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)
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.
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.
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.
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.
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.
The formula you use is d=vt.
5.) What
determines the time in the air?
The vertical velocity controls the time in
the air.
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)?
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
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