How To Add Vectors

• If the givens are collinear, set a reference direction and solve by addition/ subtraction.
• If givens are not collinear, draw head-to-tail arrows in the direction of travel.
• Draw and label the resultant vector. From start of first to end of last component vector.

• Label your positive axis, for example North and East are positive, therefore South and West are negative.
• Group and add all the X components. Do the same for Y components. (N and S are Y components, E and W are X components)
• Using c²= a²+b² ( Pythagorean theorem), find magnitude (c²).
• Now use SOH CAH TOA to find the angle of direction. 

Therefore, the final hypoteneuse is the resultant vector and the final angle is the angle of direction.

Deriving the Big 5 Equations

Equations are used as they are more versatile and easier to manipulate than graphs. In total there is a set of 5 equations which can be derived from a velocity vs. time graph. 


The first equation: constructed by taking the slope of the graph
a= rise/ run
a= v2-v1/ Δt       rearrange it:
v2= v1+ aΔt


Equation two: found by calculating the area under the graph (displacement)
Δd= ½ (v2+ v1)Δt


Now we can manipulate these two equations to create three more equations.


Substitute the expression for v2 into equation 2 to find equation 3:
Δd=½ (v1+aΔt+v1)Δt
Δd=½Δt (2v1+ aΔt)
Δd= v1Δt+½aΔt²


To find equation 4: first isolate v1 in equation 1, then substitute this in equation 2:
v1=v2-aΔt      subs. in equation 2:
Δd= ½ (v2+v2-aΔt) Δt
Δd= ½Δt(2v2-aΔt)
Δd= v2Δt- ½aΔt²


To find the final equation 5, isolate Δt in equation 1 and substitute it into equation 2:

Δt= v2-v1/a      subs. in equation 2:

Δd= ½ (v2+ v1) v2-v1/a

Δd= ½ (v2²- v1²) /a

2aΔd= v2²- v1²

v2²= v1²+ 2aΔd


These are the five fundamental equations in kinematics. They are applicable only in problems that have constant acceleration.

Motion Graphs

Graph 1: Distance vs. Time

Starting at 1m from the origin

Rest for 1sec

Walk 1.5m away from the origin in 2secs

Rest for 3secs

Walk 0.5m towards the origin in 1sec

Rest 3secs

Graph 2: Distance vs. Time

Starting 3m away from the origin 

Walk 1.5m towards the origin in 3secs

Rest for 1sec

Walk 1m towards the origin in 1sec

Rest for 2secs

Walk 2.5m away from the origin in 3secs

Graph 3: Velocity vs. Time

Rest 2secs

Walk away from place of origin and speed up to 0.5m/s for 3secs

Rest 2secs

Walk towards the place of origin at a speed of 0.5m/s for 3secs

Graph 4: Velocity vs. Time

Speed up slowly away from the origin until reaching 0.5m/s at 4secs

Walk at 0.5m/s for 2secs

Walk towards the origin at 0.4m/s for 3secs

Rest 1sec

Graph 5: Distance vs. Time

Start 0.8m away from the origin

Walk away 1m in 3.5secs

Rest for 3secs

Walk away 1.5m in 3.5secs

Graph 6: Velocity vs. Time

Walk away from point of origin at 0.35 m/s for 3secs

Walk towards point of origin at 0.35m/s for 3.5secs

Rest for 3.5secs

Building an Electric Motor

On Thursday, our class was given the task of building an electric motor. We had previously decided to work in either pairs or to work alone. In preparation, my partner (Bojana) and I collected all the materials we would need for the task at hand: a piece of non compressed wood, 4x 4inch nails, smaller nails, thumb tacks, sand paper, a soda can, paper clips, a kebab stick and a cork. We were provided the power supply, magnets, copper wire, and tools. Another member was added to our group the day of (Emily).

We started by hammering the 4 4inch nails into the piece of non compressed wood, while other members hammered the two commutator pins on either side of the cork and slid the kebab stick through the centre. We twisted two paper clips into loops having to change the shape many times in order to allow the kebab stick enough space to freely spin when place with these loops. the paper clips were thumb- tacked to the wood. Then we cut our pop can to get two thin strips which we sanded on both sides, this would be our brush. 

                     

Next we took the copper wire we were provided and wrapped it in the same direction around the cork and the two commutator pins. the two ends of the wire were well sanded previously. Now that everything was in place, the brushes were thumb-tacked so that they would touch the commutator pins when spun. Our model was ready to be tested.

Unfortunately, our model could not be tested because of several factors, the nails happened to be two far apart and the brushes did not reach the pins when the axel was spun. The design overall was very unstable. My group decided to take our model home and fix it. 

Later that day, my partner and I met in hopes of fixing our model. We took out the 4inch nails and carefully hammered them back in according to the given measurements. We remodeled the paper clip bearings we had made so that they were equal and the axel could lay parallel. We hammered the commutator pins so that they were in not too far that the brushes couldn't reach them. The hardest part was getting the brushes just right. We cut and bent it many times before it finally appeared as if our model was perfect.

The next day, we were excited to test our model again. When the power supply was turned on... it did not work! we were surprised and didn't know what we had done wrong our how to fix it. Fortunately Mr. Chung figured out that it could be a problem with the wire and not the model. When he tested it again, our motor began to spin smoothly and continuously. We were so relieved! Our hard work the night before definitely payed off.