The Effect on Time as a Result in Changing Mass
By Cameron Yee and Jordan Doane
Background Info | Statement of Problem | Hypothesis | Materials/Method | Data Collection | Data Analysis | Evaluation | Bibliography | Related Sites
For our investigation, we wanted to find the relationship between the weight of a car (in this case a 1992 Toyota pickup) and the amount of time it takes that car to go a set distance when the acceleration is constant for each trial. Our basis for this experiment came from our knowledge that in order for a car to operate, the engine must apply force to the wheels which in turn applies force on the road and allows the car to move forward. We also know that there are many factors which can increase or decrease the amount of time that it takes for the car to move a distance. Air friction, the friction of the tires on the road and other factors all contribute to this. However, one of the most important is the mass of the car itself. Newton’s second law states, Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimatur (The change of momentum of a body is proportional to the impulse impressed on the body, and happens along the straight line on which that impulse is impressed).
What this means is as the mass of the car increases, in theory, it will take longer for a car to accelerate to a certain level and therefore increase the amount of time it takes for a car to go a specific distance.
We hypothesized that each time more weight is added to a car, the time it takes for that car to go a set distance will drastically increase.
To begin testing our hypothesis, we first needed to find a car that we could use in our experiments. We ended up using Cameron’s 1992 Toyota pick up because, unlike more modern vehicles, this one lacked an internal computer that would balance out the weight which would give us inaccurate results. Next, we measured out 100 yards (91 meters) along a road, marking where the truck would begin and end. The truck was then lined up with the starting line and a block of wood was placed under the gas pedal, ensuring that the acceleration would remain constant throughout the experiment. We would have the timer at the starting line announce the start of the timing. As the car would reach the finish line, Jordan will drop his arm to signal to stop the timing. For the timers that we will use are stopwatches on cell phones.
Our first trial was the control; the total mass only consisted of the weight of the car (5350lbs/2431kg) and the weight of the driver (180lbs/81kg). The truck was driven the set distance and was timed by three separate timers who only stopped timing after the front wheels crossed the end line. After this trial, the truck was driven back to the starting line and loaded with 100lbs (45kg) of sand before the next trial began. We repeated this process for each trial, loading bags of sand in increments of 100lbs (45kg) until we reached 500lbs (227kg). After we had finished every trial, we took all of our data points and averaged them. With the averaged data and the original data we were able to create a graph that looks like this:
We designed the experiment this way because it was very similar to drag racers. By having a person signal both the drivers and the far timers, we were able to get multiple perspectives on the time. The way we added the weight was predetermined as it was described in the experiment details.
Our first set of data is of the different trials that we performed. We had three different people timing and then we took the average of the times for each trial and from there we were able to come up with an equation for the average time of the car. The equation itself was a power function that showed that the time the car took to go the length of the course appeared to not change as much as the weight increased. This leads us to believe that the more weight that you add does slow you down to a certain point, but after this point, then the effect is minimized. The second set of data is a comparison between a model equation that we derived and the actual times that we got as a result of the experiment. The equation that was derived was √(2s(mc + ma))/F. By finding a force that would set the first data points equal, then we would be able to compare the graphs themselves. As the graph shows, the weight added had a greater impact than the model predicted. This is despite the fact that the car we used was a truck that had rear-wheel drive and when some weight is added, the car generally performs better.
In our hypothesis we stated that we thought that the addition of more weight would drastically change the speed of the car. While it did change the times, they were not as drastic as we had originally envisioned. The possible error that could have occurred was that we went by sight on the timing and there was no way to guarantee that all of the stopwatches stared and stopped at the same time. Also, the car is pickup that had very little weight in it to begin with. Combined with the fact that the car is real wheel drive, the additional weight most likely helped the car perform better, at least to a certain extent. A more accurate hypothesis would be that if weight is added to a car, then the car will accelerate slower to a certain extent because of the additional weight but the addition of weight will eventually become negligible. To further test this hypothesis, we would need to test a car that is still non-computerized, as the computer compensates for the weight, and has an even weight and mass distribution. We would also need to test it with higher weights to get a more accurate picture of how the weight of the car affects the acceleration and time.
"Data Packet (Formulas)." TuHS Physics. Tualatin High School. 3 Jan. 2009 <http://tuhsphysics.ttsd.k12.or.us/Tutorial/NewIBPS/Data_Packet_03.htm>
Benson, Tom. "Newton’s Law of Motion." NASA Glenn Research Center. 15 June 2007. N.A.S.A. 8 Jan. 2008
<http://www.grc.nasa.gov/WWW/K-12/airplane/newton.html>.
Bernard Cohen and Anne Whitman, translators: Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy. Preceded by A Guide to
Newton's Principia, by I.Bernard Cohen. University of California Press 1999
Newton's Laws of Motion - A basic description of Newton's three Laws of Motion
Ratio of Thrust to Weight - A similar experiment using a plane instead of a car
Applying Newton's Second Law - Several related experiments that demonstrate Newton's Second Law
Basic Properties of Acceleration - Overview of acceleration and how different scientists came up with the theory of acceleration
Forces Acting Upon the Car - Details on the forces acting on the car (thrust, friction, etc.)