How to Add Vectors

When presented with various vectors, and we're asked to add them up, how do we do it? Do we just add the length of the displacements together? If only it were that simple...

Here are the steps on how to add vectors.

1.) First, look at the equation given to you. If there are negatives (eg A - B), change it around so that it's adding the negative (eg A + (-B)). The negative only affects the direction of the vector, not the value. So if B was going East, negative B will be going West.

2.) If the vector is at a degree, change it so that it is represented by a horizontal x and a vertical y.

3.) Solve for x and y.

4.) Add up final x and final y with the Pythagorean therom.

5.) Use some simple trigonometry to solve for the angle.

Deriving equation 3 and 4 from the v-t graph

The standard velocity-time graph.

Equation 3 is written as d = V1Δt + ½aΔt².

On a v-t graph, when we are looking for distance, we find the area of the trapezoid shape.

We can do that by dividing the trapezoid into a square and triangle.

The formula to find the area of the triangle is ½(V2-V1)t. Equation 1 states that at= V2-V1. Sub equation 1 into the formula. ½at²

The formula to find the area of the rectangle is V1*t, also known as V1Δt.

Combine these 2 formulas to create equation 3, d = V1Δt + ½aΔt².

Equation 4 is written as d = V2Δt - ½aΔt².

On the v-t graph, we can derive equation 4 by making the graph look like this big rectangle.

First, find the area of the rectangle as a whole. V2*t, or V2Δt.

Then find the area of the triangle within the rectangle. ½(V2-V1)t. We know from equation 1 at = V2-V1.
½aΔt².

Combine the two formulas to create V2Δt - ½aΔt².

Motion in Graphs

Last week, we did a lab on distance/time graphs and velocity/time graphs. Here are the 6 graphs we made:

In this Distance/Time graph, the motion is first not moving at 1 m away from the detector. Then walking away from the detector at a constant speed. Next walk towards the detector at a constant speed. Finally, stop moving for the last couple of seconds.

In this Distance/Time graph, The motion is walking towards the detector at a constant speed. Then one stops for a few seconds. Next, walk towards the detector again in a faster constant speed. Then stop for a few seconds. Finally, Walk away from the detector in a constant speed.

In this Distance/Time graph, The motion is walking away from the detector at a constant speed. Then stop moving for a few seconds. Finally, walk away from the detector at a faster constant speed.

In this Velocity/Time graph, The motion is walking away from the detector at a slow speed, but then quickly pick up speed. Then, continuing walking at a constant speed. Next, start walking in towards the detector at a constant speed. Then keep that speed for a few seconds. Finally, stop moving.

In this Velocity/Time graph, the motion is not moving for the first few seconds. Next, start walking away from the detector at a constant speed. Then stop moving again for a few seconds. Finally walk towards the detector at a constant speed.

In this Velocity/Time graph, The motion is to be already moving at a constant speed going away from the detector once it starts recording. Then one will change directions and start moving back toward the detector at a constant speed. Finally one will stop moving all together.

Motor Lab

We were asked to build motors the other day. We had one day to gather up all the materials needed to build a motor. Luckily, we were able to gather all the materials even though some of them were hard to get.
When we started building the motor, we were given 30 minutes to hammer the 4 four-inch nails into the wood. The nails had to be 2-3cm apart in width and 5-6 cm apart in length. We then sanded the pop can all the way to the point where both sides were silver. Our first problem popped up when we were trying to fit the axel into the cork. Our cork was a bit bigger than the other corks other people had so it took longer to get the axel in. The cork was also a bit rubbery which didn't help us. The second problem with the cork came up right after the first. the copper coil wasn't holding onto the cork tightly enough, and we spent a long time trying to get it to stick. In the end, our motor ended up as a fail. D=