Recap of Unit Three, Yippee!

Unit 3 was based in Newton's Third Law and its surrounding concepts and applications to real life. We covered Newton's Third Law, action-reaction pairs, how tug-of-war really works, forces in perpendicular directions, how tides work, momentum, impulse and the Law of Conservation of Momentum.

Newton's Third Law

Newton's Third Law states that for every action, there is an equal and opposite reaction. This is exemplified all around us in action-reaction pairs.


In this image, there are two sets of action-reaction pairs.

 In the first, the book pushes down on the table and, with the same amount of force, the table pushes up on the book. Note that in this action-reaction pair, the subject switches from book to table, but the verb stays the same, push.

The second action-reaction pair is a little bit different. In this pair, gravity pulls the table down and the table pulls the earth up. When writing action-reaction pairs involving gravity, the subjects will always be gravity and the earth, but the verb will stay the same.

How does tug-of-war really work?

Now that Newton's Third Law has been covered, it's time to face a harsh truth about tug-of-war. The secret to winning does not lie in the strength of one team versus the other, but in physics.

Watch this video, and consider how Newton's Third Law might be applied.

There are three action-reaction pairs at work in a game of tug-of-war.

1. Team A pulls Team B to the left, Team B pulls Team A to the right.
2. Team A pushes the ground forward, the ground pushes Team A backward.
3. Team B pushes the ground forward, the ground pushed Team B backward.

Now, because we know that for every action there is an equal and opposite reaction, we can also know that the two teams are pulling with the same amount of force. Therefore, no matter the teams are stacked, one team pulling harder than the other is not how the match is won. In fact, it is the relationship between the team and the ground that determines the winner. In the video, the team on the left won because they were pushing on the ground with more force than the team on the right was.



This same concept can be applied to a horse and cart. It may seem that because of Newton's Third Law, a horse and a cart would pull each other with equal force and therefore would remain at rest. However, the tug-of-war explanation can also be used to prove that logic to be uninformed.

Like in tug-of-war, there are three action-reaction pairs: between the horse and the cart, between the horse and the ground and between the cart and the ground. The horse pulls the cart with and equal and opposite amount of force that the cart pulls the horse with. This is because of Newton's Third Law. However, the horse pushes on the ground and the ground pushes on the horse with a greater amount of force than the cart pushes on the ground and the ground pushes on the cart with. Therefore, the cart is pulled in the horse's direction.

Forces in Perpendicular Directions

Momentum

The definition of momentum is inertia in motion. In other words, momentum is the product of an object's mass and velocity. The unit for momentum is kgm/s^2 (kilogram meters per second, squared).

The equation for momentum (symbol p) is p=mv.

NOTE: At rest, there is no momentum, which can just be written as 0kgm/s^2.

Impulse
Impulse (symbol J) is defined as force multiplied by the amount of time it takes to be applied. In other words, the equation is J=f x change in time. Impulse is measured in Newton seconds (Ns).

Momentum/ Impulse Relationship

So, now that impulse and momentum have been defined, it is now the time to explore the relationship between the two. Momentum is equal to mass times velocity and change in momentum is equal to an object's final momentum minus its initial momentum.

NOTE: The change in momentum will always be the same whether or not the object comes to a stop slowly or quickly.

Impulse is equal to change in momentum.

Let's take this further by looking at how this relationship applies to a real life situation. Why is it that airbags keep us safe?


First, remember that the car will go from moving to not moving no matter how it is stopped. Therefore impulse/change in momentum is constant. A small force therefore must mean a large change in time and a large force means a small change in time. Airbags protect the dummy because they increase the amount of time it takes for the dummy to feel the impact of the collision, therefore the force acting on the dummy is decreased. Small force = less injury.

The Law of Conservation of Momentum

The Law of Conservation of Momentum states that the momentums before and after an action are equal, so it is conserved. For instance, say that there are two carts on a track, one is at rest and the other is in motion. The law states that if these two carts collide, connect and continue down the track as a unit, the momentum of the system would be the same before and after the collision.

As an equation, this looks like p total before= p total after.

Let's use a to name the moving cart and b to label the cart at rest.

We can use the equation: mass of a times velocity of a + mass of b time velocity of b  = mass of a + mass of b (velocity of unit ab).

Now let's imagine that cart a has a mass of 2kg and is moving left at 5m/s toward cart b which has a mass of 3kg and a velocity of 0m/s. When they collide, connect and continue, is the momentum conserved?

p total before=p total after

p of a + p of b before=p of a + p of b after

mava+mbvb=ma+b(vab)

2(5)+3(0)=2+3(vab)

10+0=5(vab)

2m/s=vab

Now that we know the velocity of the unit, we can use p=mv to solve for the momentum before and after.

Before:

2kg(5m/s)+3kg(0m/s)=p

10kgm/s^2=p

After:





5kg(2m/s)=p

10kgm/s^2=p

So we've found that the momentum is conserved. 

But...is momentum conserved when to pool balls hit and then move away from each other at an angle?

Yes!

Gravity and Tides

The Universal Gravitational Law states that F=(G)(m1)(m2)/d^2, because of this we know that force is proportional to 1/distance squared. In other words, a short distance has a strong force and a long distance has a weak force.

Let's think about this in relationship to the Earth. The side of the Earth closer to the Moon experiences the Moon's gravitational force more than the side that is farther away from the Moon. The net force acting on each side of the Earth is what causes the tides. Say that the on the side closer to the Moon, the Moon's gravitational force exerts 150N and on the other side, only 50N. (note: these numbers are grossly exaggerated just to detail the concept) Additionally, the gravitational force from the center of the Earth is 100N. To find the net force on each side, the Earth's gravitational force is subtracted from the moon's force on each side. Therefore, the net force on the close side is 50N and the net force on the far side is -50N. The positive force indicates that the close side is being pulled toward the Moon and the negative force indicates that the far side is being pulled away from the moon. It is this imbalance that causes the tides. If the forces weren't opposite, tides wouldn't exist. Also, if tides were determined by gravitational pull instead of the relationship between force and distance, tides would be caused by the Sun, not the Moon.

This video explains tides really well:

Tides Explanation

The Universal Gravitational Law states that F=(G)(m1)(m2)/d^2, because of this we know that force is proportional to 1/distance squared. In other words, a short distance has a strong force and a long distance has a weak force.






Let's think about this in relationship to the Earth. The side of the Earth closer to the Moon experiences the Moon's gravitational force more than the side that is farther away from the Moon. The net force acting on each side of the Earth is what causes the tides. Say that the on the side closer to the Moon, the Moon's gravitational force exerts 150N and on the other side, only 50N. (note: these numbers are grossly exaggerated just to detail the concept) Additionally, the gravitational force from the center of the Earth is 100N. To find the net force on each side, the Earth's gravitational force is subtracted from the moon's force on each side. Therefore, the net force on the close side is 50N and the net force on the far side is -50N. The positive force indicates that the close side is being pulled toward the Moon and the negative force indicates that the far side is being pulled away from the moon. It is this imbalance that causes the tides. If the forces weren't opposite, tides wouldn't exist. Also, if tides were determined by gravitational pull instead of the relationship between force and distance, tides would be caused by the Sun, not the Moon.




This video explains tides really well:










In each day, there are two high tides and two low tides due to planetary revolution. Six hours pass between each high tide and each low tide, also meaning that from high tide to high tide is 12 hours and between low tide to low tide is 12 hours.

Unit Three Resource

So far, we've covered in class that Newton's third law states that for every action there is an equal and opposite reaction. Meaning, that as I type and rest my hands on my laptop, my laptop is pushing up on my hands with the same amount of force.

That being said, does the Earth pull on the Moon with the same force that the Moon pulls on the Earth?

This video by Veritasium gives a little explanation and debunks a common misconception.



By now, hopefully it is clearer why Newton's third law is possible.

Now: why is it that no one wins the tug of war in this video?
(note: embedding was disabled for this video, but I really thought it was helpful)

No Win Tug of War

Newton's third law also rings true in this case. The two scientists pulled on the rope with the same force, however since there was no interaction between their feet and the ground, the scientists pulled each other together instead of one dominating the other.

See an example of successful tug of war:



The team on the left won not because they were stronger, but because the action-reaction force pair between their feet and the ground was greater than that on the right.

That's a Wrap with Unit Two, Whew!

Alas, this is the conclusion of Unit 2 in Physics class. This past unit we covered: Newton's second law, free fall and falling through the air.

Newton's Second Law

Newton's second law of motion states that acceleration is directly proportional to force and inversely proportional to mass. The formula for Newton's second law is a=F/m which can also be written as a=F*1/m.

Newton's Second Law Lab

The lab we did in class on Newton's second law was centered around the question how does acceleration depend on force and mass? The purpose was to discover how the acceleration of a system is related to its mass and to its force. The system was a cart, with a hanging weight attached, on a track.

In Experiment A, we kept the force on the system constant, but added mass. Since, as Newton's second law states, acceleration and mass are inversely proportional the mass added to the system caused the acceleration to decrease. The force on the system was the force of weight from the hanger. The force on the system stayed constant because the hanging weight was unchanged.

When graphing the data from Experiment A, we used the formula y=mx+b. In order to translate that into physics, we had to be mindful of what was kept constant. The force remained constant throughout the experiment, so it became the slope. Then, I wrote out the conversion, which can be done in two way.

Conversion Type 1:

 

 

 

Since we know that F is our slope, we can look at y=mx as F=mx. Then, we can think about which of our formulas that resembles, which is F=ma from Unit 1. Now we know where to plug in force, mass and acceleration when graphing.

Conversion Type 2:

Here, we just line up the formula for Newton's second law with y=mx. We know how to line it up because we've already identified force and the slope.

In Experiment B, the mass of the system remained constant, but the force was increased. This was achieved by moving 100kg weight from the cart to the hanger, one trial at a time. For this experiment, the slope was equal to the mass.

Free Fall

Free fall is when an object falls due to the acceleration of gravity only. Remember that the acceleration due to gravity is 9.8m/s^2.

Things Falling Straight Down

The information above can be used to find out the height from which an object falls from. For instance, if a ball falls down a cliff and it takes 20 seconds for the ball to hit the ground, how high was the cliff. First of all, the acceleration due to gravity can be rounded up to 10 m/s^2 because this is a real life situation. Also, since this is a vertical situation, the equation used is d=1/2gt^2.

d=1/2gt^2

The first step is to plug in all given information into the equation.
 d=1/2(10)(20)^2

Next, simplify.

d=1/2(10)(40)
d=1/2(400)
d=200

So, d=400m. That means that the cliff was 400 meters high.

The ball's velocity can be found using v=gt.

v=gt
v=(10)(20)
v=200m/s

The ball's velocity was 200 meters per second.


This is a video created by some classmates that includes two more practice problems.

Throwing Things Straight Up


This is a video I made with two of my classmates about things being thrown straight up.

Falling at an Angle

With objects falling at an angle, it is vital to remember two types of special right triangles: 3,4,5 and 10, 10, square root of 10. Also, remember that the square root of two is equal to 1.41. In these situations, the hypotenuse of the triangle will equal the actual velocity. 

This video by some classmates gives an example problem that might be helpful.


Projectile Motion

In projectile motion, the same free fall formulas can be used, so here's the chart again.

An example of projectile motion is when someone throws a football.

REMEMBER: vertical height controls the distance in the air. Always.



This video by my classmates has a great breakdown explanation of projectile motion.

Falling with Air Resistance

A real life example of falling with air resistance is skydiving. Watch this video, and pay attention to the skydiver's velocity as he falls to the earth. The music is distracting, but there is nice display of his velocity starting at 1:00.





This is my favorite video by my classmates, explaining what happens when air resistance is included when falling, like when you have a parachute.

Here's another video about skydiving and physics.



Wrap-up

There are a few things that are vital to Unit 2. First are the formulas from the handy dandy chart I made.

Second, the acceleration due to gravity is equal to 9.8m/s^2 (in real life situations, otherwise just round to 10).

Third, vertical height controls time in the air.

Fourth, velocity is always constant and downward when falling through the air with air resistance.

Physics Fun with Unit One is Done

We've reached the end of the first unit of Physics that we'll cover this year in class. So far we've covered inertia/Newton's first law, net force and equilibrium, velocity, acceleration and using a graph to solve problems. '

Inertia/Newton's First Law

Newton's first law states that an object in motion will remain in motion and an object a rest will remain at rest unless acted upon by an outside force. This is a property known as inertia. This is a concept applicable to daily life. It can be observed when someone leaves their coffee mug on top of their car. First, the car and the coffee mug are at rest. However, when the car begins to move, the coffee mug falls over. The answer lies in Newton's first law of motion. Since the mug was at rest before the car moved out from underneath it and no outside forces acted upon it, the mug remained at rest and thus fell due to the force of gravity. Another example of this is the tablecloth trick, as shown in the video below.



Net Force and Equilibrium

The net force is the total of all the forces acting on an object. Any time there is a net force, the object is accelerating. For instance, if there is a box being pushed with 6N to the right and 4N to the left, the net force is 2N. This is because the 4 cancels out and then there are two N left over.

There are two instances in which equilibrium occurs: when the net force is 0N and when an object is moving at constant velocity. Therefore, if a box is being pushed upon with 5N to the right and 5N to the left, they cancel out and the net force is 0N. That means that the box is at equilibrium. An object moving at constant velocity is also at equilibrium. That would be like our hovercraft experiment where we moved at a constant speed in one direction without any force from a push or pull.

This is a great video demonstrating other real life examples of equilibrium and net force by some classmates.



Velocity

Velocity can be defined as the distance traveled divided by the time passed.

Velocity, measured in meters per second (m/s) is relative to change in direction and change in speed. Therefore, if a bicycle moves forwards at a constant speed, the bicycle is moving with constant velocity. However, there are three ways that the bicycle's velocity could change:

• If the bicycle is moving at a constant speed, but turns around a corner, the bicycle's velocity will change.
• If the bicycle is moving forward and speeding up, its velocity will change.
• If the bicycle is moving forward and slowing down, its velocity will change.

When dealing with problems involving constant velocity, there are two major types of questions. There are questions looking for distance traveled and questions looking for the velocity.

• How far ? These are questions looking for the distance traveled (m) these will be solved using the equation distance equals velocity multiplied by time, or d=vt.
• How fast? These are questions looking for the velocity (m/s) and will be solved using the equation velocity equals distance divided by time, or v=d/t.

These can also be rearranged to find the time.

This is a video I made with my classmates about these topics.



Acceleration

Acceleration can be defined as the change in velocity divided by the time passed. Acceleration is measured in meters per second squared, or m/s^2.

There are three ways to recognize acceleration:

1. change in direction
2. speeding up
3. slowing down.

Note that these three things are also what cause change in velocity. Therefore if an object is accelerating, it does not have constant velocity. Acceleration is not possible with a constant speed, unlike velocity.

Acceleration is different from speed in the sense that there can be an object with increasing velocityand decreasing acceleration. What that means is that as the object rolls down a ramp its velocity is increasing, but it is increasing by smaller increments as it goes. A toy car could have a speed of 1m/s then after one second the velocity could be 2.5 m/s, but after another second goes by, the velocity could be 3 m/s. That indicates that while it is still speeding up, the rate at which it is speeding up is decreasing.

There are two types of questions asked  about acceleration. There are questions looking to find the distance and there are questions looking to find the acceleration.

How far ? These are questions looking for the distance traveled (m) these will be solved using the equation distance equals one half multiplied by the acceleration multiplied by time squared, or d=1/2at^2.

How fast? These are questions looking for the velocity (m/s) and will be solved using the equation velocity equals acceleration multiplied by time, or v=at.

These can be rearranged to find acceleration and time as well.

This is a handy video explaining acceleration and its units.



Using a Graph to Solve Problems

A graph can be used to show constant velocity or constant acceleration. In these graphs, the distance (m) will always be on the y-axis and the time (s) will always be on the x-axis. A graph for constant velocity will have a straight line. If everything is not squared for the constant acceleration graph, it will produced a curved line.

The first step is to look at the information and see what is missing. Looking at what is already provided by the graph will give a hint as to what is missing. The slope will be equal to whatever is missing. For example, if the equation of the graph is y= 3.8651x + 0.2 (if b is close to zero, disregard it) and you know from the graph that the time is squared, it is simple to find out what the slope represents. Writing out the equation in words makes it easier to identify these parts: the distance is equal to the slope (3.8651) multiplied by the time squared. And since you know that the time is not just seconds but seconds squared, it is clear that the equation is d=1/2at^2. With that information, you know that the slope represent half of the acceleration, because it is the only part of the equation that the graph has not provided you with. In order to find the acceleration, you multiply the slope by 2 and then fill it into the spot where 1/2a would be in the formula.

This video explains how these graphs work.

Hovercraft Lab Refelction

Today in Physics class we rode hovercrafts in order to better understand inertia, net force and equilibrium. The hovercraft was a large, circular wooden board with a plastic sheet covering it. In order to hover, we put a leaf-blower in a cutout in the craft. Riding the hovercraft felt pretty strange. We had to hold the extension cord into the leaf-blower and sit really close to it. The leaf-blower was really powerful and the entire hovercraft vibrated. My feet still felt like they were shaking even after I got off of the hovercraft. Riding a hovercraft is different from sledding or riding a skateboard because there is no friction acting against the hovercraft. The friction from snow or the road eventually slows down a sled or a skateboard, but hovercrafts don't have any friction to slow them down. From this experience, I can come to the conclusion that acceleration depends on whether or not there is a force force acting on an object. When the hovercraft was being started and when is was being stopped it had an accelerating velocity. The only time at which the hovercraft's velocity was constant was when it was gliding. More mass means more inertia and less mass means less inertia, therefore the tallest and heaviest person was hardest to stop and the shortest and lightest person was easiest to stop.