The Physics Behind the Flick Throw in Frisbee

This semester, I joined the women's club frisbee team here at Colgate. And originally I couldn't throw the forehand throw (also called a flick) at all. I'm honestly still not great at it, but I was curious to see how physics tied into the throw. So first things first, there are two main forces that act on a frisbee while it's in flight: drag and lift. Neither of these forces were discussed in a lot of depth in class, but these forces can be modeled by rotational motion and fluid dynamics, which we did go over. So let's start with some important equations:
 Bernoulli's Equation:

P1 + 1/2ρv1^2 + ρgh1 = P2 + 1/2ρv2^2 + ρgh2

P= pressure

ρ= density of fluid

v= velocity

g= gravity

h= height

 Angular momentum:

L= Iω 

I= moment of inertia

ω= angular velocity

With these equations in mind, we can start to analyze a frisbee throw. To start, a frisbee is a disk and in order for it to travel anywhere, it must have some rotational motion. This is because of angular momentum as it helps to stabilize the frisbee while in the air. Because angular momentum is conserved (unless torque is applied to it), a frisbee will continue its rotational path going the same speed it started with. Also, because the frisbee travels with a linear velocity, the frisbee will remain on a relatively straight path if thrown flat. However, as I can attest to, if you tilt the frisbee and it is released at an angle in a certain direction, it will quickly move to that direction and hit the ground. Now this gets into Bernoulli's equation as air pressure greatly affects the frisbee's path. In this case, air is our fluid in question. So with a faster traveling fluid, pressure decreases as shown by the relationship in Bernoulli's equation. This occurs on the top of the frisbee when thrown because air can more quickly travel over the smoothed side of the disk than below it. This change in pressure causes the frisbee to move upwards, rather than down into the ground. This is because of the equation pressure= force/area. The area of the frisbee remains the same, but as the pressure decreases, force must also decrease. So because the pressure on the top of the frisbee is lower, the force pushing down on the frisbee is also lower than the force pushing upwards. Therefore, the force up will cause the frisbee to lift up. So, basically, in order to get a frisbee up in the air, all you have to do is give it a rotational velocity and make sure it is pretty parallel to the ground. If the frisbee is angled, it will follow an unpredictable path that will most likely never go where you want it to. There should be a slight upwards angle on the frisbee when thrown initially because there is air that is pushing it down so an upwards takeoff angle will help with the lift. But now, how do you get the frisbee to go far? That is something I've personally struggled with a lot when throwing. And this is because when trying to throw far, we have a tendency to put more force in the linear direction, which will only cause the frisbee to hit the ground harder. Rotational velocity is far more important than linear velocity in the distance a frisbee travels. This is again due to angular momentum. The more stable a frisbee is during flight, the farther it will go. So basically, the more spin you put on the frisbee, the more angular momentum it will have to go a farther distance. So focus on increasing your angular velocity, not linear velocity. The more force you put into the flick of your wrist, the more angular velocity the frisbee will travel with. And that is the key to a long frisbee throw. There are definitely more forces at work on a frisbee than I discussed in this post that we have not talked about but these are some of the basic physics explanations for frisbee flight. Hopefully if you ever decide to throw a frisbee, you'll apply these physics tricks better than I do!

Image from: https://ultiworld.com/2015/07/09/the-forehand-part-four-best-practices/
For a more detailed explanation of the physics behind frisbee, check out this article: http://www.cs.cmu.edu/afs/cs/academic/class/16741-s07/www/sample_projects/spurushw_report.pdf

Should the Rules of Field Hockey Be Changed?

According to NCAA rules, in the sport of field hockey, a player's swing (whether it's a backswing or a follow-through) should not be raised above "hip-height."  If the swing exceeds the height of a player's hip the swing is considered "dangerous," and possession will be turned over to the opposing team.  Is this rule preventing players from shooting the ball as hard as they can?  Should the rules of NCAA field hockey be changed in order to allow for players to shoot the ball with the maximum force that they can, or does the height of a player's back swing not matter in the speed at which the ball travels after it is shot?
The mass of a field hockey stick (M) = 0.535 kg
The mass of a field hockey ball (m) = 0.163 kg
Let the hip height of a field hockey player (h1) = 0.75 m
Non-conservative forces such as air resistance are ignored in the calculations.
The field hockey stick can be treated as a pendulum (this ignores the force that the field hockey player is putting on the stick).
 

If the field hockey stick is treated as a pendulum, then a backswing beginning from a height that is higher from hip height, then the field hockey stick will hit a ball with a higher velocity than if it is swung from hip height, therefore, if field hockey players were to be allowed to swing from heights higher than that of their hips, then they would be able to hit the ball much harder.  Even though a higher swing is more dangerous, NCAA rules should change to allow for field hockey players to be able to swing at heights higher than their hips in order to allow them to hit the ball harder and be a more competitive player on the field.

Push or Pull? The Physics of Opening a Door

When people hold doors for each other it seems easier to push than pull a door. When considering forces however, it should be equally as hard to push and pull.

When pushing a door, we can assume push is directly on the door and pull is pulling on a knob. The Forces include the force of gravity, the force of friction, and the force applied. When pulling a door, the same forces apply, except force is applied to the knob and pulled onto the knob which then applies force to the door.

So why is it harder to pull than push? Although friction between the door and the handle in the opposite direction of force applied takes a bit of force away, this is not significant enough to cause a big discrepancy in difficulty. The major factor when considering door pulling and pushing is momentum. Since when you push you generally are walking and continue at a constant velocity, your momentum helps you push the door in P=mv. When you pull however, you will have to go backwards and not be able to use your forward momentum. Thus due to the loss of momentum, pushing a door seems easier than pulling a door, but if one were to push a door without momentum, it would be almost as easy.

Why can you jump into a pile of snow and not get hurt?

Generally, when you jump off of a 3-meter wall onto the ground you would experience a great deal of pain. Assuming a person weighs 60kg, the max height they reach in their fall is 3 meters off the ground, and they are slowed down by the ground over the course of 0.10s, then they will experience a force of 4600.8N. This would be quite the painful fall and you would likely experience some bruising at the very least if you were unable to catch yourself and slow your fall down further. Fortunately, with a good amount of light snow on the ground, let’s call it 1 meter of unpacked snow, the snow compacts down as a person falls through it and gradually slows your fall. The exact compactness of the snow and how far it allows you to fall through it are difficult to know exactly, so I just assumed a regular fall onto the ground would take 0.1s and when falling through the snow it would take 0.15s. If this were the case, then the force a person experiences to stop their fall when there is snow would be 3067.2N. The snow allows them to slow down over a much longer course of time, causing their acceleration in the upward direction to be much slower. This in turn causes the force they experience to also be much less than when they fall directly onto solid ground. Hopefully when we get some more snow we are all able to test this out from a safe height.

How are we able to turn the wheel of a car with such little force and somehow overcome the force of friction between the tires and the ground?

Power Steering

While this does utilize a lot of physics we haven’t learned in class, I thought it relates well enough in understanding the force a person has to apply and the much greater force that is eventually applied to the wheels of the car. This much larger force is also required to overcome the force of friction, so with all that in mind I figure at the very least we can get an idea of how big of a difference power steering makes in our everyday lives. Power steering takes advantage of hydraulics to make it so a driver can apply a small force to the wheel and rotate the tires of the car. While you drive and steer the force required to turn the wheels varies so it is difficult to say exactly how much force is required to turn the wheels. In particular, power steering is more important at lower speeds since this is when it is more challenging for the wheels to turn. I started thinking of this idea in the first place because of how your car can be parked and you can somehow turn the steering wheel and the tires turn while the rest of the car stays in place. I think it’s really cool to think of how much force the hydraulic system in power steering is able to generate just from us applying a small amount of force to the steering wheel. Hopefully this video helps to explain this idea in some more detail. https://www.youtube.com/watch?v=i6J9kvdSg7E

Brownian motion and cell culture

Physics News 2:

When we learned about Brownian motion and the physics behind it, this obscure term and
phenomenon that had been a mystery for a while to me now started to make sense.

Brownian motion occurs when small objects are floating in water or a water-based solution. If these
objects are small enough, you can observe them interacting with the water molecules under a
microscope in a zigzag like motion.

 When you work in cell biology and cell culture, you have to become acquainted with
Brownian motion. If you look under a microscope, non-adhered objects (floating objects,
cell debris etc) will appear to be moving. Some might mistakenly get worried and consider
these moving objects alive; ie contamination into the cell culture flask. However, any
experienced-eye will be able to recognize this motion as Brownian motion. On the other
hand, one way to tell that the cells are indeed contaminated with bacteria or other
contaminants, is to look for non-random directional motion in the cell culture flask.
Such directional motion (for example moving in a straight line) would then indicate the
presence of contamination. 

Here is an example of Brownian motion vs motility in a cell culture flask:

https://www.youtube.com/watch?v=oYsEid5YES4

Image source:

https://commons.wikimedia.org/wiki/File:Csm_Brownian-Motion_f99de6516a.png

The Physics of Proper CPR

When it comes to performing high quality CPR, the key thing that you want is consistency. To ensure that your patient has the highest possible chance of survival you need to make sure that you are compressing your patient's chest at least 5-6 cm, allowing the chest to fully recoil and then repeating at a rate of 100-120 beats to minute. While this might sound easy at first, in practice you will realize that your biggest enemy quickly becomes your own fatigue in performing this task. That is why one of the most important parts of performing high quality CPR is ensuring that you position yourself with your shoulders over top of the patient and are pushing straight down on them.

The amount of force that is required to compress the patient's chest is about 500 N. This means that each time that you push down on your patient's chest you are performing 25 N⋅m of work. While this may not seem like a lot at first, when you consider that you will need to do this at least 100 times every minute the amount of work that is required to perform CPR begins to add up. In fact, every minute that you are doing CPR, you are performing about 2500 N⋅m of work on your patient. As you could imagine this becomes very tiring, very quickly, and can lead you to inadvertently decreasing the rate, depth and or quality of your compressions. This is why it is recommended if there is more than one person present at the scene, that you switch off doing compressions about every 2 minutes. 

One of the most common mistakes that people who are first learning CPR often make is not positioning themselves with their shoulders directly over their patient. This is because when many people first start out learning CPR they think that they will be able to go for longer if they lean back and get themselves into a more comfortable position. However, by doing this they are actually likely to become tired more quickly because they are quite literally creating more work for themselves to do. This is because it requires significantly more force to compress the patient's chest 5-6 cm when pushing down at an angle than it would when pushing straight down on the chest. In the example depicted above, we can see that by leaning back 30 degrees the amount of force that is required to compress the patient's chest increases from 500 N to 577.35 N. This translates to the person performing CPR needing to exert 2886.75 N⋅m of work on their patient every minute, which is significantly higher than the 2500 N⋅m of work needed when CPR is performed properly. This is why it is so important to perform CPR with your shoulders directly over the patient.