In Class with Dr. Prince: May the FORCES be with You!

Standards:
S8P3a. Determine the relationship between velocity and acceleration.
S8P3b. Demonstrate the effect of balanced and unbalanced forces on an object in terms of gravity, inertia, and friction.

Goal:
Explain the relationship between force, mass, and the motion of objects.

Objectives:
SWBAT explain the relationship between velocity and acceleration.
SWBAT create original examples of balanced and unbalanced forces in their daily lives.
SWBAT graph velocity and acceleration and find the slope of the line.

Big Ideas:
1. An object in motion changes position.
2. Speed measures how fast an object's position changes.
3. Acceleration measures how fast an object's velocity (speed) changes.
4. Forces change motion.
5. The force and mass of objects determine their acceleration.
6. Gravity is a force exerted by the mass of and distance between objects.
7. Friction is a force that opposes motion.

Vocabulary:
motion, reference point, speed, velocity, acceleration, force, net force, inertia, balanced force, unbalanced force, gravity, friction, mass, weight, slope, meters (m), seconds (s), x-axis, y-axis, independent variable, dependent variable, initial velocity, final velocity
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Have you ever tried to explain to someone whether or not something move and needed to prove it to them? Our next unit is all about moving objects, what causes their motion, or the lack thereof. Let's look at this from the basis of each BIG IDEA.

B.I.1: An object in motion changes position.

I know an object was in motion if the distance between it and other object changes. The other object that I am using to determine if motion occurred is called a reference point. Look at my diagrams below.

In the first picture, the beach ball is far away from the tree. In the second picture, the beach ball is closer to the tree. The tree is my reference point. I use the tree to help me determine if the object--the beach ball--moved. I can also measure the distance between the point A and point B to also confirm my observations. The SI unit for measuring length is meters.

B.I.2: Speed measures how fast an object's position changes.

Do you remember learning about slope? Well, there is a relationship between slope and an object's speed: they are one in the same. Slope measures the steepness of a line and you can find it by the ratio of the rise and the run.

To graph the speed of an object, you use a distance-time graph. This graph is similar to the one used in calculating the slope of a line. In this case, the x-axis (the independent variable) is always time. The y-axis (the dependent variable) is distance. Remember to label the axes accurately because time never depends of the distance traveled. The distance traveled depends on the amount of time in which to travel that distance.

Let's look at a few speed graphs.

To calculate the slope of a line, you find the change of y over the change of x. The rise of a line is along the y-axis and the run moves along the x-axis. The rise of the line is 1 and the run is 2. The slope, which is m, equals 1/2. Since the slope is 1/2, the speed of the object is 1/2 meters per second. This means that there is a constant rate of change. For every second, the object is moving 1/2 meter.

Now look at this graph. Can you see the connection between the slope and the speed? For every second, the object is moving 3 meters. Now look at the next graph.

Do you notice something in this graph about the steepness of each line? The steeper the slope (the higher the line), the faster the object is traveling. There is clearly a relationship between the steepness and speed of a line. Now what about the next example?

What do you think a horizontal line or zero slope means? Let's start with the time. As the line moves fro the left to the right, it appears to be increasing. What about the distance traveled by the object. It looks like this object has been in the same position (3 m) for some time. Remember time is also going whether the object moves or not. This object has a slope and speed of 0 m/s, which means it is simply not moving at all.

B.I.3: Acceleration measures how fast an object's velocity changes.

How many ways can an object accelerate? Is 1 your guess? I am sure you are thinking of acceleration in terms of an object speeding up. There are actually to other ways for an object to accelerate: by slowing down (negative acceleration) or change direction! Yep, that's right. So that's a total of three ways for an object to accelerate.

An object speeding up (positive acceleration): If an object is moving faster than the speed at which is first started moving, you will see a positive acceleration. So let's say that an object had an initial speed of 1 m/s and had a final speed of 7 m/s over a period of 3 seconds. Here is how that is calculated:

An object slowing down (negative acceleration): If an object is moving at a slower speed than which it started, you will see a negative acceleration. For example, if an object has an initial velocity of 10 m/s and then has a final velocity of 0 m/s, over a period of 20 seconds, it would look like this:

An object changing direction: Velocity is defined as the speed in a given direction. So whereas an object's speed might be 3 m/s, its velocity would be 3 m/s going North (or whatever direction).

Need more on calculating acceleration? Watch this video that shows how to calculate acceleration.

Sunday, March 3, 2013

May the FORCES be with You!