Fairness of test
To ensure the test is fair, I shall record the results of each variable three times, and find the mean, I will also ignore any anomalous results when finding the mean. Moreover, the variables which must remain the same, such as height of ramp etc., shall be as accurate as possible. Finally human error may force the distance travelled and starting speed to vary slightly, as the trolley has to be release by hand, and there for human error may cause anomalies via the start. The only way I can keep this as fair as possible is by releasing the trolleys as carefully as possible, and by finding an average, it should stop the results from becoming too inaccurate.
All results shall be recorded to at least three decimal places when possible, to make results more accurate
This is an image of the experiment assembled (photo taken by Katie Fitzgerald)
Experiment 1
The results from the first experiment are shown below:
Using my recorded data I need to find a viable formula for acceleration;
Final velocity^2 = initial velocity ^2 + 2 x acceleration x distance
Final velocity^2- initial velocity ^2 = 2 x acceleration x distance
(Final velocity ^2 – initial velocity ^2/distance) /2 = acceleration
The corresponding results are shown in the table with the rest of the data:
The Angles in my data were worked out by using Pythagoras theorem, as there was a 90° angle, and three known and measured sides.
The results suggest that as the angle and heights increase correspondently, the final velocity and acceleration increase also. Moreover, when the height decreased to below 1.5 cm the effects of friction were too great for the trolley to continue movement, and stopped before it reached the light gate.
Using the results from my experiment, I have used an add on off Microsoft excel to continue the same average increase through all of the rows, all the way up to 90° (up to 90 is shown in a table below). The acceleration reaches about 9.4; this suggests that my target velocity for g should be around 9.4, perhaps slightly above, as there would be only air resistance at 90°, as no track would be necessary, and therefore, much lower friction.
Knowing that at 90° the size of g should be around 9.4, I can now use my primary data and use equations to try and figure out a more accurate answer which I can compare to each angle.
Working out G for each angle
Using the tables I can conclude I have the following data:
u = initial velocity
v = final velocity
a = acceleration
m = mass of trolley
Ѳ = angle of the slope
s = length of the slope.
Equations I know:
Component of weight acting on the trolley =mg sin Ѳ
Equation of Motion: v^2 = u^2 + 2 a s
And acceleration=g
And u=0
Therefore: v^2 = 2 (g sin Ѳ) s
final equation: g = v^2 / (2 * sinѲ * s)
Using the Equation I have worked out, I shall work out g for the tables shown previously.
The reason for the graph showing g to be curved may be due to friction, and that is the reason for my estimate of g to be 9.4 and not 9.8, if friction is taken into account then I believe my estimate may be closer to the true value.
Friction=mass of trolley (N) cos Ѳ = 0
Height of point of release before trolley moves is 4mm
Sin^-1 = 0.229183729= Ѳ
0.7cos Ѳ=0.69478 N
Flim = µR
µ= 0.1
New g equation including friction=
g = 0.8881^2/[(sin(9.2000)) – (0.1 x cos (9.2000))]
=12.9118715
This result is much over my estimate, but perhaps it was less than 4mm to more the trolley and this error is due to human error.
Conclusion:
In conclusion, using my results from the first experiment, I can conclude that as Ѳ increases, the value of acceleration and the value of g will increase until Ѳ = 90, at this point, the object is falling directly to gravity, and g should be a value >9.4.
Experiment 2
Momentum = mass x velocity
Looking at the results from the tables, it is apparent that as the mass of the trolley is increased, it naturally increases in acceleration; this may be due to as the object increases in mass, its momentum also increases, and therefore the effects of friction will reduce respectively to how much more momentum the trolley has. As a higher momentum mean larger friction is required in order to stop.
By comparing both graphs above, it is apparent that acceleration and mass increase momentum accordingly
Furthermore, by comparing the table on the right, it is apparent that as mass has increased, it has also allowed the final velocity to increase suggesting the increase in mass also increases speed of the trolley, this may be due to friction having less of an effect on the trolley, as the momentum is effected less by the friction
Experiment 2 conclusion:
In conclusion the increase in mass, gave the trolley more momentum, and as a result meant friction had less of an effect on the trolley, furthermore this allowed the trolley to increase in acceleration as more weight was added.
Evaluation
If I was to repeat the experiment again, and re-asses the results there are several things I would change:
Instead of releasing the trolley by hand I would find another method of releasing it to guarantee it starts from the same point and starts with zero velocity, potentially use electromagnets to hold it at the same spot and then the trolley can be released with the push of a button.
I would also use more precise measurements, for example, I would measure the height of the ramp to the nearest half a mm rather than to the nearest cm, as it would give me more precise results.
I would similarly figure out a more effective method for finding the true value for g when including friction, as my friction estimates seem to be much too high.
Finally, I am pleased with my overall results, some estimates, and answers are slightly wrong,, but I believe those are purely down to human error.
Websites used for mechanical equations:
