Hot+Wheelz

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The goal for this lab is to find the work done by the Hot Wheelz cars engine. We measured time with photo gates to find the velocity for the car with and without the car’s engine. We used both engines off and on to find the work done by the friction and the total work done which we were able to calculate the amount of work done on the engine, .0392J. =====

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For this lab, energy equations were the majority. The first part of the lab deals with velocity and friction for the track; how the track causes the car to slow down or speed up accordingly. As the car moves down the ramp, the force of gravity will accelerate the car. At the top of the ramp the car has potential energy. The car only has kinetic energy at the end, but there is also a nonconservative force, friction. Then use this knowledge to compare how the effect is seen through the changes in velocity and the force of friction. =====

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The second part of the lab is similar to the first part but deals not with the car itself but the car’s engine. Ultimately, to find the effect of the track on the amount of force the engine produces. Again the car has PE initial, KE final and Wnc. The Wnc part of the equation are two different forces; friction and thermal energy. As the car goes along the track, the car will convert the some of the stored energy in the motor in to thermal energy. The friction of the track will also cause a loss in energy. The loss in energy due to friction is accounted for in the first part of the experiment. The energy lost will be in the form of thermal energy. Knowing how much energy is lost we can then find the amount of work done by the cars engin e. =====

** Methods: **


__materials__:Photogate timers, bricks, a hot wheels car, hot wheels tracks, a car charger, a protractors, a meter stick, and a string
 * As shown in the photo above, the track consists of an incline of 45 degrees to the horizontal. The angle then flattens out to a straight track. To collect the data needed we placed photo gates at the start and end of the track. In order for the photo gates to accurately and consistently read the car as it passes through, tape a flag on the top. The flag is 3.5 cm wide. As the flag passes through the gate, the gate measures how many second the flag took to pass through. Then use the time and the width of the flag to calculate the cars velocity. ** T he first part consisted of 3 trails with the engine off were the car was simply set the car at the top of the ramp and released down the ramp. The second part consisted again of 3 trails but this time the car was first charged for 5 seconds (to the count of 5 slowly) and then put down the ramp. After each run the time displayed on the photo gates is recorded and reset for the next trial.


 * Results: **

__measuement__: Theta: 45 degrees Car Mass: 37g -> .037kg Inital Height of Ramp: 22cm -> .22m Distance of the track: 69cm -> .69m Flag length: 3.5cm -> .035m

__Data__:
 * **Engine off ** |||| **Trial 1 ** |||| **Trial 2 ** |||| **Trial 3 ** ||
 * ^  || Time (sec) || Velocity (m/s) || Time (sec) || Velocity (m/s) || Time (sec) || Velocity (m/s) ||
 * __Top __ || .0698 || .501 || .0708 || .494 || <span style="display: block; font-family: 'Times New Roman',serif; font-size: 12pt; line-height: 115%; margin: 0in 0in 10pt; text-align: center;">.0668 || <span style="display: block; font-family: 'Times New Roman',serif; font-size: 12pt; line-height: 115%; margin: 0in 0in 10pt; text-align: center;">.524 ||
 * __<span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;">Bottom __ || <span style="color: black; display: block; font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 0pt; text-align: center;">.0384 || <span style="color: black; display: block; font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 0pt; text-align: center;">.921 || <span style="color: black; display: block; font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 0pt; text-align: center;">.0398 || <span style="color: black; display: block; font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 0pt; text-align: center;">.879 || <span style="display: block; font-family: 'Times New Roman',serif; font-size: 12pt; line-height: normal; margin: 0in 0in 0pt; text-align: center;">.0351 || <span style="display: block; font-family: 'Times New Roman',serif; font-size: 12pt; line-height: normal; margin: 0in 0in 0pt; text-align: center;">.997 ||


 * **<span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;">Engine on ** |||| **<span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;">Trial 1 ** |||| **<span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;">Trial 2 ** |||| **<span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;">Trial 3 ** ||
 * ^  || <span style="color: black; display: block; font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 0pt; text-align: center;">Time (sec) || <span style="color: black; display: block; font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 0pt; text-align: center;">Velocity (m/s) || <span style="color: black; display: block; font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 0pt; text-align: center;">Time (sec) || <span style="color: black; display: block; font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 0pt; text-align: center;">Velocity (m/s) || <span style="color: black; display: block; font-family: 'Times New Roman',serif; font-size: 12pt; line-height: normal; margin: 0in 0in 0pt; text-align: center;">Time (sec) || <span style="color: black; display: block; font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 0pt; text-align: center;">Velocity (m/s) ||
 * __<span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;">Top __ || <span style="color: black; display: block; font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 0pt; text-align: center;">.0488 || <span style="color: black; display: block; font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 0pt; text-align: center;">.717 || <span style="color: black; display: block; font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 0pt; text-align: center;">.0448 || <span style="color: black; display: block; font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 0pt; text-align: center;">.786 || <span style="display: block; font-family: 'Times New Roman',serif; font-size: 12pt; line-height: normal; margin: 0in 0in 0pt; text-align: center;">.0381 || <span style="display: block; font-family: 'Times New Roman',serif; font-size: 12pt; line-height: normal; margin: 0in 0in 0pt; text-align: center;">.919 ||
 * __<span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;">Bottom __ || <span style="color: black; display: block; font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 0pt; text-align: center;">.0196 || <span style="color: black; display: block; font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 0pt; text-align: center;">1.781 || <span style="color: black; display: block; font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 0pt; text-align: center;">.0184 || <span style="color: black; display: block; font-family: 'Times New Roman',serif; font-size: 12pt; margin: 0in 0in 0pt; text-align: center;">1.902 || <span style="display: block; font-family: 'Times New Roman',serif; font-size: 12pt; line-height: normal; margin: 0in 0in 0pt; text-align: center;">.019 || <span style="display: block; font-family: 'Times New Roman',serif; font-size: 12pt; line-height: normal; margin: 0in 0in 0pt; text-align: center;">1.842 ||

<span style="font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 115%; margin: 0in 0in 10pt;">__Data Analysis__: <span style="display: block; font-family: 'Times New Roman',serif; font-size: 12pt; line-height: normal; margin: 0in 0in 0pt; text-align: center;">=.0844J <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">TME <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">f <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">= (1/2)(.037)(.921) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 12pt;"> 2 <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> + 0 <span style="display: block; font-family: 'Times New Roman',serif; font-size: 12pt; line-height: normal; margin: 0in 0in 0pt; text-align: center;">=.0157J
 * **<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Calculation ** || **<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Engine off ** || **<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Engine on ** ||
 * __<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Trial 1 __ || <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">TME <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">i <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> = (1/2)(.037)(.501) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 12pt;">2 <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> + (.037)(9.8)(.22)

<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">TME <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">f <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">- TME <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">i <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> =W <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">friction <span style="display: block; font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: normal; margin: 0in 0in 0pt; text-align: center;">= -.0687J || <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">TME <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">i <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> = (1/2)(.037)(.717) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 12pt;">2 <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> +(.037)(9.8)(.22) <span style="display: block; font-family: 'Times New Roman',serif; font-size: 12pt; line-height: normal; margin: 0in 0in 0pt; text-align: center;">=.0893J <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">TME <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">f <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">= (1/2)(.037)(1.781) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 12pt;">2 <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">+ 0 <span style="display: block; font-family: 'Times New Roman',serif; font-size: 12pt; line-height: normal; margin: 0in 0in 0pt; text-align: center;">=.0587J

<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">TME <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">f <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">- TME <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">i <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> =W <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">total <span style="display: block; font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: normal; margin: 0in 0in 0pt; text-align: center;">= -.0306J ||
 * ^  |||| <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">W <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">friction <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> + W <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">engine <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> = W <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">total

<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">-.0687 + W <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">engine <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">= -.0306 <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">W <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">engine <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">= .0381J || <span style="display: block; font-family: 'Times New Roman',serif; font-size: 12pt; line-height: normal; margin: 0in 0in 0pt; text-align: center;">=.0843J <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">TME <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">f <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">= (1/2)(.037)(.879) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 12pt;">2 <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> + 0 <span style="display: block; font-family: 'Times New Roman',serif; font-size: 12pt; line-height: normal; margin: 0in 0in 0pt; text-align: center;">=.0143J
 * __<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Trial 2 __ || <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">TME <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">i <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> = (1/2)(.037)(.494) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 12pt;">2 <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> + (.037)(9.8)(.22)

<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">TME <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">f <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">- TME <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">i <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> =W <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">friction <span style="display: block; font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: normal; margin: 0in 0in 0pt; text-align: center;">= -.0700J || <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">TME <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">i <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> = (1/2)(.786)(.501) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 12pt;">2 <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> + (.037)(9.8)(.22) <span style="display: block; font-family: 'Times New Roman',serif; font-size: 12pt; line-height: normal; margin: 0in 0in 0pt; text-align: center;">=.0912J <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">TME <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">f <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">= (1/2)(.037)(1.902) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 12pt;">2 <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> + 0 <span style="display: block; font-family: 'Times New Roman',serif; font-size: 12pt; line-height: normal; margin: 0in 0in 0pt; text-align: center;">=.0670J

<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">TME <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">f <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">- TME <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">i <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> = W <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">total <span style="display: block; font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: normal; margin: 0in 0in 0pt; text-align: center;">= -.0243J || <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">-.0700+ W <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">engine <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">=-.0243 <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">W <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">engine <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">= .0457J || <span style="display: block; font-family: 'Times New Roman',serif; font-size: 12pt; line-height: normal; margin: 0in 0in 0pt; text-align: center;">=.0849J <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">TME <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">f <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">= (1/2)(.037)(.997) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 12pt;">2 <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> + 0 <span style="display: block; font-family: 'Times New Roman',serif; font-size: 12pt; line-height: normal; margin: 0in 0in 0pt; text-align: center;">=.0184J
 * ^  |||| <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">W <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">friction <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> + W <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">engine <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> = W <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">total
 * __<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Trial 3 __ || <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">TME <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">i <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> = (1/2)(.037)(.542) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 12pt;">2 <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> + (.037)(9.8)(.22)

<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">TME <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">f <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">- TME <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">i <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">=W <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">friction <span style="display: block; font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: normal; margin: 0in 0in 0pt; text-align: center;">= -.0665J || <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">TME <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">i <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> = (1/2)(.037)(.919) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 12pt;">2 <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> + (.037)(9.8)(.22) <span style="display: block; font-family: 'Times New Roman',serif; font-size: 12pt; line-height: normal; margin: 0in 0in 0pt; text-align: center;">=.0954J <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">TME <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">f <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">= (1/2)(.037)(1.842) <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 12pt;">2 <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> + 0 <span style="display: block; font-family: 'Times New Roman',serif; font-size: 12pt; line-height: normal; margin: 0in 0in 0pt; text-align: center;">=.0628J

<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">TME <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">f <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">- TME <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">i <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> = W <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">total <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">= -.0326J || <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">-.0665+ W <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">engine <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> = -.0326 <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">W <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">engine <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> = .0338J ||
 * ^  |||| <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">W <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">friction <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> + W <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">engine <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> = W <span style="font-family: 'Times New Roman','serif'; font-size: 8pt;">total

=
First of all, in order to find both total mechanical energy of initial and final, we calculated the velocity for both top and bottom dividing the length of flag by the time that we collect with the photo gate timers for all three trials with an engine off and engine on. Then using the equation TME = PE + KE, we found the work that was done at the top and the bottom of the track. Although the calculations for both engines off and on are the same, calculating purpose was a little different. When the TME of initial and final for engine off were found, the subtraction from the final to the initial gives the work that was done by the friction. However, for the engine on, the subtraction from the final to the initial gives the total work that was done by both friction and engine. Now, we knew the work of friction and work of total, we simply solved for the work that was done by the engine from this set of equation: Wfriction + Wengine = Wtotal. Fortunately, each trial for both engines off and on was very close to each other except the second trial for engine on was a little bit off than the other trials due to the human error. Finally, we calculated the average work of engine that we found for all three trials for the best answer to our goal.=====

** Conclusion: **
After extensive calculation, the average work done by the engine is .0392J. This lab demanded a vast knowledge about work and energy as well as some basic knowledge about friction and velocity. When playing with Hot Wheelz cars the forces acting upon the car is not typical thought about. But as the little car makes its way down the ramp it has friction pulling it back, gravity pulling it down and sometimes an engine pushing the car long. As the car runs the course the amount of power put out by the engine decreases due to time as well as the demand of the track on the engine. This power at first appears to magically disappear but what most 7-year-old boys don't know is that the energy that disappears from the car turns into heat or thermal energy. The amount of thermal energy produced is so small that the heat is not noticed. .0392J is that average amount of work done by the engine throughout the course. At the start of the track the car's engine has more power and therefore puts out more energy. But as the energy is burned the car slowly puts out less and less energy until the engine completely stops. So while the work done at the start is much larger then at the end, .0392J is still an accurate measurement for the amount of work done by the car’s engine.