Mass-Acceleration Experiment:
Hypothesis:

In this series of experiments we tried to determine the relationship between the mass of an object and its acceleration. Based on Newton’s second law of motion we know that F=m*a, where F is the force exerted on an object, a is its acceleration and m is its mass.  From this equivalence we know that a=F/m, which means that mass and acceleration are inversely proportional. Thus, our hypothesis is that the more the mass increases the less the acceleration of the object will be.

Procedure:

In this experiments, we tied a mass to a string that was pulled up by a motor. By using the NXT program we kept the power of the motor constant and changed the mass of the object every time. The results for the power, speed, time and acceleration were produced by the NXT program.

Data:

 

In the table above the colored columns signify the important variables in our experiment. In this case, the speed and time of the object are used to determine the acceleration, which is denoted in the red column entitled(surprisingly) acceleration.

Data Analysis:

Our hypothesis in the beginning was that mass and acceleration are inversely proportional and our table seems to verify our hypothesis. As we can see the acceleration of the object decreases as its mass increases. Also, the graph below seems to reinforce our hypothesis.

Conclusion:

Our hypothesis stated that the two variables were inversely proportional to each other, which was verified by our results (look at Table 1 and Graph 1). However, the relationship between the two variables was of the form y=m/x, which is does not produce a linear function between y and x. Even though, that seems to be the result for our graph that is not the case, due to the fact that the change of the acceleration is not constant. In the beginning the change is 39.1-35.24= 3.8, then it becomes 44.3-39.1=5.2 and then 50.02-44.3=5.72. Since, the difference between its acceleration is not constant the gradient of the graph is not constant either, which means the graph cannot be linear. The fact that it appears linear though is an indication of the fact that we needed to carry out more experiments to fully confirm our hypothesis.

 

Acceleration-Power Experiment:

Hypothesis:

In this series of experiments we wanted to determine the relationship between the power exerted on an object and the acceleration of that object. Based on Newton’s Second Law of Motion we know that F=m*a. Also, we know that power is P=F*Δx/Δt where P is power, F is force, Δx is the displacement of an object and Δt is the difference in time. Since the Power is directly proportional to the force, we expect it to be directional proportional to anything the force is proportional to. Therefore, our hypothesis is that Power and acceleration are directly proportional and their relationship is linear.

Procedure:

This series of experiments had an identical setup to the previous one, with just one difference. This time, the mass of the object was kept constant and the power exerted on it was changed with the NXT program.

Data:

In the table above we can see the acceleration in the red column and the Power percentage used by the NXT motor.

Data Analysis:

From the table we can see that as the power of the motor pulling up the object increases, so does the acceleration of the object. The relationship between the two seems to be directly proportional and probably linear. We can also create a graph for the above data to visualize the relationship between the two variables.

Knowing that the relationship of the two variables is linear, we can determine the gradient of the line which is equal to m=Δy/Δx= (89.98-10.3)/(100-50)=1.59. This gradient should give us the value of Δx*m/Δt, since P=a* Δx*m/Δt.

 

Conclusion:
Our hypothesis stated that the power exerted on an object would be directly proportional to the acceleration of the object and thus produce a linear function. As we can see from our results the acceleration of an object is definitely directly proportional to the power applied to it. This was verified by the results of table 2 and Graph 2. Even though, the graph we produced did not produce a perfectly linear line, we can attribute that to some errors that took place in our experiment. The first and foremost error was that we had to manually stop the object’s ascend, which means we manually affected the estimated time (through which the acceleration was calculated). Therefore, our natural human error(please don’t kill us for it) affected the acceleration itself and prevented us from obtaining a linear graph. Also, we know that our results were random due to the fact that the difference in the acceleration does not follow any sort of pattern, rather it seems to change randomly(unlike in the mass-acceleration experiments. Ultimately, we can assume that our hypothesis was verified as our results were quite close to what they should have been in reality.

Power Percentage-Power Output

Hypothesis:

In these calculations we were trying to determine the relationship between the power percentage levels of the motor and the final power output. Since, all other variables remained the same we expected these two variables to be directly proportional and in some way the same quantity(apparently they are both called POWER).

Data:

Data Analysis:

The above table shows the results of the two variables and illustrates their relationship. As we can see, the two variables appear directly proportional and their graph(below) seems to verify this point. Also, since the relationship between the two variables is linear we can find the gradient for function, which is m=Δy/Δx= (0.34-0.12)/(100-50)=0.0044.

Conclusion:

In the beginning we hypothesized that the power levels and the power output would be directly proportional to each other and produce a linear function. Our data seems to have verified our hypothesis, since the results indicate proportionality and the graph produced is a linear one with a positive slope.

Discharge-Mass:

Hypothesis:

In this experiment we were trying to determine the relationship of the battery discharge and the mass, when the power is kept constant. Since, the battery discharge is the energy spent, we expected it to be directly proportional to the mass of the object. The energy equation for kinetic energy is E=1/2*m*v*v, so the energy and the mass are directly proportional, and the more the mass the more energy will be spent by the battery.

Data:

Data Analysis:

The results above produce the following graph.

Conclusion:

Our hypothesis in the beginning was that Energy(discharge) would be directly proportional to mass. However, our results are not in agreement with our hypothesis. In fact, our results do not seems to indicate any sort of relationship between the two, which means that they were either they were seriously inaccurate or physics is entirely wrong. Due to the fact, that the latter case seems too improbable (not impossible though), we can conclude that our results for this experiment were wrong and produced nothing less than nonsense.