Unit 3 Summary

Hey physics fanatics, I'm back again! It's time to sum up what our class learned about in unit three. In this unit, I learned about 6 critical concepts...

1.) Newton's 3rd Law + Action/Reaction- Pairs

2.) Tug of War/ Horse and Buggy

3.) Forces in Perpendicular directions

4.) Gravity and Tides

5.) Momentum+ Impulse relationship

6.) Conservation of Momentum (including the lab)

In each of these concepts, I learned an exceptional amount of formulas, information, and applications to everyday situations. As usual, to avoid confusion, I'm going to break it down into sections. However, what'll be different about this section is that I will include more exercises from the textbook our class uses. The exercises help to test your knowledge and whether or not you retained any of the actual information I included in this unit summary. Don't panic, I will also have my usual crazy made up problems, to leave you with a little smile!

Part One: Newton's 3rd Law + Action/Reaction- Pairs 

1.) What is Newton's 3rd Law?

For every action there is an equal and opposite reaction.

2.) What is the relationship between acceleration and force?

They are directly proportional.

3.) What is the relationship between acceleration and mass?

They are inversely proportional.

4.) What would an action reaction pair look like?

Apple pulls Earth up
Earth pulls apple down

5.) What do action reaction pairs have in common? (refer to the previous answer)

The verb/action is the same. If the action is "pull" for the top one, then the bottom action will also be "pull."

6.) Are action reaction pairs equal and opposite to other action/reaction- pairs?

No, each pair is only equal and opposite to itself and not another pair.

Examples and Practice Problems (Some are from our assigned textbook) 

1.) Its 5:30am and I enter the library with my backpack, which weighs probably half as much as I do. I'm tired and decide to drop my bag on the desk. Can you name the action-reation pair or pairs in this situation?

First pair: Table pushes Bag up
                 Bag pushes table down

Second pair: Bag pulls Earth up
                     Earth pulls Bag down

2.) It's almost christmas and I want to hide a present on the top shelf of my closet. I'm pushing up on the present and the earth is pushing down on the present. Do these two forces form an action and reaction pair? Why or why not?

No, because according to Newton's 3rd Law, "for every action there is an equal and opposite reaction." This means they must have the same action in order to have equal and opposite reactions.

3.) The Polar Express runs into a sled. Which one exerts the larger force on the other? Explain why.
     Which one will have the greater acceleration? Explain why.

They exert the same amount of force because according to Newton's third law, "for every action there is an equal and opposite reaction. This means the amount of force one vehicle applies the other one will apply the same amount. The vehicle with the greater acceleration is the sled because the mass is smaller. According to Newton's 2nd Law, " mass is inversely proportional to acceleration." So as one increases, the other decreases.

Instructions: Now is the section where I will pull a few question from my textbook. If you happen to have the book
Conceptual Physics eleventh edition, by Paul G.Hewitt, refer to the sections I state before I begin the questions.

Chapter 5 exercises 1,8, and 11

1. ) "A rocket becomes progressively easier to accelerate as it travels through space. Why is this so?"

. In the beginning the mass was larger compared to the force because it was still inside the Earth's atmosphere  Gravity was weighing it down, but once it entered space there was no gravity. With gravity being absent, the mass of the rocket decreased and the acceleration increased. In other words, a greater acceleration due to a smaller mass.

8.) "What physics is involved for a passenger feeling pushed backward into the seat of an airplane when it accelerates along the runway during takeoff?"

Action reaction pair: Seat pushes person forward
                                  Person pushed seat backward

In this situation, Newton's 1st Law states that, "An object at rest or in motion will remain at rest or in motion unless acted upon by an external force." Therefore, you stay at rest because you are already at rest. Now Newton's 3rd Law states that, " for every action there is an equal and opposite reaction." Therefore, the chair pushes you and you react with an equal and opposite reaction.

11.) " Is it true that when you drop from a branch to the ground below, you pull upward on the Earth? If so, then why is the acceleration of the Earth not noticed?

Yes, because the Earth's mass is so great that it's acceleration is so small.

Part two: Tug of War/Horse and Buggy 

Answer the practice problems using knowledge I taught you in the lesson above and...

1.) What are two things that can affect the force of friction?

The nature of the the surfaces (this has nothing to do with speed or surface area) meaning rough or smooth. Secondly, how hard the surfaces are pushed together.

Examples and Practice Problems 

The dogs and sled example uses the same concept as the horse and buggy.

1.) You are sledding down one of our many wonderful snowy hills in the midst of winter. The team of asheville faculty dogs have been assembled and are running you and your friend all over campus. Your friends thinks the sled is moving forward because the dogs are pulling really hard on the sled. However, she is incorrect. How would you correct her? Use the labeled vectors in your explanation (when attempting this on your own, try to draw the picture I've given you and label the vectors on your own, then compare.)

The pull of the sled doesn't matter. The forces are equal and opposite according to Newton's 3rd Law which states, "for every action there is an equal and opposite reaction." What matters is how hard one pushes on the ground. The dogs press harder on the ground, so the sled will accelerate in the direction of the dogs.


2.) How does a team win a tug of war match?

In a tug of war, both teams pull on each other with equal and opposite force. We know this because Newton's 3rd Law states, "for every action there is an equal and opposite reaction." The strength of the pull does not matter. The team that wins is able to push on the ground harder than the team that looses. Therefore, both teams will accelerate in the winners direction. The result is that one team wins.

Part Three: Forces in Perpendicular Directions 

1.) The box is placed halfway down a steep ramp, what three things must be acting on it if it is not moving?

     The three things acting on the box are a downward force ( F weight)/ up force (F support), net force, and friction.

The vector in blue= force of friction

The vector in purple pointing upwards= the F support

The vector in purple pointing downwards= F weight (force of gravity pulling down on the object)

The vector in red= Net Force

The dotted lines in green= how to find the net force using a drawing

2.) What are tension vectors?

The tension vectors here are in pink. They show the amount of tension in each of the ropes. The dotted lines are the net force upward, which is equal and opposite to the weight. The are drawn from the top of the arrow and continue downward, but parallel to the line opposite of it. The circle is the weight and the line straight down is the f weight (force of gravity pulling down on the ball).

2.) If one vector is longer than the other, is there more tension in the longer vector than the shorter one?

     Yes!

3.) If there are equal angles, is there equal tension?

    Yes!

4.) If you have a hanging weight on a rope, why can it never be straight?

It can never be straight because there always has to be an upward force. If it was straight, then there would be no upward force.

5.)  What can you correctly say about two vectors that add together to equal zero?

They are equal and opposite.

6.) Can a pair of vectors with unequal magnitudes add to zero? Can three unequal vectors add to zero?

No and yes.

7.) When can a nonzero vector have a zero horizontal component?

When the vector is pointing straight down.

Examples and Practice Problems (With a problem from our textbook) 

Chapter 5 exercise 29.) " Two people of equal mass attempt a tug-of-war with a 12m rope while standing on frictionless ice. When they pull on the rope, each of them slides toward the other. How do their accelerations compare, and how far does each person slide before they meet?:"

Their accelerations will be the same because without friction their mass doesn't matter because they can't press on the ground. They will each slide 6 meters.

Your super cute orange, but majorly obese cat is laying in your lap playing with a ball of string. Suddenly, an angry bird comes flying through the window, trying to hit your green pig poster. Your cat goes crazy and is flying around the room. They land on your banner hanging above the mirror. Will their be more tension in the banner if it sags a little or a lot?

There will be a greater tension in the banner if it sags a little.

Part four: Gravity and Tides

1.) Everything with mass ________ all other things?

The answer is attracts.

2.) What does force depend on?

The mass of the objects and the distance between them.

3.) What is the relationship between force and mass?

They are directly proportional.

4.) What is the relationship between force and distance?

They are inversely proportional. It follows the inverse square law.

5.) The farther apart the objects get, the less _____ there is on the two objects.

The answer is force.

6.) What is gravity written in scientific notation?

       6.67x10^-11

7.) What is the universal gravitational formula?

F= (G) (M1)(M2)/ (d^2). This is how strong a force is between any two objects anywhere in the universe.

8.) If the distance is doubled, what happens to the original force?

It is 1/4 of the original force.

9.) If the distance is tripled, what happens to the original force?

It is 1/9 of the original.

10.) If the distance is cut in half, what happens to the original force?

The force is four times the original.

11.) If the distance is cut in third, what happens to the original force?

The force is nine times the original.

12.)  Between the ____ and the Earth, there is a large force?

Th answer is the sun.

13.) Between the _____ and the Earth, the force is ______ than that of the sun?

The answer for the first blank is moon. The answer for the second blank is smaller.

14.) How is the blob of water around the earth going to affect the force of the moon?

The moon is pulling the Earth towards itself and with the same amount of force the Earth is pulling the moon toward itself. The forces are equal and opposite.The difference is the diameter. The Earth's diameter side A and B, the water will not experience the same force. It's not the fact the moon is pulling the Earth. It's the fact side A and B are experiencing a difference in force. The water is rushing to the areas of high tides.

15.) The earth takes _______ to spin around completely?

The answer is 24 hours.

16.) The moon takes _______ to do one rotation around the earth?

The answer is 27 days.

17.) What is the important location relationship?

The important location relationship is where the moon is in relationship to the sun and the Earth.

18.) During what phases of the moon do the spring tides occur? Are the high tides higher than normal or lower? Are the low tides higher than normal or lower than normal?

 The spring tides are occur during a full and new moon. The high tides are higher than normal and the low tides are lower than normal.

19.) During what phases of the moon do the neap tides occur? Are the high tides higher than normal or lower? Are the low tides higher than normal or lower than normal?

The neap tides occur during the half moon. The high tides are lower than normal and the low tides are higher than normal.

20.) How long is there between a high to high tide and low to low tide?

There are six hours.

21.) How many hours is there between a high to low tide?

There are twelve hours.

22.) When the sun, moon, and Earth are in _____ we have spring tides? When the sun, moon, and Earth are on ___ and _____ we have neap tides.

The answer for the first blank is line.  The answer for the second blank is top. The answer for the third blank is bottom.

23.) The moon has a greater ____ due to the difference in side A and B than the sun has a ____ on side A-B on the Earth.

The answer for both of the blanks is pull.

Example Problem

Use the Gravitational formula for this problem. We already know the gravity, but if the first mass was 8x10^30, the second mass was 3x10^24, and the distance (which is squared) was 2x10^6, what is the force? For the sake of simplicity, we are going to round the 6.67 for gravity and raise it up to 7.

Part five: Momentum+ Impulse relationship

1.) The total momentum before a collision or explosion is____ to the total momentum after a collision.

The answer is equal.

2.) P total before equals ________ after

The answer is P total.

3.) If the objects are stuck not stuck together then are after, what is the formula?

(Ma)(Va)+(Mb)(Vb)= (Ma+b)(Vab)

4.) The change in Pa equals what?

The negative change in Pb.

5.) Pa+Pb equals what?

Pa+ Pb because P total before equals P total after.

6.) If the objects are separate before and after, what is the formula?

 It is (Ma)(Va)+(Mb)(Vb)= (Ma)(Va)+(Mb)(Vb)


7.) What is the formula for impulse?

    J= Ft.

8.) what is the formula to find the change in momentum?

The change in p (represented by a delta symbol followed by the capital letter P) = P final - P initial.

9.) What is needed to cause bounce?

There has to be two changes in P, two impulses, and two forces. The bouncing doubles the force.

10.) What is impulse measured in?

It is measured in Newtons seconds.

11.) Are impulse and force the same thing?

No, they are not because impulse depends on time while force itself does not.

Part six: Conservation of Momentum 

1.) How does the total momentum of a system compare before and after a collision or explosion? How do we know?

They are equal because it'd only be zero after, if it was zero before.

2.) What causes a change in momentum? what is the formula to calculate this?

The impulse causes a change in momentum. The formula to calculate this is JA= - JB.

3.) What is the relationship between the change in momentum and impulse?

They are equal and opposite.

4. ) If a bug crashes into a window, how does the change in the momentum of the bug compare to the change in momentum of the window the movers are transporting?

They are equal and opposite.

Example and Practice Problems 

1.) Two little kids are reenacting the tragic marshmallow battle of 2001. One takes out his marshmallow gun and the other takes out his gummy bear gun. The criminal with the marshmallow gun fires a fluffy bullet....

a.) Which experiences the greater force?
b.) Which experiences the greater change in momentum?
c.) Which experiences the greater impulse?
d.) Which experiences the greater impulse?
e.)Justify that both the gun and the bullet were at rest at the start, so the net momentum is 0kgm/s, but at the end they both moved so there is momentum for each. How is this possible?

a= equal and opposite
b= equal and opposite
c= equal and opposite
d= one will be greater, the bullet
e= The change in the momentum of the bullet is equal to the change in momentum of the gun.

2.) Comparing total momentum before and after a collision

Cart A with a mass of 5kg was pushed toward another cart B of 1kg, which was at rest. After a couple of trials, the velocities of cart A before the collision and cart A and B after the collision. To find out the momentum the class had to graph the momentum of cart A (Pa) on the y-axis and the velocity (Vab) of the carts when stuck together on the x-axis. See the graph below for more information and questions.

a.) Translate the equation of the line for what is on the x and y-axis. 

    Y= PA

    Slope= Ma+b 

    X= Vab 

b.) Based on this graph and the knowledge I've presented in this unit summary, what does the slope represent? 

The slope represents the total mass of the carts put together. 

c.) Using the picture above, calculate what the slope should be? 

The slope should be 6.0676. 

d.) Compare the value above to the slope. Does this data confirm the law of conservation of momentum? 

Pa= (Ma+b)(Vab) 

Pa= ( (5) + (1) ) (Vab) 

Pa= (6)(Vab) 

Using our translated equation of a line, we see that the slope is 6kg. If we compare this to our calculated 6.0676 in question c, then we can see that it is within 10% if the value. Therefore, our data does confirm the law of conservation. 

3.) You decide to go shopping at Publix (a grocery store further down south). As you wander the isles at 10m/s, you start to fill up your cart. The cart with groceries in it now weighs 15kg. You bump into an another shoppers cart, which weighs 5kg and was parked in front of the ice cream isle! As if it wasn't enough they were blocking the creamy goodness, a broken section of their cart catches yours. The two carts are now stuck together. How fast are they moving? 

They are moving at about 4 m/s.

Tide Resource

Within a single day, each part of the earth will experience 2 high and 2 low tides. The amount of time between a high and a low tide is 6 hours. While the amount of time between a high tide and another high tide is about 12 hours. The amount of time between a low tide and another low tide is also 12 hours. Now one may be wondering what causes the difference in the force felt by opposite sides of the earth. The cause of the difference in force felt by opposite sides of the earth is the diameter of the earth. The moon is closer to side A (the near side) than side B (the far side). Since force is inversely proportional to distance squared, side A will have a greater force than side B. The difference in force is important in creating tidal bulges because without it the amount of force between the center of earth to side A and the center to side B would be unequal. The unequal amount of force would result in the water rushing to one side of the earth. Thankfully we have tides, in fact, we have what are called spring and neap tides. Spring tides occur when the moon is aligned with the sun and the earth. During this time, the moon is in either a full or new moon phase. When the moon is full or new, the high tides are higher than normal and the low tides are lower than normal. All of this stands in contrast to the neap tides. Neap tides occur when the moon is misaligned with the moon and the earth, usually located at the top or bottom of the planet. During neap tides, the moon is in the half moon phase. This causes high tides to be lower than normal and the low tides to be higher than normal. 

Tide Chart- with phases of the moon 

http://www.tides4fishing.com/us/florida-east-coast/daytona-beach-shores-sunglow-pier

Tide at time of post: Low tide 

Type of tide Daytona beach is experiencing: Neap tide 

How I know the type of tide Daytona beach is experiencing: The moon is a half moon meaning it is neap tide because neap tides occur when the moon is a half moon. 

Newton's 3rd Law

Newton's 3rd Law states that, "for every action there is an equal and opposite reaction." In the video, I learned that when the force of gravity is pulling down on you, you are simultaniously pulling up on the force of gravity. I also learned that in an action reaction pair, the forces will always be equal. However, if the larger the mass of the object, the smaller the acceleration of that object will be. Therefore, if the acceleration of the the object is larger, the mass will then be smaller. To demonstrate this he showed a person who's mass was 50 Kg, in deep space, pushing on a basketball who's mass was 1 kg. Then using the formula F=ma, which is Newton's second law, he gets the acceleration of the object. Now, Newton's Second Law states that," acceleration is directly proportional to force and acceleration is inversely proportional to mass. In Formula form that looks like a=F/m or f=ma. That is why the acceleration of the person was 1/5 m/s^2 while the acceleration of the basketball was 10m/s^2. 

Unit 2: Blog Summary

In this unit, I learned about 7 additional key concepts in physics...

1.) Newton's Second Law

2.) Newton's Second Law Lab (A lab we did to test the law!)

3.)  Free Fall- Falling Straight Down

4.) Falling Through the Air (With air resistance-Sky Diving)

5.) Throwing Things Straight Up (Free Fall)

6.) Falling at an angle (Free Fall)

7.) Throwing Things Up at an Angle (Free Fall)

Just like in the last unit, in each of these concepts, I learned numerous formulas, concepts, and everyday applications. However, what was different was that the concepts became increasingly complicated in knowing which formula to use and when. In addition to explain why exactly a certain reaction occurs. In order to avoid the unnecessary complication, I will break it down for you.

Part One: Newton's Second Law 

1.) What is Newton's Second Law?

     In word form, the answer is Force is directly proportional to acceleration, mass is inversely proportional to acceleration. In symbols that would be written as a=f/m. 

2.) What is the relationship between f (force) and a (acceleration)?

      They are directly proportional meaning if one increases, then the other increases. If one decreases then so does the other. In symbol form that would be written as....

3.) What is the relationship between m (mass) and a (acceleration)?

     They are inversely proportional. If something is inversely proportional with something else that means that as one increases the other would decrease.

4.) What is the formal to find the f weight of an object?

   The formula is written as w=mg.  In word form, this translates to mean force weight=(mass)(gravity).

Examples and Practice Problems 

1.) Imagine a friend is moving out of their apartment! You both see a box already packed up, so you both head for the box. You push on the left with 40N and your friend pushes on the right with 20N. The box has a mass of 10kg. What is the acceleration of the box?

The formula we need to use is a=f/m. Now that we've chosen the correct formula we can begin step one.

Step one: subtract the 20N your friend pushed with from the 40N you pushed with.

- 40N-20N= 20N

Step two: (20N) /  (10kg) = 2 m/s^2

The answer is 2m/s^2!

2.) You are a mover on the second floor of a mansion. You need to get a piano to the second floor, but the door is too small, so you use the window. You hook up a pulley system, attach the piano, and begin to pull.  If the piano has a mass of 15kg and has an upward force of a pulley of 40N and a downward force of only its weight, what is the acceleration of the box?

The formulas we will need are w=mg and a=f/m. We need these formulas because we don't know the total force on the piano just yet. To figure that out we need to use w=mg, then subtract that from the 40N of force we already know is applied on the piano. Then we can divide that by the mass and get the acceleration.

Step One: w=mg

w= (15kg)(10N) <--- (The 10 can from the amount of gravity that is applied on all free falling objects without taking air resistance into account).

w= 150N

Step Two: a= f/m

a= (150N-40N) /  (5kg)

a = (110N) / (5kg)

a= 22m/s^2


3.) If something has a mass of 2kg, what is its weight?

   Step one= w=mg
 
    w= (2kg)(10N)

    w= 20N


4.) If something has a weight of 20N, what is its mass?

    Step one: w=mg

     20N= (m)(10)

     Step two: (20N) / (10) = m

     m= 2kg !

Part Two: Newton's Second Law Lab 

 In this lab we learned how acceleration depends on force and mass! Before beginning we had to answer the following questions...

Pre-lab

1.) What will apply the force that causes acceleration?

The hanging weight

2.) How will you calculate the force?

First, we will need to use w=mg. After, we will use a=f/m.

3.) If the net force on a body is zero, what is the acceleration of that body?

  The acceleration is zero because force and acceleration are proportional.

4.) When the net force on a body is constant, what should the acceleration of that body be?

The acceleration of that body should be constant because force and acceleration are proportional.

Lab- Part A 

After answering those we could get started! The first step was to figure out the mass of the cart and the hanging weight (kg). Using a scale we figured out the having weight's weight was .0497 kg and the cart was 0.4886 kg.  Then we had to use the formula w=mg to calculate the weight of the hanger (N). The answer was .48706. After running a few trials we answered the following questions...

1.) As the mass of the cart was increased, what happened to the acceleration?

    The acceleration decreased

2.) What remained constant in the experiment?

The force

3.) What part of the system exerted the force that caused the acceleration?

The hanging weight.

Now when we entered this all in excel, we had to use the equation of a line.

1.) What is the equation of a line?

y=mx+b

2.) If we assume the y intercept is zero (the b symbol) What do the other parts of the equation of a line stand for from the Newton's Second Law equation?

On the y axis we would graph the acceleration. The slope (m) would be representative of force, which we kept constant. Finally, on the x axis we would graph the mass.

3.) What would the equation of a line look like with the replacements of Newton's Second Law?

(a)= (f)(1/m)

4.) What equation does (a)=(f)(1/m) look like, from a concept in the previous unit?

   a= 1/2(g)(t)

Lab- Part B 

In this portion of the overall lab, we again asked how the acceleration changes. However, in part B the mass is constant throughout the experiment and we just increase the force. To begin the lab we were asked the following questions...

Pre-lab (Part B)

1.) What do you need to find the masses of in order to know the total mass of the system?

    The mass of the cart, hanging weight, and an additional weight

2.) What do you need to do to find the force of the system?

    You need the weight of the hanging weight and the added weight. Then we will use the formula, w=mg.

During the lab

1.) What happened to the acceleration as the force of the cart increased?

      The acceleration increased because acceleration and force are proportional.

2.) What remained constant during the experiment?

      The mass remained constant because we didn't remove the weight, we just moved it from what was being pulled to what was pulling the cart (the force).


 Analysis 

1.) Now assume the y intercept is zero, what could the other parts of the equation of a line stand for form the Newton's Second Law equation?

The acceleration will be on the y axis. The mass is what we kept constant and is what will represent the slope. Finally, the force will go on the x axis.


Post Lab- Questions

1.) If you add mass from the cart to the mass hanger, what will happen to the acceleration of the system? Why?

The acceleration will decrease because the mass and acceleration are inversely proportional.

2.) If you move the mass from the cart to the mass hanger, what will happen to the acceleration of the system? Why?

The acceleration will increase because the force was increased. Force and acceleration are proportional.

3.) Why did we move the mass from the cart to the hanger, instead of just adding mass to the mass hanger

We moved it because otherwise the force would've remain constant.

Why were we able to add mass to the cart when testing the effects of mass acceleration instead of having to move the mass from the weight to the cart?

This is because we were testing different things. The first time we were testing the effects of mass on acceleration. The second time were testing the effects of force on acceleration.

4.) How is Newton's Law different form the definition of acceleration.

      Acceleration is the change in speed. Newton's second law is the net forced divided by the mass which equals the acceleration.


Free Fall- Falling Straight Down

1.) What is free fall?

    When objects fall due to the acceleration of gravity only! There are not affecting by air resistance and the weight of the object doesn't matter.

2.) What is the acceleration of a falling object?
 
     The acceleration of all falling objects will be 10m/s^2.

3.) What formula you use to find out the distance of a free falling object? (How high)

      The formula to use is d=1/2(g)(t^2). In words, this translates to distance equals half of the acceleration due to gravity (10 m/s^2) multiplied by the squared time (t^2).

4.) What formula do you use to find the velocity of a free falling object? (How fast)

     The formula you use is v=gt. In words, this translates to velocity equals the acceleration due to the force of gravity (10m/s^2) multiplied the time.

Examples and Practice Problems 

1.) An avalanche is coming! You are at the edge of the cliff and have to jump, but you want to know if you have a chance of surviving the fall. You take a puff ball of of your helmet and drop it off of the edge of a cliff. The ball falls for 8 seconds. Since the ball started from rest, how high was the cliff. How fast was the ball moving when it hit the ground?

To figure out the height of the cliff we have to use the formula d=(g)(t^2).

Step one: d=1/2(g)(t^2)

d= 1/2 (10)(8^2)

d= 1/2 (10) (64)

d= 1/2 (640)

d= 320 meters

Now we need to figure out how fast the ball was moving when it hit the ground.  To do this, we will need the formula v=gt.

Step one: v=gt

v= (10)(8)

v= 80 m/s

2.) For this next problem we are going to take the same situation, but in this case we do not know the time. We want to know how the far the ball will have fallen after 5 seconds? In addition to, how fast will a ball be going after 5 seconds.

To figure out how fat the ball has fallen after 5 seconds, we need to use the formula d=1/2(g)(t^2).

Step one:

d= 1/2(g)(t^2)

d= 1/2 (10)(5^2)

d= 1/2 (10)(25)

d= 1/2 (250)

d= 125 m (meters)

To figure out how fast the ball is going after 5 seconds, we need to use the formula v=gt.

Step one: v=gt

v= (10)(5)

v= 50 m/s


Falling Through the Air (With air resistance-Sky Diving)

For this section, refer to the worksheet posted below to figure out the answers. I will mark the ones the questions you need to use the worksheet for by saying, " Refer to worksheet" in bold. However, for some of  the questions I pose, I will explain why it happens.

1.) What is the relationship between velocity and air resistance?

      They are directly proportional. This means that as one increases, the other increases and as one decreases, the other decreases.

2.) what is the relationship between force and acceleration?

You should remember this from a concept I introduced in this blog. If you don't then you haven't learned it. Return to section #1- Newton's Second Law and redo the practice questions. Then return to this question.

3.) What formula do you use to find the net force?

      The formula is f net= f weight- f air.

4.) What do we use to find mass and force when falling through the air?

    To figure this out subtract the f weight from the f air. In formula form, f weight- f air.


5.) What changes when skydiving?

     The net force changes because your speed changes. In other words, the change of one causes the change of the other.

6.) What is terminal velocity?

      Terminal velocity is when you reach equilibrium and are moving at a constant velocity. At this point your velocity is at its highest point. You acceleration and f net are at their lowest points.


7.) At what points are you velocity, acceleration, and f net before you jump out of the plane?

    At the start your velocity is at 0m/s,  your acceleration and F net are at there highest points.

8.) What happened as you fell? Refer to worksheet 

    You speed up because your f air increased. This causes your F net to decrease which causes your acceleration to decrease.

Now imagine you are skydiving, you are falling... 

1.) What happens to the force of air resistance as you fall through the air?

It increases.

2.) Why does this change occur?

It increases because your f air is increasing. Your f air is increasing because your velocity is increasing and f air is proportional to velocity.

3.) What are the two things that affect the amount of the force or air resistance?

     The two things that affect it are the velocity and the surface area. These are directly proportional meaning that as one increases the other will decrease or as one decreases the other decreases.

Now you have reached Terminal Velocity A….

1.) What causes you to reach terminal velocity?

You surface area increasing or your body position changing can cause your air resistance to increase or decrease. This can cause you to reach terminal velocity.

 2.)  At what points are the net force and acceleration at terminal velocity?

They are at their lowest points when they are at terminal velocity. 

     Now your parachute has opened….

1.) What happens to the net force and the acceleration once the parachute opens? Refer to worksheet

As soon as you open in it the surface area increases which causes the acceleration and net force to go in the upward direction. Now in the upward direction, they are both increasing which causes the f air to be larger than the f weight.

2.)  After your parachute opens, what happens to your velocity and why? Refer to worksheet

The velocity is decreasing because acceleration and velocity are going in opposite directions. 

 3.)  As you are falling you eventually reach terminal velocity A. Then you open your parachute and after a little while you reach terminal velocity B. How does terminal velocity A and B compare with each other? Why?

Terminal velocity B is slower because acceleration and velocity are going in opposite directions. Plus B has a larger surface area meaning that you cannot accelerate as quickly because your air resistance will have increased.

4.)  Is the force of air resistance larger in terminal velocity A or B? Why? Refer to Worksheet

It is the same because B and A have reached a constant velocity. Velocity is one of the things that affect the force of air resistance. Plus they are still both equal and opposite of the same f weight.

Practice Problems

1.)  Why does a steel ball hit the ground before a Ping-Pong ball?

Once they’ve both hit terminal velocity is when you will see the difference between the two balls. Until that point they are both traveling at the same speed. Once they’ve hit terminal velocity, the steel ball will continue to accelerate to a faster velocity to increase and equal the larger weight. While the Ping-Pong balls acceleration will start to decrease.

2.) What does a crumpled paper hit the ground before a flat sheet of paper?

The crumpled piece of paper has a smaller surface area than the flat sheet of paper. The flat sheet then has a greater f air and a lower net force, which means the acceleration, will be slower. If the acceleration is slower then it will take the flat sheet a longer time to fall after reaching terminal velocity. If acceleration is slower that means the velocity won’t increase in a great of a rate as the crumpled sheet of paper.

 Throwing Things Straight Up (Free Fall)

1.)  How do you find the height of a ball being thrown straight up?

First you find the total distance fallen. Then you calculate the distance fallen to the point of interest. Afterwards, you take first number and subtract the number you got in step two.

2.)  What formula do you use to find the distance?

d= ½(g)(t^2) 

3.)  If air resistance can be neglected, how does the acceleration of a ball that has been tossed upward compare with its acceleration if simply dropped?

The acceleration rate will decrease by 10 m/s^2 each second while the acceleration rate of a free falling object will continue to increase by 10 m/s^2 each second.

4.)  By how much does the speed of a ball decrease while going in the upward direction? When a ball is falling, how much does it increase?

The balls speed decreases by 10 m/s each second while ascending and increases by 10 m/s each second while descending. One more second is required for ascending than descending because it’s starting from zero.

5.) What is the velocity of the ball at the top of its path?

     The velocity is at 0 m/s at the top of its path. This is because it has reach equilibrium.

Examples and Practice Problems

1.)  You toss a ball straight up with an initial speed of 30m/s. How high does it go and how long is it in the air (neglecting air resistance) ?

To figure out the time in the air, just draw is out or use the formula d=1/2gt^2….

To figure out how high is goes you need to use the formula d=1/2 (g)(t^2).

Step one: d= ½ (g)(t^2)

d= ½ (10)(3^2)

d= ½ (10)(9)

d= ½(90)

d= 45 meters

2.)  A ball is tossed with enough speed straight up so that it is in the air several seconds….

a.)   What is the velocity of the ball when it reaches its highest point?

The velocity is 0 m/s

b.)  What is its velocity 1 second before it reaches its highest point.

        The velocity is 10 m/s

c.)   What is the change in its velocity during the 1-second interval?

The change is 10 m/s.

d.)  What is its velocity 1-second after it reaches its highest point?

                           The velocity is 10 m/s.

e.)   What is the change in its velocity during the 2-second interval? (Careful!)

The change is 20 m/s.

f.)    What is the acceleration of the ball during any of the timer intervals and at the moment the ball has zero velocity?

     The acceleration is 10 m/s^2.

Falling at an angle (Free Fall) (Projectile Motion)

1.) When an object has constant acceleration when falling (vertical), what do you use to find the velocity?

The formula you is v= 1/2gt

2.) What do you use to find the distance?

The formula you use is d= 1/2 gt^2

3.) When moving with a constant velocity (horizontal), what formula do you use to find the velocity?

           The formula used is v=d/t.

 4.) What formula do you use to find the distance?

 

            The formula you use is d=vt.

5.) What determines the time in the air?

The vertical velocity controls the time in the air.

 6.)  What are the special triangles you are likely to find?

You are likely to find 1-1-1 root 2 and 3-4-5 triangles. Now remember that the root of 2 is 1.41 in decimal form.

7.) What do you use to calculate how long the object will be in the air? Why?

To calculate how long an object will be in the air, use the formla d= 1/2gt^2. This is because we would already know the distance and the acceleration. We already know the acceleration because the acceleration of any free falling object Is 10m/s^2. We already know the distance because it will be stated already.

8.)   How do you calculate how far downfield an object will get after it is dropped (assuming it has some sort of an initial horizontal velocity)?

You will use the formula v=d/t. 

9.)  Why do you use 1/2gt^2 and v=gt for the vertical distances and velocities but rather v=d/t for the horizontal distances and velocities?

We use the formulas for the vertical distances and velocities because it has a constant acceleration of 10 m/s^2 while an object traveling horizontally may not have a constant acceleration, but it will have a constant velocity.

1    10.) Why does an object have a constant acceleration in the vertical direction?

This is because an object going downward in the vertical direction is considered a free falling object if we are neglecting air resistance. The acceleration of a free falling object will always be 10 m/s^2.

1    11.)  Why does an object have a constant velocity in the horizontal direction rather than a constant acceleration?

            

      This is because it is not a free falling object and there is no force acting on it that could increase it’s rate of acceleration.

1     12.) What kind of path does an object actually take?

         The object takes a diagonal path.

13.) Why do a bullet and its shell hit the ground at the exact same time even though the bullet travels farther down field? 

They hit the ground at the exact same time because they fall from the exact same height.

Examples and Practice Problems

You are on spring break with all of your friends and possible crushes. You are all about to jump off of a cliff, but before you do you dropped a shiny pebble to get the height. You find it is about 80 meters tall. After deciding that is a safe height, you run off of the cliff at a velocity of 20 m/s. How long were you in the air? How far from the cliff were you when you hit the water? 

'How long were you in the air? 

First use the formula d=1/2gt^2 

80= 1/2(10)(t^2) 

80= 5 (t^2) 

80/5= t^2

16= t^2

t= 4 seconds 

How far from the cliff were you when you hit the water?

To figure this out, use the formula v= d/t. 

20=d/4

20(4)=d

d= 80m 

Throwing Things Up at an Angle (Free Fall) 

1.) For objects thrown up at an angle, what controls the time in the air? 

    

     The velocity controls the time in the air. 

2.) What is one way in which objects being thrown up at an angle are different than objects being thrown straight up? 

    Objects at an angle have a constant velocity while object being thrown straight up have a velocity that decreases going up and increases going down.  

3.) The vertical velocity of an object being thrown straight up and at an angle is 0 m/s, however the object being thrown up at an angle is still moving. How is this possible? 

They have reached equilibrium. This means they can have a constant velocity of 0 m/s, but still be moving. 

4.) What formulas do you use to calculate the vertical velocities, distances, and times? 

    The formulas are v=gt and d=1/2gt^2. 

5.) what formulas do you use to calculate the horizontal velocities, distances, and times? Why is this is different from the ones you use to calculate the vertical velocities?

    The formula is v=d/t. You just have to rearrange it based on what you are trying to find. This is different because vertical objects are free falling objects, the acceleration will always be 10 m/s^2.  This is because the only force acting on it is the force of gravity with out the force of air resistance. While a horizontal object has forces acting on all sides with air resistance. 

6.) What are the two special right triangles we use? 

      If you do not remember this, return to the previous section and redo those problems. After you correct and check the questions, you may return and answer this again. 

Example and Practice Problem 

1.) You throw your dogs tennis ball up at a 45 degree angle. The ball has a velocity of 20 m/s in the horizontal direction, and 40m/s of speed in the vertical direction. How long will it be in the air? How fast will it be moving at the top of its path? How far downfield will it land? 

For this situation you can draw the picture instead of using a formula if you would like, but if you would like to use the formula you may.

Answer: The ball was in the air for 8 seconds! 

How fast will the ball be moving at the top of its path? 

The ball will be moving at 0 m/s at the top of it's path because it will have reached equilibrium. 

How far down field will it land? 

To figure this out, you need to use the formula v=d/t. 

Step one: 

20 = d/8 

d= 20(8)

d= 160m 

Answer: 160 meters