In Unit Three, many of our topics were focused on and about Force. We discussed Newton's 3rd Law, Action/ Reaction Pairs, Forces and Vectors, Tides, and Momentum and Impulse.
Newton's 3rd Law
Newton's 3rd Law states that every action has an equal and opposite reaction. When writing these reactions, called action/reaction pairs, we switch the subject of the sentence, but keep the verb the same. Below are some examples.
Also under the category of Newton's 3rd Law is the infamous Horse and buggy problem. Below is a diagram detailing all of the action/reaction pairs that take place.
Notice that each of the action reaction pairs are equal in force and opposite in direction. We know this because of Newton's 3rd Law, which states that every action has an equal and opposite reaction. The Horse and Buggy moves forward because the force between the horse in the ground is greater than the force between the buggy and the ground. This means that the horse and buggy moves in the horse's direction.
Forces and Vectors
Tensions in ROPES create net force. The farther apart the rope, th more tension.
Which side of the rope has more tension? Side A or Side B?
The force of gravity creates an "f weight". To find the tension in the ropes, we recreate the "f weight above the ball, and create lines
parallel to the ropes. Shown in the green is the tension. We see that rope B has more tension, as its green line is longer.
The next part of vectors is learning why things slide down hills.
Through the example below, we learn that the box accelerates
down the hill because the the f net downwards.
Tides
Tides occur as a result of the differences in force, as shown below. The Universal Gravitational Law states that Sides A and B experience different forces.
Tides occur as a result of the moon. We know that the moon has a larger pull on the earth than the sun because of the Universal Gravitational Formula.
There a couple different kinds of tides. NEAP tides occur when the Moon is perpendicular to the Sun. SPRING tides occur when the Moon is in line with the Sun.
Momentum and Impulse
Momentum is inertia in motion. It is represented by the formula "p=mv". The greater the mass of an object, the greater the momentum.
Impulse is the change in momentum- "(change in p)= J". It is represented by the formula "J=(F)(change in t)".
The Conservation of Momentum
The Law of Conservation of Momentum states that the amount of momentum is the same before and after an equation. This is proved by Newton's 3rd law, which states every action has an equal and opposite reaction.
Below is a video that helps to explain Momentum and Impulse, and the Law.
For tides, I found a helpful website. It was very helpful, but the most helpful part was the animated Gif that I found midway through the page. It helps to show the the rotation of the moon and how that effects the tide. The link is posted below!
Tides occur as a result of the difference of force between the moon and the different sides of the earth. We know this because of the Universal Gravitational Law, which states the larger the Distance, the smaller the force. The smaller the distance, the greater the force.
On side A of the Earth, labeled above, there is a small distance from the moon, and thus a large force. Side B has a longer distance from the moon, making the force smaller. Sides A & B experience different forces.
From the moon to Side A, the net force is towards the moon, while on Side B, the net force is away from the moon.
The best chart on the page is midway through the website.
At 8:35, Boca Grande is in transition from High to Low tide. The moon is just about a half-moon. I know this because the cart has a convenient moon chart next to it.
Newton's Third Law states that for every
action there is an equal and opposite reaction.
To better my understanding of these "action/reaction pairs", I turned to the ever-helpful www.physicsclassroom.com and found this diagram.
The website asked for us to identify at least 6 Action/Reaction pairs.
1. Tractor pushes ground to the right, ground pushes tractor to the left
2.Elephant pushes ground to the the right, ground pushes elephant to the left
3. Tractor pulls elephant to the left, elephant pulls tractor to the right
4. Man pulls tractor to the right, tractor pulls man to the right
5. Man pulls elephant to the left, elephant pulls man to the right.
6. Man pulls left rope to the right, left rope pulls man to the left
7. Man pulls right rope to the left, right rope pulls man to the right
This example, along with many other exercises on the site, provide practice with stating Action/Reaction pairs. Practice makes perfect, making this resource ideal for this section.
For full access to the website, check either one of these helpful pages:
Unit Two Summary What I Learned
In this Unit, we talked about a number of things. The first was Newton's Second Law, which then transitioned into the Newton's Second Law lab. We then discussed Free Fall in relation to both Objects Falling Straight Down and Throwing Objects Straight Up. Next came Falling at An Angle, and Throwing Things Upward at an Angle. Lastly, we discussed Falling with Air Resistance. Each of these topics greatened our understanding of the world around us. Newton's Second Law
Newton's Second Law states the relationship between acceleration and Mass and Force. The law can be written in multiple ways. By definition, Newton's Second Law states that Acceleration is directly proportional to Force, and that Acceleration is indirectly proportional to Mass. This can also be written as a=f/m, or a=f(1/m).
Above is a helpful diagram from Demario and Xavier's podcast.
It accurately depicts the relationship between Acceleration, Mass and Force.
Newton's Second Law Lab
Our knowledge of Newton's Second Law was demonstrated in the Lab that we did. Each lab group had a track and cart, complete with a hanging weight, which was the force that caused the system to accelerate.
To find the Mass of the system, we add the mass of both the hanging weight and the cart. For example, if the mass of the cart was 3 kg and the mass of the hanging weight is 2kg, then the Mass of the System is 5kg.
To find the force on the system, we use w=mg. In the example above, we would plug in 2 for mass and 10 for g. w=(2)(10). We then find that the weight on the system is 20N.
In Part A of the experiment, we added mass directly to the cart. This causes the mass of the entire system to decrease. Since Newton's Second Law states that Acceleration is indirectly proportional to Mass, the acceleration DECREASED as mass was added. Since the hanging weight did not change, the force was our constant. We can compare the equation of a line, y=mx, to Newton's Second Law, a=f/m.
Seeing as the force was constant, we would insert that for the slope (m).
Thus, a=1/m(f)
In Part B, we moved mass from the cart to the hanging weight. This meant that the overall mass stayed the same, but the force increased. Seeing as Acceleration is directly proportional to Force, as the force increased, so did the acceleration. In this part of the experiment, the Mass remained constant. We can also compare the equation of a line, y=mx, to Newton's Second Law, a=f/m.
Seeing as the Mass was constant, we would that in for the slope.
Thus, a=(1/m)f
Falling Straight Down
This section relates to the falling of an object when air resistance is negligible. This means that the only force acting on the object is Gravity. For real-life experiments, we use 9.8 for gravity, but in class we used 10.
For Free Fall, we used two equations.
d=(1/2)gt^2 can be used to find either the hight or the time, depending on what is given in the question.
v=gt can be used to find the velocity or the time, also depending on what is given in the problem.
Sample Problem: A ball is thrown off of a cliff with a velocity of 50m/s. a) How high is the cliff?
b) How fast is the ball going at 3 seconds?
Thrown Upwards
Also under the category of Free Fall is what occurs when an object is first thrown up and then falls back down with no air resistance.
Here, we also use d=(1/2)gt^2. However, this equation assumes that the object is starting at rest. Should a question ask how high the object is at, for example, 2 seconds, there are a number of steps which need to be followed.
1.) Find the total height that the object reaches, using d=(1/2)gt^2.
2.) Find the height from the top of the objects path to the desired height. d=(1/2)gt^2 is used again here.
3.) Subtract the 2nd height found from the first.
For a much more in depth explanation, a helpful podcast is included above.
Falling at an Angle
There are three equations we use for Falling at an Angle.
In The Vertical Direction
-d=1/gt^2
-v=gt
In the Horizontal Direction
-d=vt
There are also 2 special triangles that we use to find the velocity:
3,4,5
10,10,10 root 2
(root 2=1.41)
To best explain Falling at an Angle, I have put some of the questions from one of Ms. Lawrence's ONQ's and will answer them below.
1) A plane is flying at 100m/s and is trying to drop a package on a target. The pilot estimates that it will take approx. 4 s to reach the ground.
A) How far before the target does the plane need to release the package?
d=vt
d=100(4)
d=400
B) How high is the plane?
d=1/2gt^2
d=1/2(10)(4)
d=1/2(160)
d=80m
C) What is the final vertical velocity of the package?
v=gt
v=(10)(4)
v=40m/s
D) What is the final horizontal velocity of the package?
d=vt
400=v(4)
v=100m/s
E) What is the actualVelocity of the package 1s after being released?
Throwing up at an Angle
For throwing up at an angle, we use two different sets of equations.
For Horizontal, or Constant Velocity
d=vt
For Vertical, or Constant Acceleration
d=1/2gt^2
v=gt
*Only used when starting at rest!
Here is another sample problem to help with your understanding:
A ball is thrown up with an initial vertical velocity of 30m/s and a horizontal velocity of 5m/s. Find the descending velocity at 5 seconds.
Above is the path that the ball took.
At 5 seconds, the ball has a horizontal velocity of 5m/s and a vertical velocity of 20m/s.
To find the velocity, we use The Pythagorean Theorem.
a^2+b^2=c^2
5^2+20^2=c^2
25+400=c^2
425=c^2
c=20.6
The velocity=20.6m/s.
The same ball is thrown with the same velocity both vertically and horizontally. How far away from the thrower does the ball land?
d=1/2gt^2
d=1/2(10)(6^2)
d=1/2(360)
d=180m
Remember, time in the air is controlled by the angle at which the object is thrown!
Falling with Air Resistance
Skydiving is the part of the unit in which air resistance is NOT negligible.
Below is a helpful chart describing what occurs at each stage of Falling with Air Resistance.
Below is a more extensive explanation of Falling with Air Resistance.
Connections Made This unit had major connections to things that we see almost everyday, how they work, and why. Although we couldn't always make air resistance negligible, in the large majority of our tests, the distance was too short for air resistance to take effect. This unit, I could really see the effect that physics has on everyday life.
In Unit Two, I struggled most with the concept of falling at an angle. To help me better understand this topic, I found these helpful diagrams from the ever-trusty "physicsclassroom.com"
Each of these pictures shows the process an object (or a cannonball, in this case) would take when the forces of both gravity and horizontal velocity are acting on it. I think each picture demonstrates something important in one's understanding of projectile motion.
In the first unit of the year, we covered 4 main topics: Newton’s First Law, Velocity, Acceleration, and Net Force and Equilibrium. Each topic built off of the other topics, increasing our comprehension of the subjects.
Newton’s First Law states clearly:
“An object in rest tends to stay at rest, while an object in motion tends to stay in motion, unless an unbalanced force acts upon it.”
Tablecloth example:
The dishes stayed on the table because the force (pulling) was on the tablecloth, not on the dishes themselves. A perfect example of Newton’s First Law, the dishes remained at rest as there was no force acting upon them.
Velocity
Velocity is measured in meters per second, or m/s.
Like speed, Velocity measures distance over time, or d/t. However, unlike speed, velocity requires a specific direction. CONSTANT VELOCITY requires no change in direction. This is perhaps best understood through an example of a race car on a track. A car has speed while on the track, however since it is constantly making changes in direction, it is unable to have constant velocity.
As a result of the curves in the racetrack, race cars do not travel with constant velocity.
There are two formulas used to measure velocity. To answer the question “How Far?” the equation d=vt is used.
For example: If an albino alligator is traveling at a constant velocity of 15m/s, how far will it travel in 10 seconds?
d=vt
d=(15m/s)(10)
d=150m
The second formula that is used to measure velocity answers the question “How Fast?” v=d/t
For example: If an armadillo travels 100 meters in 25 seconds, how fast is it going?
v=d/t
v=100/25
v=4m/s
Velocity can be changed in three ways: by speeding up, by slowing down, and by changing direction. As soon as any one of these three things occur, Constant Velocity is impossible.
Acceleration
Acceleration is the change in speed, both increasing and decreasing. The units used to measure acceleration are m/s².
To find Acceleration, the equation “acceleration=change in velocity/time” is used. This can also be written as “a=△v/t”
Acceleration is well explained through examples of ramps with varying steepness:
If a ball was placed on the ramp, it would begin at 0m/s². As it rolled down the ramp, the acceleration would change from 0m/s² to 2m/s², then to 4m/s², then 6m/s², and so on. Because the change from one acceleration rate to another is 2, the acceleration of the ball would be 2m/s².
This ramp has a steeper incline, so let’s say that if a ball was placed at the top and the acceleration changed from 0m/s² to 5m/s², then to 10m/s², then to 15m/s². This would mean that the acceleration of the ball would be 5m/s².
When a ball is dropped straight down and is not affected by any drift of air, it is ALWAYS accelerating at a rate of 10m/s².
There are also two equations used to find acceleration. To answer the question “How Far?”, d=1/2at² is used.
For example: If a emu is traveling at a constant acceleration of 16 m/s², how far will it travel in 10 seconds?
d=1/2at²
d=1/2(16m/s²)(10²)
d=1/2(16)(100)
d=1/2(1600)
d=800m
To answer “How Fast” for acceleration, v=at is used.
Another example: If a badger started at rest and began accelerating at a constant 5m/s², how fast would it be going after 20 seconds?
v=at
v=(5m/s²)(20)
v=100 m/s
Any time that the acceleration of an object is changing, (increasing OR decreasing), the velocity of that object is Increasing. However, if the acceleration is constant, the velocity is also Constant.
Net Force and Equilibrium
Newtons (N) are used to measure Force (a push or a pull). Approximately 1/4 of a pound is equal to 1 N. NET FORCE is the total force on an object. Any time that the net force is anything other than zero, the object is accelerating.
If 5N of force are being pushed from the top arrow on to the box and 5N are being pushed on to the box from the bottom arrow, the Net Force on the box would be (5N)+(5N), or 10N.
Equilibrium occurs when the Net Force is equal to 0N.
If 6N are being pushed by the arrow on the right
and 6N are being pushed by the arrow on the left, the Net Force is (6N)-(6N), or 0N.
Equilibrium occurs in to instances: when an object is at rest or when it is moving at constant velocity.
*MASS is a measure of inertia, while WEIGHT is the force with which the Earth pulls on any given object.
Connections Made
Although it is a simple connection, solving with variables, such as d=vt, etc., helped me extensively with understanding these concepts, specifically Velocity and Acceleration. My simple Algebra I problem solving skills made both the answering of the questions as well as understanding how the graphs come into play.
