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.
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.
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.
Third, vertical height controls time in the air.
Fourth, velocity is always constant and downward when falling through the air with air resistance.
