v0 = ∆d / ∆t
The releasing of the crate was one difficulty encountered whilst conducting this experiment. Each round the crate was released to motion with the help of rubber bands. By attaching two rubber bands to the end of the track the releaser for the crate was set up. Pulling the crate with varying extensions with the band would result in differing initial velocities. No specific way was ensured to give out specific forces on the crate. The only way was to repeatedly release the crate with varying extensions of the elastic band. Thus it was problematic to control the initial velocity.
Quick Steps
- Set up track under light gate
- Release crate by extending the rubber bands behind the crate
- Observe the distance travelled by crate with the use or ruler
- Repeat releasing with varying extensions
1.4 Variables
The variables are as follows. The dependent variable was chosen to be the distance traveled by the cart, meaning it’s braking distance. Whilst the independent variable was the initial velocity obtained by the cart. There were two controlled variables within this experiment, which are as follows: frictional force of the track surface and mass of the metal crate itself.
3. RESULTS
The final results of the experiment conducted followed the original hypothesis to a certain degree.
3.1 Raw Data
The raw data gathered is demonstrated below.
Table 1.1
Table 1.1 demonstrates the very first data received from the light gates and the measuring ruler. The data has not yet been converted to necessary units.
Table 1.2
Table 1.2 on the other hand shows the previous data from table 1.1 only in the correct units for further calculations for processed data. The error chosen for the time was a systematic error of ±0,0005 s. The error for the measuring ruler was a reading error of ±0,05 m.
3.2 Processed Data
The width of the cardboard flag was 5.2 cm. In the calculations this must however be converted to 0.052 m for the right calculations to be made. When counting the initial velocity the distance of the cardboard flag is divided by the time it takes for the flag to pass the photocell.
Table 2.1
Graph 2.1.1
The data provided by the graph can be seen to show a linear graph. With two anomalies within the set of values, which are inconsistent and can be ignored.
4. CONCLUSION
In conclusion it can be asserted that there is a dependency between the initial velocity of a moving object and the braking distance then travelled by it. Obviously there are multiple factors affecting the braking distance of a moving object. Very important factor is the frictional force between the track and wheels of the crate. It has become clear that even slight increase in speed greatly increases braking distances.
4.1 Support of Hypothesis
As the hypothesis was that there is a dependency between the initial velocity and the braking distance a graph of velocity squared is plotted against the braking distance. The graph data is distributed in a fairly linear way. Thus it can be said that the graph 2.1.1 is evidence of the hypothesis that the velocity squared is in direct proportion to the braking distance of the crate.
4.2 Explanation
There are two issues, which are to be mentioned concerning the data in graph 2.1.1. Two value seem to be inconsistent with the rest of the data. These values are marked on the graph having a the values for v2 0.2910 and 0.5524. These values obviously had some critical errors to them thus they should will be excluded from the range of compatible values. The values on the graph do not begin from 0 on both axes but with the appropriate values. If the lowest uncertainties were taken into account a line passing through zero would be possibly visible. The line of best fit does pass through most of the error bars on each value.
5. EVALUATION
The experiment was not flawless and certainly needs a few improvements to further enhance the strength of the hypothesis.
5.1 Problems
The main problem faced during the conduction of the experiment was the launching of the crate into motion. At first it was relatively hard to come up with apparatus that could launch the crate into motion in a controlled manner. Thus in the end I had to resort to the use of rubber bands with which it was hard to control the velocity of the crate. Estimations had to made of the ranging launchings of the crate. There was a problem with the track being used. Since the tracks were not long enough to reach 1 meter I had to attach two tracks to each other. Causing a slight gap in the track system. This gap distinctly slowed down the motion of the crate. Affecting the initial braking distance the crate was supposed to travel. There were limited values for slow initial velocities. These are related to the previous problem in releasing the crate into motion.
5.2 Further Developments
The initial problem of launching the crate should have been solved with special apparatus. Some sort of spring that could launch the crate into motion. A spring which when compressed and then released would launch the crate into motion. Thus it would have been possible to systematically compress and release in ranging lengths. To remove the additional braking of the motion on the crate a singular 1 meter long track should have been in use. For more realistc results the wheels could have included tyres. Thus the information gathered could be applied to vehicles. The frictional force between tires and the roadway are highly variable. The friction depends on the tire pressure and tire composition.
