The surface area of the object could affect its velocity because if the surface was large, then more work would be against air resistance, causing its velocity to drop. The mass could also affect it because if its mass was small, it would reach terminal velocity before it had reached the bottom of the runway. In this experiment, the object should not reach its terminal velocity. The runway itself could also affect the velocity. If the surface was not smooth, then there would be lots of work done against friction, which would cause the velocity to drop.
Trial Investigation
In my trial investigation, I tried all three methods of calculating the velocity as the object left the runway. They are:
- Dividing the distance of the runoff by the time taken for the object to go from the beginning of the runoff to the end of the runoff. This method assumes that the object does not accelerate or decelerate when it goes on the runoff.
- Dividing double the distance of the runway by the time for the object to go from the beginning of the runway to the end of the runway. This method assumes that doubling the average velocity will give you the velocity at the end.
- Dividing the distance between the beginning of the first interrupter and the second interrupter by the time shown on the stop clock connected to a light gate. This technically is the most accurate because it does not rely on human reaction time.
The best method will be the one that gives a value closest to the maximum value. This is what I found in my trial investigation.
Table showing the results of my trial investigation
*I could not get the light gate to work as it was not sensitive enough. The car went through it too fast for it to register.
Apparatus
- 2 runways
- A 1 metre ruler
- A marble
- A digital timer
- A clamp stand
- A boss
Diagram
Method
Two runways will be set up. The end of one will be raised 0.065 m and held up by a clamp. Because the run way itself has a thickness of 0.15 m, I will have to add this to the height. The second runway will be connected to the end of the first one – this will be the run off. A marble will be placed at the top and will be released. The time taken for it to travel down the runway will be recorded on a timer. I chose this method because in my trial investigation, this gave me the most accurate value as it was closest to the maximum value. This will be repeated ten times for better accuracy. I chose a marble because it was the heaviest and therefore it will not reach terminal velocity.
After the repeats, this will be done again, increasing the height of the runway by 0.05 m each time, until I reach 0.6 m. I chose a maximum if 0.6 m because in my trial investigation, I found that the higher the runway, the more inaccurate my results became as they were further away from the maximum value. Also, I chose an interval of 0.05 m because then I would get more results and there would be more points on the graph.
Once I have all the times, I will average each set and calculate the velocity. I will do this by doubling the distance of the run way divided by the time.
Fair Test
To ensure a fair test, I will keep the mass and the surface area of the ball the same each time. I will release it from the same spot on the runway each time and use the same run way each time.
Obtaining Evidence – Results
Table showing the results of my investigation
Analysis
Graph
Graph showing the results of my investigation
Conclusion
As the height of the runway increased, the velocity of an object leaving the bottom of the runway also increased. There is not a linear relationship between the height and the velocity; there is a power relationship. As the height increased progressively, the velocity also increased but there was a smaller increase each time.
This is because when the runway was lifted, the marble on it gained gravitational potential energy. The amount of energy gained can be calculated with this formula:
GPE (J) = mass (kg) x gravitational field strength (≈9.81 ms-2 on Earth) x height (m)
When the marble travelled down the runway, its gravitational potential energy was converted into kinetic energy. Because no energy transfer will be 100% efficient, some energy was transferred into sound and heat energy as well. All the kinetic, heat and sound energy at the end added up to the gravitational potential energy at the beginning because of the Law of Conservation of Energy. The Law states that energy cannot be created or destroyed; it is only ever converted from one form to another.
As the marble lost gravitational potential energy, it gained kinetic energy. The amount of energy gained can be calculated with this formula:
KE (J) = 1/2 x mass (kg) x velocity2 (ms-1)
In a perfect physics world, the gravitational potential energy at the beginning will equal the kinetic energy at the end. So increasing the height of the also runway also increased the velocity of the marble.
From my graph, I can see that there is a positive power relationship between the height and the velocity. There is a power relationship because of the √ in the equation.
My prediction was correct. The power trend I predicted came true. Also, my velocities were smaller than the maximum velocities as predicted because we do not live in a perfect world. Work was being done against friction and air resistance so the marble was slowed down. Because of this, the mathematical relationship v=√(19.62h) I predicted did not come true. The coefficient of h turned out to be smaller, around 15.
Graph showing the results of my investigation superimposed onto the graph of the maximum velocities
From the graph above, you can see that my results are smaller than the predicted maximum velocities. This means that the energy transfer is not 100% efficient. The actual efficiency can be calculated by dividing the useful energy output by the total energy input:
The useful energy output at the end is the kinetic energy and the total energy input is the gravitational potential energy at the beginning. So the equation becomes the kinetic energy at the end divided by the gravitational potential energy at the beginning.
The equations for GPE and KE can be substituted into the equation.
The mass can be cancelled out and the gravitational field strength on Earth is ≈9.81 ms-2.
This becomes…
This table and the graph below show the efficiency for each of the heights.
Looking the graph, there seems to be no correlation between the height and efficiency. It fluctuated until it reached a peak efficiency of 82% at 0.3 m and then it carried on fluctuating. However, the efficiency was notably at its lowest at the smallest height. This is because the work done against friction is at its largest since the marble was travelling at its slowest. As the height rose, the work done against friction would have dropped since the marble was travelling faster, so the efficiency rose. After 0.3 m, the work done against air resistance would have risen since the marble is now travelling faster, so the efficiency dropped.
Evaluation
The quality and range of the results are good enough to be sure that the conclusion is correct. My results look accurate because they are all within tenths of a second of each other. My results also look reliable because they are very close to the line of best fit. I have 2 significantly anomalous results: at 0.45m and 0.6m. The reason for these inconsistent results might be because of my reaction time. Also, the higher the runway, the faster the ball will go, so the harder it is harder to see when the ball has left the runway.
The experiment worked and it answered the problem set. However, the marble might have reached terminal velocity as it was not heavy enough when the height has small. Also, human reaction time is never going to be as accurate as the reaction time of a light gate. The runway was not entirely smooth and this could have increased the work done against friction. I could do a number of things to improve the reliability of the data, such as doing the experiment twenty times instead of ten for even more accurate results. I could use a heavier object as it would definitely not reach terminal velocity. I could get a smoother runway to reduce the work done against friction. I could lubricate both the runway and the marble to further reduce the work done against friction. Also, I could get a more sensitive light gate as the ones we were given did not register when the car went too fast. The reaction time of a light gate would be instant whereas human reaction time is extremely slow compared to it.
I could carry out a further experiment to investigate the relationship between the height of a runway and the average velocity of an object leaving the bottom of the runway. I could use a 2 metre runway so it is easier to see when the object has left the runway. Also, I could raise the runway further – up to 2 metres. This would show how the trend would continue and it would prove whether the relationship is actually a power relationship. If it is, then as the height is progressively increased, the velocity would also increase but less each time. I will repeat each height twenty times for extremely accurate results.