Investigating a Rolling Ball
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SPG
Investigating a Rolling Ball
Paul McAdam - 10A
Introduction
The aim of this experiment is to determine whether or not energy is conserved when a ball bearing is rolled down a slope. Six weeks of preliminary work have been carried out ensuring that measurements can be taken quickly with the correct instruments needed for the measurement. Previous knowledge of energy conservation says that energy cannot be created or destroyed.
What factors need to be controlled or varied in this experiment?
In this experiment many factors need to be considered, some need to vary, some need to remain the same. Measurements must also be taken.
There are two independent variables that need to vary, these are :-
. The height of the track.
2. The mass of the ball.
There are three factors that need to remain constant if this is to be a fair test, these are:-
. The starting point of the ball.
2. The starting speed of the ball.
3. The length of the track.
Measurements to take are:-
. The height of the track.
2. The time taken for the ball to roll from the top of the track to the bottom.
3. The speed of the ball.
4. The mass of the ball.
5. The length of the track.
6. Potential energy of the ball at the starting point.
7. Kinetic energy of the ball at the end of the track.
Instruments to use are:-
. A metre rule for lengths.
2. A stopwatch for times.
3. A beam balance for masses.
Length will be measured in metres.
Time will be measured in seconds.
Speed will be measured in metres per second.
GPE and KE will be measured in Joules.
In order to carry out a fair test the same equipment will be used for each measurement, each measurement will be repeated from the same point at least twice. A constant length of track will be used. The effects of friction and sound will be taken into account as ways in which energy is lost. The height of the track will be changed as will the mass of the ball but the starting point and speed of the ball will remain constant.
Prediction
Mass will have no effect on the speed of the ball bearing, if ...
This is a preview of the whole essay
In order to carry out a fair test the same equipment will be used for each measurement, each measurement will be repeated from the same point at least twice. A constant length of track will be used. The effects of friction and sound will be taken into account as ways in which energy is lost. The height of the track will be changed as will the mass of the ball but the starting point and speed of the ball will remain constant.
Prediction
Mass will have no effect on the speed of the ball bearing, if mass increases so will the weight, the weight will act on a larger amount of matter, so the two forces will cancel each other out.
If height increases so to will velocity because as height increases so will GPE, if energy is conserved then this energy will be transferred to kinetic energy giving an increased velocity.
Use scientific understanding to explain the prediction
The formula for GPE is mgh.
The formula for KE is 1/2mv².
Mass is common to both equations so it can be removed.
mgh = 1/2mv²
2gh = v²
20h = v²
Therefore v² is proportional to h.
If h quadruples so does v² therefore v doubles.
ie. 4h and 4v²
To find the value of v:- \/4v² = 2v. Doubled velocity.
What measurements should be taken, and with what?
The mass of the balls will be measured using a beam balance.
The length of the track will be measured with a metre rule.
The height will be measured at ten different heights using a metre rule.
The time taken for the ball to roll from start to finish will be measured ten times at each height using a stopwatch.
Describe the procedure
Diagram 1
. Set up the equipment as shown in diagram 1.
2. Measure the length of the track.
3. Adjust the track to the height to be investigated, measure the height.
4. Measure the mass of the ball.
5. Place the ball on the starting point and release, start the stopwatch.
6. When the ball reaches the end of the track stop the stopwatch.
7. Record the time taken.
8. Repeat steps 4-7 seven times for each height investigated.
9. Discard the highest and lowest times, take the average of the remaining five times.
0. Divide the length by the average time taken to find the speed of the ball.
1. Multiply height by mass of ball by gravity (10) to find GPE.
2. Multiply a half of the mass of ball by speed² to find KE.
3. Subtract KE from GPE in order to find energy lost as heat and sound.
How is the experiment made as accurate as possible?
The experiment is made as accurate as possible by measuring variables to the most accurate unit possible, ie. Length is measured to the nearest thousandth of a metre.
The ball is rolled down the track seven times for each height investigated, the highest and lowest readings for time are discarded and an average of the remaining five times is found.
The ball is released at the same speed and at the same start point in each experiment.
Results
See attached sheets for graph and results tables.
Explain what the results show
The three lines on the graph seem identical within the margins of experimental error so the results show that mass has no effect on the speed of the ball and that as height increases so does velocity, this relationship is proportional as the lines on the graph are straight and pass through the origin.
What trends, patterns or relationships can be found in the results?
As the height of the track quadrupled, the velocity of the ball bearing roughly doubles, and v² roughly quadrupled, this is a direct square correlation.
Explanation of results using scientific knowledge learnt
The results turned out as they did because of basic scientific rules and principles. The more gravitational potential energy (mgh) an object has, the more energy will be converted to kinetic energy (1/2mv²), since mass does not change the mass factors in both equations can both be cancelled out. Therefore, the energy an object has from GPE being converted to KE must have an effect on that object's velocity.
The closer an object is to the vertical, the greater the speed due to acceleration caused by gravity, an object on a slope 40cm high will fall to Earth slower than an object on the same length slope at a height of 80cm.
The prediction for this experiment was correct, mass had no effect on the speed of the ball bearing.
Not all of the GPE was transformed into KE, only about 15% of GPE was used as KE, this means that 85% of the energy was lost as heat due to friction and as sound.
Analysis suggests that v² is proportional to h for this experiment, the results fully support this.
Mass does not continue throughout the analysis.
How accurate are the results and are there any anomalous results?
The graphs are identical for all three ball bearings, within the limits of error, showing mass not to be involved.
Each graph is a straight line through the origin confirming that v² is proportional to h.
Analysis shows that if metres are used the gradient should be close to twenty. If centimetres are used then the gradient should be close to 2000. This however relies on the final speed of the ball bearing being used, this experiment calculated the average speed of the ball bearing. The average speed is half the final speed so v² on the graph is only a 1/4 of its true value. Therefore the gradient should be close to 5m/s² or 500 m/s².
The actual gradient of the graph is 3?m/s².
The anomalous results occurred at the higher heights, the ball travelled down the ramp quickly and human reflexes could not stop the timer at the correct value.
How could the experiment be made more accurate?
To make this experiment as accurate as possible high quality equipment is needed. To eliminate air resistance the experiment would need to be carried out in a total vacuum. To reduce friction on the slope and on the ball, glass or polished metal should replace the plastic slope and the ball bearing.
To make measurements of time more accurate, computers could be used to release the ball and light gates used to give accurate timings of the ball rolling down the track. The final speed of the ball should be found instead of the average speed. Large micrometers could be used to measure lengths and highly accurate digital balances used to measure mass. This would eliminate human delays due to slow reflexes.
