Ticker Tapes

NG1: Key Question - what is the relationship between position/time on ramp  and...?

The relationship between the position and time on the ramp is that as time increased, cart's position grew further and further. Thus the movement of the cart can best be described as speeding up as it went traveled down the ramp in every 0.1 second interval. The relationship between velocity and time for the cart rolling down the ramp is that the slope of the velocity increased proportionally over the same time interval.

NG2: Investigate - photo, summary of what you did to get data

                         

The ticker timer was used to gather data for position and time by counting every 4th dot on the tape used. We counted every 4th dot because the timer that we used recorded 40 hertz which means 40 dots per 1 second; which was then 4 hertz  dots per 0.1 second. I used the ticker timer tape to create my velocity vs time graph by cutting them up for every 0.1 seconds that passed and then aligned them together in order to create a linear graph. This linear graph represents the rate of change of the object on every interval of 0.1 seconds, or the velocity of the object in other words.


NG3: Analysis - graph, verbal model, math model (units), describe motion of cart






VM: As the time increases, the position increases (not proportionally)
MM: Position = (33 cm/sec²)x time²
Y-int: 0 sec, it represents initial position

VM: As the time increases, the position  velocity increases proportionally
MM: Vfinal = (66 cm/sec²)x time + 0 cm/sec
Slope: When time increases by 1 second, then the velocity increases by 66 cm/sec called the....?
Y-int: At 0 seconds, it represents initial position

Average velocity: V = ∆x / t
V = 91.2 cm / 1.6 sec = 57 cm/sec


NG4: Models

The two new equations that were developed in this lab are a parabola and a linear line respectively.  those are shapes, not equations.  WHat are the equations that we will now take and use in other situations?>   The position vs. time graph was discovered by rolling the cart down an incline with ticker tape; the velocity vs. time graph was discovered by taking the tape pieces, flipping them on its side to represent cm/sec, and creating a new graph. The area under the velocity graph thus represents the total distance traveled over the time interval

NG5: Explaining

The position vs time graph and the velocity vs time graph did not have the same numbers for the slope, but did for the constants. The constants were both zero to represent that the initial position,  ??however the slopes were different because they represented different things. The slope of the 2nd graph represents the rate of change of what?  But how did we compare across groups??. An error that I experienced in my experiment was that I did not use a more accurate ticker tape timer. Instead of using a 60 hertz timer, I used a 40 hertz one, thus my data was not as accurate as it could have been. Another source of error was deciding where my starting point would be on the tape since the cart did not go smoothly around the first few seconds. Something that I would like to test in regards to acceleration would be to test the cart going uphill instead of downhill. It would be interesting to see what the position vs time graph and velocity graph would look like when the acceleration vectors of the motion map are in the other direction. good idea

Car Plan and Justification

Material List

• CDs (x4) - Staples/at home
• Wooden block (x1) - Home Depot
• Wooden sticks (x2) - Home Depot
• Mouse/Rat traps (x2) - Home Depot
• Super and/or Hot glue
• String
• Rubber bands

Drawings

Justification Statement

The car that we designed will be propelled using two rat traps and have CDs as wheels. We decided to use rat traps because of the design of the rat traps themselves. The force from the snapping of the traps, we will, shall be enough to get the car over the hill and onto the other side. The CDs will be used as wheels because of their thinness, which will slide with little air resistance, its little inertia rotation. 

Forces: The forces that will act upon our car include the force of gravity, the normal force at an angle (since the initial position is on an angled wooden platform), the force of friction, and the applied force from the rat traps. The force of gravity and the normal force will be the same, but the friction force will be larger than the applied force since the car will not be moving at a constant speed.

Motion: The change in the velocity of the car will occur at the initial starting point. It will begin with a velocity of zero, and then will start to speed up due to the force of the rat traps. Thus, the velocity of the car will be speeding up in a positive direction until it is no longer in motion after going up the platform

Mass/Weight: Mass and weight affects the performance of the car due to impulse and change in momentum. If the car is really heavy, then the change in velocity will decrease. Likewise, if our car is very light, then the change in velocity will increase. We need to be careful when planning how much our car will weigh.

Newton's Laws: During this competition, Newton's 1st Law applies since the car will always remain at rest until it is provoked by the force of the rat traps. And on the other spectrum, it will always remain in motion until another force stops it. Newton's 3rd Law also applies if the two cars collide, for example. The forces exerted by the two will be the same no matter the mass or weight or change in velocity, which is the 3rd Law.

Momentum/Impulses: At the top of the hill, the two cars will most likely hit each other. But more specifically, the forces exerted by the two objects will be the same according to Newton's Third Law. Their impulse will also be the same since the time and the force shall be identical. However, the change in velocity will vary according to the mass of both cars. Whichever car is heavier will sustain more damage to the opposing car.

Energy: From what I've researched, I know that kinetic energy is the energy of motion. For the sake of this competition, I believe that kinetic energy (and velocity) will affect the distance required for the car to stop.