8/140810-free-diving-sperm-whales-jules-verne-reunion-booktalk/

The Physics of Broken Ornaments

The day after Thanksgiving my family usually decorates for Christmas. As anyone who has decorated a tree knows, ornaments drop, and sometimes they break. As we were decorating this year, I dropped a snowman ornament that luckily did not break. The safety of this ornament is due to physics.

To start, we know that energy is conserved, so 1/2mv2=mgh. Mass will cancel, and we can find the final velocity given the height from which the ornament fell. From there, the impact force can be found given W=KE or Fd=1/2mv2. The distance in this equation is that which is traveled after impact. In my case, this was a hardwood floor, which is very impermeable and would have a value that is very close to zero. The force, therefore, would depend on the ornament's mass, the height of the fall, and the surface onto which it falls. The impact force, however, did not exceed the force required to break ceramic and resulted in an unharmed snowman.

In order to protect ornaments this holiday season, physics would suggest a couple of things. First, having more fragile ornaments closer to the ground would reduce the potential energy and eventually reduce the overall force of the fall. Second, having the tree on some sort of mat or carpet would increase the distance the ornament would travel after the fall and further reduce the impact force. Finally, some materials, like wood or ceramic, have a higher resistance to force than other materials, such as glass. The materials that can withstand more force will be less likely to break no matter the location on the tree. Knowing this can reduce broken ornaments this holiday season.

Stronger than you thought

My family recently moved. In our new home, all of the showers have glass doors as opposed to shower curtains. These doors sit on one set of hinges. After every shower I always wipe down the shower door so that the water doesn’t start to leave marks. I always start wiping close to the hinge moving towards the door handle. I’ve noticed that once I get to about the halfway point I always accidentally push the door open. At first, I never quite understood this. I’m pushing with roughly the same force the entire time, but at this point, about halfway, the door always swings open. Then I have to hold the door shut so I can continue to wipe down the door. Now, with my physics knowledge, I understand why. Torque =rFsinθ. Since I am always pushing perpendicular to the door, sinθ=sin(90)=1. I’m pushing with roughly the same force, so F remains constant. As I move from the hinge to the door handle, the r increases as that is the distance from the fulcrum of the force applied. Without even realizing it, as I move across the door, I am increasing the torque to the bathroom door with my increasing distance. With whatever force I am using, at about the halfway point on the door, I am using enough force at enough distance that I can generate the torque necessary to push the door open.