What I Learned
In this Unit, we talked about a number of things. The first was Newton's Second Law, which then transitioned into the Newton's Second Law lab. We then discussed Free Fall in relation to both Objects Falling Straight Down and Throwing Objects Straight Up. Next came Falling at An Angle, and Throwing Things Upward at an Angle. Lastly, we discussed Falling with Air Resistance. Each of these topics greatened our understanding of the world around us.
Newton's Second Law
Newton's Second Law states the relationship between acceleration and Mass and Force. The law can be written in multiple ways. By definition, Newton's Second Law states that Acceleration is directly proportional to Force, and that Acceleration is indirectly proportional to Mass.
This can also be written as a=f/m, or a=f(1/m).
Above is a helpful diagram from Demario and Xavier's podcast.
It accurately depicts the relationship between Acceleration, Mass and Force.
Newton's Second Law Lab
Our knowledge of Newton's Second Law was demonstrated in the Lab that we did. Each lab group had a track and cart, complete with a hanging weight, which was the force that caused the system to accelerate.
To find the Mass of the system, we add the mass of both the hanging weight and the cart. For example, if the mass of the cart was 3 kg and the mass of the hanging weight is 2kg, then the Mass of the System is 5kg.
To find the force on the system, we use w=mg. In the example above, we would plug in 2 for mass and 10 for g. w=(2)(10). We then find that the weight on the system is 20N.
In Part A of the experiment, we added mass directly to the cart. This causes the mass of the entire system to decrease. Since Newton's Second Law states that Acceleration is indirectly proportional to Mass, the acceleration DECREASED as mass was added. Since the hanging weight did not change, the force was our constant. We can compare the equation of a line, y=mx, to Newton's Second Law, a=f/m.
Seeing as the force was constant, we would insert that for the slope (m).
Thus, a=1/m(f)
In Part B, we moved mass from the cart to the hanging weight. This meant that the overall mass stayed the same, but the force increased. Seeing as Acceleration is directly proportional to Force, as the force increased, so did the acceleration. In this part of the experiment, the Mass remained constant. We can also compare the equation of a line, y=mx, to Newton's Second Law, a=f/m.
Seeing as the Mass was constant, we would that in for the slope.
Thus, a=(1/m)f
Falling Straight Down
This section relates to the falling of an object when air resistance is negligible. This means that the only force acting on the object is Gravity. For real-life experiments, we use 9.8 for gravity, but in class we used 10.
For Free Fall, we used two equations.
d=(1/2)gt^2 can be used to find either the hight or the time, depending on what is given in the question.
v=gt can be used to find the velocity or the time, also depending on what is given in the problem.
Sample Problem: A ball is thrown off of a cliff with a velocity of 50m/s. a) How high is the cliff?
b) How fast is the ball going at 3 seconds?
Thrown Upwards
Also under the category of Free Fall is what occurs when an object is first thrown up and then falls back down with no air resistance.
Here, we also use d=(1/2)gt^2. However, this equation assumes that the object is starting at rest. Should a question ask how high the object is at, for example, 2 seconds, there are a number of steps which need to be followed.
1.) Find the total height that the object reaches, using d=(1/2)gt^2.
2.) Find the height from the top of the objects path to the desired height. d=(1/2)gt^2 is used again here.
3.) Subtract the 2nd height found from the first.
For a much more in depth explanation, a helpful podcast is included above.
Falling at an Angle
There are three equations we use for Falling at an Angle.
In The Vertical Direction
-d=1/gt^2
-v=gt
In the Horizontal Direction
-d=vt
There are also 2 special triangles that we use to find the velocity:
3,4,5
10,10,10 root 2
(root 2=1.41)
To best explain Falling at an Angle, I have put some of the questions from one of Ms. Lawrence's ONQ's and will answer them below.
1) A plane is flying at 100m/s and is trying to drop a package on a target. The pilot estimates that it will take approx. 4 s to reach the ground.
A) How far before the target does the plane need to release the package?
d=vt
d=100(4)
d=400
B) How high is the plane?
d=1/2gt^2
d=1/2(10)(4)
d=1/2(160)
d=80m
C) What is the final vertical velocity of the package?
v=gt
v=(10)(4)
v=40m/s
D) What is the final horizontal velocity of the package?
d=vt
400=v(4)
v=100m/s
E) What is the actual Velocity of the package 1s after being released?
Throwing up at an Angle
For throwing up at an angle, we use two different sets of equations.
For Horizontal, or Constant Velocity
d=vt
For Vertical, or Constant Acceleration
d=1/2gt^2
v=gt
*Only used when starting at rest!
Here is another sample problem to help with your understanding:
A ball is thrown up with an initial vertical velocity of 30m/s and a horizontal velocity of 5m/s. Find the descending velocity at 5 seconds.
Above is the path that the ball took.
At 5 seconds, the ball has a horizontal velocity of 5m/s and a vertical velocity of 20m/s.
To find the velocity, we use The Pythagorean Theorem.
a^2+b^2=c^2
5^2+20^2=c^2
25+400=c^2
425=c^2
c=20.6
The velocity=20.6m/s.
The same ball is thrown with the same velocity both vertically and horizontally. How far away from the thrower does the ball land?
d=1/2gt^2
d=1/2(10)(6^2)
d=1/2(360)
d=180m
Remember, time in the air is controlled by the angle at which the object is thrown!
Falling with Air Resistance
Skydiving is the part of the unit in which air resistance is NOT negligible.
Below is a helpful chart describing what occurs at each stage of Falling with Air Resistance.
Below is a more extensive explanation of Falling with Air Resistance.
Connections Made
This unit had major connections to things that we see almost everyday, how they work, and why. Although we couldn't always make air resistance negligible, in the large majority of our tests, the distance was too short for air resistance to take effect. This unit, I could really see the effect that physics has on everyday life.
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