Newton's Second Law:
The definition of Newton's Second Law is a=f/m. This can also be interpreted in that acceleration is directly proportional to force, and inversely proportional to mass. In other words, what ever acceleration does, force also does.
The other aspect of this law is how weight is applicable to an example. The formula commonly used is w=mg. The weight calculated is also the force, so this is a simple way to find the force acting on an object. When you put only a little force on an object, like the child in the swing from the video above, the child does not go very far. However, when you push with more force, the child goes farther.
Free fall:
In free fall, the only force acting on the falling object is the force of gravity, which is 9.8 m/s.
There are two formulas that are used to calculate the how far and how fast aspects of free fall. Respectively, they are d=1/2at^2 and v=at.
If a ball was falling off a building for 5 seconds, it would travel 125m because of the d=1/2at^2 formula. We don't know the distance, but we do know the acceleration (10 m/s^2) and the time, 5 seconds. Similarly, to find the speed of the falling object the formula used would be v=at. Again, we know the acceleration and time, so multiplying those together would yield the velocity.
This example shows the relationship between time and velocity because height and time always determine each other. Therefore, the more time that passes means that the object is falling from a greater height which will yield a faster speed.
These formulas and facts are also applicable to a ball thrown straight up and its descent back down. Here is a picture to help understand the relationship between the two.
Projectile Motion:
In projectile motion, an object is being dropped at an angle. A common example is how far back a plane should be in order for the box being dropped from it to hit a target. The two velocities in this example, vertical and horizontal, and both stay constant. To find how far the box falls, we can use the the height of the plane to determine the time by using d=1/2at^2 and to find the actual velocity, we would use the Pythagorean Theorem. In this example, one side of the triangle represents the horizontal velocity, another the vertical, and the hypotenuse represents the velocity of the object just before it hits the ground. To calculate the horizontal distance the box falls, the d=vt formula would be used.
As this example shows, the object falls according to the vertical and horizontal velocities and also the force of gravity.
Skydiving:
When a person goes skydiving, Newton's Second Law has a bigger connection than you'd think. During a persons fall, the net force and acceleration decrease because they are proportional, while the velocity increases simply because it is falling and therefore gaining speed. The net force and acceleration do increase but only until the person reaches their first terminal velocity. Terminal velocity is when your velocity is constant and your acceleration is 0m/s^2. When you open your parachute, your acceleration and surface area both increase while the velocity decreases. The surface area increase results in the air resistance pushing on the parachute increasing. The two factors that increase air resistance are surface area and speed.
When a person reaches their second terminal velocity, the net force and acceleration are both at 0, but the velocity is much slower because of the change in surface area.
One thing that made much more sense to me after this unit was the ascent and descent of a ball thrown straight up. I did not know before that there was so much detail in which the ball traveled. I learned about the relationship between time and velocity and how to figure out how long the ball had been in the air. Now when I throw an object straight up, I will know what is really happening.
Here is my groups podcast about Newton's Second Law Lab.
