Why we skate on the ice, why not cement? Everyone knows the answer: it is because the ice has less friction. Now, let me use the equation to prove this point.
We already learn the equation for the friction: F = μ * normal force. What is μ? μ is the coefficient and is a constant for any two materials in contact. We can calculate by using the equation the friction/normal force. For ice,μ is about 0.05. If we assume the normal weight of an adult is 70kg. Then we use the equation: Fg = M*g Fg = 70*9.8 = 686N. According to the Newton first law, for every action, there is an equal and opposite reaction. When human's weight gave a force to the ground, the ground also gives the human a same amount of force. We can see the normal force of human should be equal to his weight, which is also 686N. Now, we can calculate the static friction when an adult stands on the ice. We use normal force which is 686N times by mu of ice, which is 0.05. And we can get the answer 34.3N. However, it is the static friction. It means you need 34.4N to push a man so that he can move. Nobody wants to have 34.4N while they are ice-skating because it is too much work. In fact, while friction will decrease to about 15N which make us can easily to skate.
Elon Musk revolutionized the way people perceived electric vehicles with his company Tesla Motors. Musk created Tesla with the vision of creating powerful, visually appealing, and functional electric cars. The Tesla Model S was the first Tesla vehicle to truly embody this vision. Over time, the car has become increasingly more powerful. The highest end Model S can now do 0-60 mph in 2.5 seconds. Using the material recently taught in class, the force of friction and the friction coefficient can be estimated for the Tesla Model S.
Kinematics of the Tesla Model S
Assuming constant acceleration, the acceleration can be found from kinematics.
Tesla Model S and Lamborghini Huracan LP610-4 drag-racing (Credit: Road & Track)
∆X =
Vi = 0
Vf = 60mph = 96.56 km/h = 26.82 m/s
a = ?
t = 2.5 seconds
Vf = Vi + at
26.82 = 0 + 2.5a
26.82 = 2.5a
a = 10.728 m/s^2
Free-Body Diagram and Sum of Forces
Next, a free-body diagram can be drawn to represent the forces acting upon the car. There is Fg (the force of gravity), N (the normal force), and f (friction). It should also be noted that the mass of the car is 4,647.3 lbs, which is 2108 kg.
∑Fy = N - Fg = 0
∑Fy = N = mg
N = (2108)(9.8) = 20658 N
∑Fx = f = ma
∑Fx = μs*N ≤ ma
μs(20658) ≤ (2108)(10.728)
(20658)μs ≤ 22615 μs ≤ 1.09 f = 22615 N Accuracy of Results
Graph of the acceleration vs. time of a
Model S and a Hellcat (Credit: Consumer Reports)
The values obtained above are inaccurate due to a few factors. First, cars rarely accelerate constantly. Since acceleration would not be constant, kinematics could not be used. Second, there are other forces acting on the car, including drag. Since these forces are not factored in, the answers obtained above are too high. In fact, the coefficient of friction is impossible since the coefficient must be between 0 and 1.
It is true that if you weighed yourself while riding an elevator that is descending, the scale will read that you weigh less than if the elevator was going up or not moving at all. But why? Let's use forces to find out!
When you are standing on a scale, there are two forces acting on you: the force of gravity (Fg) and the normal force (N). Gravity pulls you down, and the normal force is the scale pushing you back up. The normal force would be your weight. Fg is equal to the mass of the object (in this case, your mass) multiplied by the gravity constant (9.8 m/s^2). So, your weight when you are not accelerating is the gravity multiplied by your mass, or mg.
Newton's second law of physics states that the total sum of forces acting on an object is equal to the mass times the acceleration. If we consider gravity to be negative because it is pulling you down, the sum of the forces acting on you when you stand on a scale is N - Fg. Applying Newton's second law, we know that N - Fg = ma. If there is no acceleration, N - Fg = 0, and N = Fg. If there is upward acceleration, N - Fg = m(+a), so N = Fg + ma, and the scale reads that you have a greater weight. If there is downward acceleration, N - Fg= m(-a), so N = Fg- ma, and the scale reads that you weigh less! This only occurs when the elevator first starts moving. Once it reaches a constant speed, the acceleration is zero.
Scientists have always been very intrigued by the flight of the Albatross. An Albatross generally has a wingspan between 6.5 and 11 feet. With their massive wings and efficient flight pattern these birds can fly up to 500 miles a day and barely flap their wings. They can fly several hundred miles without flapping their wings once.
Engineers at MIT have been able to model the wings and flight patterns of the Albatross through physics. The way an Albatross flies is known as dynamic soaring. The bird uses wind patterns that change based on how high above the water the bird is. The air moving closest the the water has the least friction and the lowest amount of wind. As the altitude of the bird increases so does the amount of wind in the air.
One of the most important factors for Albatross flight is the presence of what are known as shear layers. These layers are basically the distance between a layer of fast moving winds and a layer of slower moving winds. Based on findings by MIT engineers they were able to discover that the thinner the shear layer the less wind that is required for the bird to stay in the air. This allows the bird to save more energy because it can move in thin arcs between the fast and slow layers of air rather than in big half circle flight patterns that scientists previously assumed.
This idea may seem counterintuitive because as the bird makes large arcs it would gain much more speed than if it were to turn in small angles. However, the researches found that by examining the ratio between gains and losses due to both speed increase and air drag, the ratio was much better when the bird made smaller turns more often.
Application
Engineers have been using this data and applying it to the creation of more efficient aircrafts and drones. Research teams at MIT are trying to create drones that can use wind to power them. By flying robot powered crafts in the same flight pattern as the albatross it would allow them to use little to no fuel while covering large distances.
Looking at this from a forces perspective we can see that air friction plays a huge role in aircraft flight and drone flight today. The force of the different wind speeds on the bird allows it to use these wind forces to power its flight. By taking advantage of these forces it is able to minimize the energy expended.
The Blue Angels are an elite navy demonstration group that travels across the United States performing their show to the thousands that come and watch. However, their show is unlike anything else. When it comes down to showtime, the show takes to the sky as the Blue Angel aviators take control of their McDonnell Douglas F/A-18 Hornets. These jets are specifically tuned for aerial stunts of all kinds. This includes flips, corkscrews, and other arrays of highly precise maneuvers with little room for error . One of their most dangerous tricks includes a four man formation where each of the planes roll out left into one another. This trick is called the Left Echelon Roll and requires a lot of trust between team members to to precisely time and perform the maneuver. While it takes years of training and hard work to become a blue angel, being one is an incredible accomplishment for any Naval Aviator.
The Blue Angels and Forces
The Blue Angels must compensate and plan for high forces in each in every flight. These forces that they experience are called G-forces and the aviators experience them at take off and when they maneuver through their aerial tricks. A G-force is the force acting on any object measured in terms of g.
1 G-force = 9.8 m/s^2
Whenever the blue angels accelerate in take off, accelerate to perform a trick, or to just simply accelerate to the necessary speed to break the sound barrier, they experience intense amounts of g-forces. The most amount of g-forces that these highly trained pilots are able to handle is about 12 g's without any sort of g-suit to help them out.
In Perspective
F=ma
At 12 g's of g-force for a 70 kg person
9.8 * 70= 686
That's 686 Newtons of force on the pilot
Effects of this G-force on the Pilot
This additional g-force pulls towards the ground forcing all the blood in the body to pool at the feet of the pilot. As a result, the blood in the brain is rushed away causing blackouts and potential brain damage. In order to combat this effect of g-force, pilots utilized two major devices. The first is a g-suit that uses compression to force the blood to not leave the brain. Most pilots use this method but, due to the circumstances of the plane, blue angel pilots have to use the second device which is to do the compression process manually. The Blue Angel aviators perform what they call the "hook" maneuver which clenches different muscle groups throughout the body to prevent blood from pooling at the feet. This complicated process is all done while the pilot is performing intense aerial tricks and formations.
1) Law of Inertia - An object in motion will stay in motion unless acted upon by an outside force. An object at rest will stay at rest unless acted upon by an outside force.
2) 𝛴F = ma, where m is mass in kg and a is acceleration in m/s^2
3) For every action there is an equal and opposite reaction
Well, how do they apply here?
Newton's First Law can interestingly enough be demonstrated by the sled hitting the man. This is because the man is unmoving until the sled (an outside force) runs into him. He is clearly put into motion as he is extravagantly tossed into the air.
The Second Law would allow us to determine the force which was applied from rest if we were given the masses of the men and their sleds as well as their acceleration. Let us pretend that this takes place on a flat surface and that friction is negligible If each man and their sled weighed 70kg and their acceleration was found to be 3m/s^2 this unknown force could easily be found using
𝛴F = ma → F = 70(3) → F = 210 N
Also, since this shows that Force and acceleration are proportional, a greater force will yield a greater acceleration, allowing one to go faster.
Newton's Third Law may not be as apparent due to how fast the sleds are going, but as the sledder makes contact with the man standing still, the force which he exerts on the man is reciprocated with the force which the man exerts on him. However, since he puts the man into motion, the force which he applied was able to overcome the force which the man exerted back on him.
Friction:
When people think of ice and snow, they often do not think of friction. Although it does appear that objects are able to effortlessly glide over these surfaces, friction is still present. The slipperiness just reveals that the coefficient of friction (μ) is probably lower.
"Friction Always Opposes Motion"
Therefore, if one is trying to achieve a high speed, such as in the sport of skeleton, the force which the person exerts to propel themselves forward must be greater than the force of friction applied by the ice. Those involved in this sport are constantly looking for ways to complete a run with as little friction as possible.
Sledding Downhill & Forces on an Incline:
More often than not, sledders choose to sled downhill, or on an incline. All three laws of motion, as well as friction, apply in these scenarios as well.
This diagram shows all of the forces acting on the sled:
Gravity - acts straight down, given by mg
Normal - acts perpendicular to sled, noted as N
Friction - acts opposite the sleds motion, written as f *remember f=μN
As soon as sledders are able to overcome static friction, they allow gravity to propel them the rest of the way.
Fraction force is a force between two surfaces, preventing them from sliding or slipping away. There are two types of friction force: static friction and kinematic friction. (Source)
StaticFriction Force: the friction that exists between a stationary object and the surface on which it's resting. It can be represented by the function Fs ≥ μs*N.
KinematicFriction Force: Kinematic friction force is a force that acts between moving surfaces. It can be represented by the function Fk = μk*N. (Source)
Real LifeApplication:
There are many real life application of the friction force. One of them is the brake system in car. To stop a car, the brakes have to get rid of that kinetic energy. They do so by using the force of friction to convert that kinetic energy into heat. By doing so, the car wheels stop moving. However, if there is no friction force, the car will just keep moving. This is why it is hard for cars to brake on smooth surface such as wet snow and ice. (Source)
We've all been there- you were outside on a nice summer night, and you wake up the next morning with a bunch of itchy, red bites.
How did you not notice the mosquito on you?
The answer lies within the mechanics of their takeoff from your skin!
In a study done at UC Berkley, the takeoff methods of mosquitoes were compared to those of fruit flies using three high speed cameras. Mosquitoes are just as fast as fruit flies, but only use about a quarter of the leg force that fruit flies do to push off.
61% of the force used to accelerate the mosquito comes from its wings!
In addition to the greater wing use, mosquitoes legs are much longer, which extends the takeoff time for mosquitoes, dissipating the acceleration further.
Okay, so how does this relate to class?
Let's say we compared a fruit fly flight to a mosquito flight, and we assumed they were travelling the same distance. NOTE: we are only comparing the acceleration from caused by their legs pushing off- not wings.
deltaX = Vi(t) +1/2at^2
deltaX will be the same for both. Vi will be the same for both (0m/s). We know from the study that mosquitoes take longer to takeoff from their long legs. So, t will be larger for mosquitoes. If deltaX is to remain the same as the fruit fly's deltaX, then acceleration of the mosquitoes must decrease to equal the fruit fly! So the acceleration of a mosquito is smaller than that of a fruit fly.
Is there anything with forces here?
Yes! We know that F = ma. If the mass is negligible, as it would be for a mosquito/fly, then the only thing that determines the force on your skin is acceleration. So, the force for a mosquito pushing on us would be smaller than that of a fruit fly, because the acceleration is smaller. So we usually won't notice a mosquito leaving our skin!
A mere two weeks ago on October 3rd, the Nobel Prize in Physics was awarded to Rainer Weiss, Barry C. Barish, and Kip S. Thorne. The three men received the prize "for decisive contributions to the LIGO detector and the observation of gravitational waves." The LIGO is the Laser Interferometer Gravitational-Wave Observatory.
Gravitational waves are disruptions in the fabric of space-time that are caused by violent energetic processes. Stronger waves can be emitted by the rotation of imperfectly-shaped neutron stars, the fusion of white dwarf or neutron stars, supernovae, the collision of two or more black holes, and the remains of gravitational radiation from the creation of the Universe.
This video shows how gravitational waves can be emitted as a result of two coalescing neutron stars.
These waves were predicted in 1916 by Albert Einstein through his general theory of relativity. He calculated that ripples could be created in space-time by enormous accelerating objects. These ripples could travel at the same speed as light and could be used to figure out more about gravity and the origins of the waves. In 1974, proof of the existence of gravitational waves was discovered by astronomers in Puerto Rico, who tracked a binary pulsar and discovered that the two stars were getting closer together at the same rate the theory predicted they would get closer. Thus, it was clear that gravitational waves were being emitted.
In 2015, LIGO was able to feel gravitational waves. These were being generated by the collision of two black holes 13 million light years from where they had been felt. This was the first “physical” sensation of the waves, proving their actual existence.
This video explains how the LIGO works. Essentially, the LIGO detects the presence of a gravitational wave by observing the sizes of two tunnels that will stretch or squish when a wave passes. This can be detected by flashes of light that occur when a light shot out by the LIGO is recombined and does not cancel out.
Rainer Weiss, Barry C. Barish, and Kip S. Thorne published a paper in 2016 that explained how the gravitational waves had been detected by the LIGO in 2015. The LIGO itself has created major changes for astronomy. It has allowed scientists to observe the universe from a new angle and uncover secrets that could never have been uncovered without this new technology. Barish himself stated, “"I can't imagine that now that we have another way to look at the universe that there isn't going to be some enormous surprises.”
Uniform circular motion is used to describe the motion of an object moving in a circular path. An object moving in a circle is constantly changing directions, however the tangental velocity will remain constant throughout. This idea is an essential part of uniform circular motion because it allows kinematics equations to be applied to an object moving in a circle. An object moving in a circle is also affected by an acceleration towards the center, centripetal acceleration.
Important Equations
Non-Uniform Circular Motion
In non-uniform circular motion the net acceleration is not longer pointing towards the center. The tangental velocity is changing. When the radius of the circle remains constant, the changing velocity changes the centripetal acceleration. So not only is the tangental velocity changing, the centripetal velocity is changing too. They are proportional to each other, so when the tangental velocity increases/decreases, then the centripetal acceleration increases/decreases too.
The red arrow is the net acceleration and the green
arrow is the magnitude of the tangental velocity.
Projectile motion is the motion under the influence of gravity. For example: if Mr. Gray throws Colin out of a window, the motion of Colin in the air would be considered as a projectile motion (Source).
II. Factors of Projectile Motion:
III. Math! Fun!:
IV. Real Life Application:
There are many factors that affect projectile motion:
When hearing the word "projectile" the first thing that comes up in many people's mind is the bullet. Indeed, projectile motion plays an important role in ballistics--the science that deals with the flight, behavior, and the effect of projectiles. By studying ballistics, the police are able to determine when, where, and how a firearm was used (Source).
For the first lab in the physics class, we did the sugar pack lab, which measures the acceleration of the little car. In the lab, we use the time and the distance of the car traveled to calculate the acceleration. Basically, we put our data(distance and time) into the plot and draw a best-fitted line to get the acceleration. On the second part of the lab, we used the distance and the time to calculate the velocity and eventually get the deceleration of the little car.
In the lab the equations we used are:
Average velocity = delta distance/delta time
distance = velocity * time
Average acceleration = delta velocity/time
velocity final = velocity + acceleration *time
I think we can also utilize these equations in our real life besides the lab, for example, ROLLER COASTERS.
The roller coasters always give people exciting feeling by their fast speed. Usually, the acceleration of the roller coasters is high because it needs short time and short distance for reaching its maximum speed, but how high does it usually is?
Let's use the example of the Kingda Ka, the tallest and the second fastest of roller coasters in the world.
According to the official data, the train can reach 128 miles per hour (206 km/h) in 3.5 seconds.
Now we knew the V final is 206km/h, which equals to 57.2m/s. We can assume the V initial is 7m/s because the start of the roller coaster is kind of slow; 7m/s is probably a little bit faster than the average human walking speed. The time we use is 3.5 second.
According to the equation V final = V initial + accleration * time:
57.2m/s = 7m/s + a * 3.5
then we can get the acceleration of Kingda Ka is about 14m/s^2.
SpaceX Falcon 9 Launching at Vandenberg Air Force Base (Credit: SpaceX)
On 11 October 2017, Elon Musk's company SpaceX successfully launched a reused rocket for the third time in history. The Falcon 9 rocket launched the Echostar 105 / SES-11 communications satellite into orbit using a previously used first-stage rocket booster. SpaceX is able to reuse the rocket boosters due to an incredible landing and retrieval process.
Autonomous Spaceport Drone Ship
One of SpaceX's Autonomous Spaceport Drone Ships (Credit: StackExchange)
SpaceX has developed autonomous spaceport drone ships (ASDS) to recover rocket boosters for reuse. The approximately 90 meter long ships, cleverly named "Just Read the Instructions" and "Of Course I Still Love You," help to provide a safe and feasible landing site for the rocket boosters. The autonomous ships can be overridden by a team of engineers, but they are fully capable of maintaining their location to within 3 meters using GPS and an array of motors to carefully guide the ship.
First-stage rocket boosters are used to carry the cargo and other stages of the rocket to the upper levels of Earth's atmosphere. Upon carrying the rocket about 80 kilometers in altitude, the rocket booster detaches from the remainder of the rocket and then initiates a landing sequence. The rocket booster, traveling at around 4800 km/h rotates 180° and orients itself with an ASDS. The rocket booster and ASDS communicate with each other and use computer controlled guidance systems. These guidance systems use physics (including projectile motion) to aim and land the rocket booster. By calculating position and velocity, the rocket booster can maintain the proper trajectory and speed.
The following video from SpaceX shows a rocket booster landing on an Autonomous Spaceport Drone Ship in April of 2016.
Why Land at Sea?
The first time SpaceX demonstrated the landing of a rocket booster, the landing site was on land. This is much easier for SpaceX to pull off due to the removal of a moving target (due to ocean currents and waves). As this video from The Verge explains, the rocket boosters do not have enough fuel to make it back to land for about two-thirds of SpaceX's launches. In order to follow the trajectory of the original launch, the landing point must be at sea. The below diagram from SpaceX helps to demonstrate the landing process.
Diagram of the landing of a rocket booster (Credit: SpaceX)
Further Use
Musk and SpaceX first plan to use this rocket landing technology to allow for frequent rocket reusability. However, the company has recently shown off plans to use rockets for passenger transportation around the globe. Using rockets allows for people to arrive at their destination in under 60 minutes, no matter the location on the planet. The rocket would travel the globe from landing pad to landing pad multiple times per day. Musk hopes the airfare (or rocket-fare) would be no more than a traditional airfare.
The widely known story usually tells of a monkey up in a tree who is trying to outsmart a hunter. The hunter takes his time and lines up his shot directly at the monkey. The monkey, who has probably not taken a physics course, thinks that if it drops from the branch as it hears the gunshot (ignoring the sound of speed), the bullet will go over its head. Unfortunately, the monkey does not outsmart the hunter, as the hunter knows of something called gravity.
We set up this scenario in class using a circuit and a magnet which would release the monkey as the flow of electricity was cut off by the "bullet". We aimed the projectile launcher directly at the monkey and observed that the bullet and monkey collided. But why did this happen? Why didn't the bullet go over the monkey?
What are we trying to show?
This experiment is used to emphasize that the x and y components of an object moving as a projectile are independent of each other. By aiming directly at the monkey rather than above or below, it is evident that gravity (a constant of 9.8 m/s^2) is acting on each object, causing them to fall at the same rate and eventually to collide, regardless of the velocity or x-component of the bullet.
Demo of Experiment
Note: In this demo, the laser confirms that aim is being taken directly at the monkey. Also, notice that the shot is taken with projectiles of various initial velocities. The only resulting difference is the height at which the bullet collides with the monkey.
Why this works:
If the bullet's height (deltaYb) is set equal to the height of the tree (h) minus the distance the monkey falls (deltaYm), we can then prove that aim should be taken at the monkey by finding tan(x) = h/d.
Setup:
Using Kinematics Equations,
deltaYm is given by: -g/2 * t^2 and
delta Yb is given by: vsin(x)t - [g/2 * t^2]
Therefore,
h - [g/2 * t^2] = vsin(x)t - [g/2 * t^2]
h = vsin(x)t
We also know that,
d = vcos(x)t
Since we want to demonstrate that tan(x) = h/d, we should divide the top equation by the second:
h = vsin(x)t
d = vcos(x)t
Velocity and time cancel, and sin(x)/cos(x) can be condensed to tan(x) giving us: tan(x) = h/d, proving that if aim is taken directly at the monkey, the two objects will eventually collide.
“Resource Lesson: Monkey and the Hunter.” PhysicsLAB, Catharine H. Colwell, dev.physicslab.org/Document.aspx?doctype=3&filename=Freefall_monkey.xml.
“Shoot the Monkey.” Youtube, Harvard Natural Sciences Lecture Demonstrations, 22 Aug. 2013, youtu.be/0jGZnMf3rPo. “The Monkey and Zookeeper.” The Physics Classroom, The Physics Classroom, www.physicsclassroom.com/mmedia/vectors/mzf.cfm.
According to the Newton first law, for every action, there is an equal and opposite reaction. When human's weight gave a force to the ground, the ground also gives the human a same amount of force. We can see the normal force of human should be equal to his weight, which is also 686N. 
