- Newton's 2nd Law of Motion
- Newton's 2nd Law Lab
- Skydiving
- Free Fall - General
- Free Fall - Throwing things straight up
- Free Fall - Throwing things straight down
- Free Fall - Falling at an angle
- Free Fall - Throwing things up at an angle
#1.)
Newton's 2nd Law in words is "Force is directly proportional to acceleration and inversely proportional to mass. (F~a), (F~1/m).
Weight is the force of gravity on an object's mass.
Mass is the amount of matter in an object / also a measure of inertia.
Formula: Weight = Mass * Gravity (W=mg)
Gravity is always 9.8m/s2 unless we are solving problems, which is when we simplify it to 10m/s2.
EX: A box is pushed to the left 30N and to the right 10N. The force of gravity on the box's mass, (weight) is 200N downward. What is the box's mass and acceleration?
w=mass*gravity a=net force/mass
200=m(10) a= 20/20
m= 20kg a= 1 m/s2
We solved for the mass first, then plugged the 20kg into the other equation to find the acceleration!
EX: If the mass of a system is kept constant and the force of the system is doubled, what happens to the acceleration? Let's use some numbers:
- f=ma
- 6=2*3
- 12=2*?
- a=6, it doubled.
#2.)
Newton's 2nd Law Lab: cart, hanging weight, pulley/string, discs (extra mass).
Experiment A...
-- We kept the force of the system constant throughout this part of the lab. By adding masses to the cart each time by 0.1kg, we used the computer to see how the acceleration varied.
-- The acceleration decreased because as more mass added to the system, less force acts on it. (Inversely proportional).
As the mass increased, the acceleration decreased.
The force of the system remained constant.
-- To calculate the force on the system, use w=mg and plug in "mass of system" and "gravity."
Experiment B...
-- We kept the mass of the system constant throughout this part of the lab. By removing masses from the cart to the hanging weight each time by 0.1kg increments, we used the computer to see how the acceleration varied.
-- The acceleration increased because the more mass added tot he hanging part, the more weight, (force of gravity on the object's mass). Which means more force!
As the force of the cart increased, the acceleration increased.
The mass of the system remained constant.
Using y=mx+b:
Newton's 2nd Law: a = Fnet * 1/Mass
y = m * x
The equations line up! Whatever variable is kept constant is the slope (m). The "y" is usually acceleration, as we observed this after changing the force and mass of the system. The "x" is either the force or 1/mass depending on the experiment.
To confirm N's 2nd Law, we can use the slope (a number) and compare it to what the calculated/predicted number was. If they differ by less than 10%, it is verified. If not, there is an issue.
#3.)
Skydiving: we spent a good chunk of time looking at and understanding what goes on in skydiving and how it relates to N's 2nd Law. Here are some things that we need to know at the start:
- Terminal velocity is when the force of air resistance (Fair) equals the force of gravity on the diver's mass (Fweight).
- At terminal velocity, because the net force is 0Newtons, the acceleration must be 0m/s2. It's in equilibrium.
- At terminal velocity, the diver is at his/her maximum speed, which is constant.
Speed and Surface Area are directly proportional to the Fair. So, the more speed an object gains, the more air resistance. Same with the surface area of something such as a parachute.
Paul G. Hewitt's drawings (practice page handout) are a good visual of the entire motion.
- Bronco, the diver, falls out of a helicopter at a time of 0 seconds, with no Fair, and his velocity is least here, which shows us that his acceleration is most.
- Next, as Bronco continues to fall (1000N Fweight) the Fair gradually gets bigger because he gains speed over time. His acceleration decreases because the net force decreases.
- As he reaches terminal velocity, his net force and acceleration are 0. The velocity is constant.
- When Bronco pulls the parachute, his Fair gets big because of the increased surface area. His net force, (now negative and upward), makes the acceleration both negative and upward. His velocity is still downward though!
- After the parachute is pulled, Bronco's Fair is most. His net force is least, and his acceleration is least.
- Once he regains terminal velocity by slowing down (the whole purpose of a parachute), his net force and acceleration are 0. The velocity is now constant.
The terminal velocity before the parachute is opened is much higher than after, because of the slower speed due to the increased surface area and more Fair.
#4.)
Free Fall - General explanations.
Free fall is when the only force acting on a falling object is the force of gravity.
The formulas for vertical distance, time, and velocity are as follows:
Because the only force is gravity (10m/s), the ball (object) accelerates at 10m/s2 each second.
When it falls, the ball is at t=0seconds and velocity=2m/s.
At 1 second, the ball's velocity is 10m/s and its acceleration is 10m/s2 still.
At 2 seconds, the ball's velocity is 20m/s and its acceleration is 10m/s2 still.
At 3 second, the ball's velocity is 30m/s and its acceleration is 10m/s2 still.
After 3 seconds, it lands. How do we calculate the vertical distance from the ground at each second?
d=1/2(a)(t2)
d=1/2(10)(32)
d=45 meters high / total!
After 1 second, the ball is
d=1/2(a)(t2)
d=1/2(10)(12)
d=5 meters high off the ground.
We can use what we know for each second.
#5.)
Free Fall - Throwing things straight up.
When thrown up, the ball must have an initial velocity (not 0m/s). No Fair.
The time starts at 0 seconds.
It is the same concept as being thrown down, but in the opposite direction.
After each second, the velocity decreases by 10m/s, even though the acceleration is 10m/s2 still.
At the top of its path, the ball's velocity is 0m/s.
We can look at a picture and see the time it takes to go up, down, and add them to get the total time in the air.
To use d=1/2(a)(t2), we must plug in the time it takes to go up. We can get the vertical distance.
We can also use v=at to find the velocity/time depending on what we are given!
If the question asks "how far from the ground is the ball after 5 seconds," we must find the distance from the top of the ball's path to that second, and subtract it from the total vertical distance.
#6.)
Free Fall - Throwing things straight down
When thrown down, the ball's initial velocity is not 0m/s. The acceleration is 10m/s2 still.
The time starts at 0 seconds.
It is the same concept as being thrown up, but in the opposite direction.
After each second, the velocity increases by 10m/s.
This is the same concept as throwing things straight up, but the velocity increases.
We can use d=1/2(a)(t2) to find the distances.
THE ONLY THINGS THAT DETERMINES HOW LONG AN OBJECT IS THE IN THE AIR IS THE VERTICAL DISTANCE.
#7.)
Free Fall - Falling at an angle
EX: Let's say that a plane 125 meters high drops a box while it is moving at a constant horizontal velocity of 90m/s.
- Everything is the same in Free Fall with the time at 0 seconds, no Fair, and The acceleration is 10m/s2 still.
- We can plug 125m into the equation d=1/2(a)(t2) to find the time. 5 seconds.
- Drawing a picture for help, we want to find the horizontal distance now. Using v=d/t, we plug in 90m/s and 5 seconds to get out 450meters.
- The horizontal velocity,time, and gravity NEVER change.
Sometimes we want to find the actual velocity of the box at a certain point. After 2 seconds, the box should be at a vertical distance (from the top) of 10 meters and a horizontal distance of 180 meters.
-- Even though the numbers are not the same, we use a2 + b2 = c2. Then we get the actual velocity looking at the right triangle.
Here is my podcast!
#8.)
Free Fall - Throwing things up at an angle
EX: Let's say that an object is thrown up at a 45-degree angle and has a velocity of 20m/s in the horizontal direction, and 40m/s in the vertical direction. Look below.
a. How long will it be in the air total?
b. How fast will it be moving at the top of its path?
c. How far downfield will it go?
a~ It starts with 40m/s in the vertical direction, so after 4 seconds, it'll be at the top (and 4 seconds to go down) = 8 seconds total.
b~ The horizontal velocity never changes = 20m/s.
c~ v=d/t
20=d/8
d=160 meters
#BONUS.) Extras!!!!
- A high-speed jet flies really high in the air. When it flies exactly over you, it drops an object. If you don't move, will it hit you? Why or why not?
- What is the square root of 2? How does this help us?
- We know that force is directly proportional to acceleration and inversely proportional to mass, but why? It'll be nice if you know this.
- If you drop a lead ball and a ping pong ball for the same height at the same time? Which one will hit first and why? What if they are at a super high distance form the ground?
- In the absence of air resistance, why do a feather and a penny hit the ground at the same time if dropped fro equal heights at the same time?
Part 2A: Difficulties, help, effort, skills, etc.
The most difficult idea that I had issues with was the idea that "what happens to an object's velocity if it is traveling with a decreasing acceleration?" This question was on the quiz, and I missed it. I understand it now though!
Also, the Newton's 2nd Law Lab was scattered. The 2 different experiments were separate, but the analysis after, which confused me tons.
I overcame these difficulties by asking about them in class. Drawing pictures and memorizing the formulas/constants really helped.
My effort has been consistent, and I am glad that the class has been going well for me thus far. I like the other students in the class and we help each other. The dynamic is great until someone goofs off and I can't focus. My problem solving has improved!
My goals for the next unit are to:
- Stay attentive in class and be active when learning about new topics.
- Keep up my grade and try hard, even if it leads to failure.
- Persevere and stay positive no matter the consequences, because a good attitude is necessary.
- Attempt not to breeze through, but to challenge myself more.
Newton's 2nd Law of Motion can be found everywhere. Anything that is thrown, dropped, rolled, pushed, forced, or acted upon...will move. We can visualize the relevance to our topic - acceleration, force, and mass.
Just the other day, I threw a water bottle upward at an angle (to a friend during swim practice), and he caught it. I thought about the gravity and the velocity and how they worked together.
