Investigating The Effect Of Distance Between Dominoes And Time Taken To Fall
Zachary Bishop
The effect of distance between dominoes and time taken to fall
Introduction
By collecting data whilst keeping all variables constant apart from the independent and dependent variables of an experiment, it is possible to determine a relationship between them. One relationship that can be observed in a laboratory is the relationship between the distance (denoted by symbol d) of separation of dominoes in a domino chain and the time taken (denoted by symbol t) for all dominoes to fall over.
It is expected that greater distances of separation will result in greater time taken for all dominoes to fall over. This is due to the fact that when they are separated by greater distances, the dominoes will have to cover more distance (and …show more content…
consequently fall for a longer period of time) before they hit the subsequent dominoes.
In this practical, dominoes will be allowed to fall over (after being supplied a very small force [outlined in Variables and Method section]) with various distances of separation. The time taken for each value of d will be observed and recorded. Once these data have been obtained, the relationship between d and t will be determined through the use of Microsoft Excel.
Research question (aim)
Given that the dimensions, mass and arrangement of the dominoes are kept constant in addition to the initial force applied to the first domino in the domino chain, what is the relationship (e.g.
d∝t,d∝1/t,d∝√t,d∝t^2) between the distance (d) of the separation between each domino and the time taken (t) for all of the dominoes to fall over?
Variables
Independent variable: The distance between each domino. This will be changed by moving the dominoes. The distance will be measured using a 30cm ruler. The distances being used in this experiment: 0.5cm, 1.0cm, 1.5cm, 2.0cm, 2.5cm, 3.0cm.
Distances greater than 3.0cm are not used as the dominoes would fall over without making contact with each other if the distance between them is greater than 3.0cm. Likewise, a distance of 0.0cm is not used as the ‘domino effect’ would not occur since the force applied to the subsequent dominoes as a result of the ‘gentle push’ (outlined in the Variables and Method sections) applied to the first domino would not be great enough.
Dependent variable: The time taken for all 40 dominoes to fall over. This will be measured through the use of a stopwatch.
Controlled …show more content…
variables:
Variable Significance of controlling Method of controlling
Experimental surface The surface that the dominoes are placed on must be kept constant as the material of the surface they are placed on will have varying friction, which will slightly influence falling times of the dominoes.
Furthermore, the surface must be uniform (i.e. flat). If it is not, then for each trial, dominoes will be inclined at different angles (e.g. some will be leaning over a bit more than others, this will cause their falling times to be slightly lower). Overall, if the surface is not kept constant, then random error will result. All trials will be done on the same surface (a bench in the
laboratory).
Force applied to first domino If the force being applied to the first domino is not kept constant, there will be random error. This is due to the fact that if the first domino is pushed with a greater force, then it will fall over faster, thereby decreasing the time taken for all 40 dominoes to fall over. If a large force is only applied to some of the trials, then there will be imprecision of the data.
The aim of the experiment is to observe the effect of only changing the distance between dominoes, thus this variable must be kept constant. This variable is slightly difficult to manage, but it will be kept as constant as possible by starting each ‘domino effect’ by carefully and gently pushing the first domino until it just begins to fall over.
Properties of the dominoes The properties of the dominoes, namely their dimensions (length, width, height) and their masses should be kept constant as they are likely to have an effect on the falling time of the dominoes. Variation in these properties should result in random error. For instance, a more massive domino should apply a greater force to the subsequent domino (due to the relationship: force = mass × acceleration due to gravity, [F=mg]). If very massive dominoes are used in one trial but not another, then there will be an imprecision in the data as the mass of the dominoes will be affecting the falling times in addition to the change in distance. The same dominoes will be used for all trials.
Pattern of placement of dominoes
(does not include distance between dominoes) The pattern of placement (e.g. in a straight line, in a spiral pattern) of the dominoes must be kept constant as different arrangements of the dominoes should affect the time taken for the dominoes to fall over. For instance, if dominoes are falling onto each other at 45o angles in one trial but at 0o angles (i.e. in a perfectly straight line) in another trial, the dominoes in the straight line will fall over more quickly. This is because in the trial with the straight line arrangement, all of the force being applied to subsequent dominoes is acting in the same direction that the subsequent dominoes are facing. This means that they will fall over more quickly. Conversely, in the trial where the dominoes are arranged at 45o angles to each other, the force imparted on subsequent dominoes is only partially acting upon the direction that the subsequent dominoes are facing. This is a source of random error if it is not kept constant. For each trial, the dominoes will be arranged in a straight line. This will be managed by placing two one metre rulers alongside the dominoes as they are being set up (the rulers will act as a guide for laying out the dominoes in a straight line)
Start and end points of experiment The start and end points of each trial should be clearly defined and kept constant for each trial. If the stopwatch is started and stopped at different points in time for different trials, then there will be imprecision in the data. This change in time taken will not only be due to the change in distance between dominoes.
For instance, if in one trial the experiment was deemed to be finished when the final domino began to fall over, while in another trial the stopwatch was stopped when the final domino finished falling over, then there would be a discrepancy. The start point will be defined as the point in time when the first domino just makes contact with the second domino. The end point will be defined as the point in time when the final domino hits the surface (i.e. finishes falling over).
Environmental conditions (i.e. wind conditions) If the experiment is undertaken in a windy environment for one trial but in a windless environment for another, then there will be random error. This is because the wind in the trial undertaken in windy conditions will give the dominoes some initial velocity, which should slightly affect the time taken for the dominoes to fall over. The experiment will be undertaken in the laboratory with the air conditioner turned off and windows shut for all trials.
Apparatus
40 identical dominoes Stopwatch (±0.005s) 30cm ruler (±0.05cm) 2 one metre rulers
Method
Before starting, ensure that all windows are shut and that the air conditioner is turned off. Find a flat bench that is at least 2m in length. Place the two one-metre-length rulers side by side on the bench, separating them by a width slightly greater than the width of the dominoes. Ensure that they are parallel. Set up the 40 dominoes as shown in the diagram below (a side view is given of the experimental setup):
NB Use the two metre-length rulers as guides to ensure that the dominoes are aligned in a straight line. Set the value of d to 0.5cm by using the 30cm ruler to measure the distance between dominoes. Have one person hold the stopwatch and stand at one end of the chain of dominoes, and another person (without the stopwatch) at the other end. Have the person without the stopwatch gently push the first domino until it just begins to fall over. As soon as the first domino makes contact with the second domino, the person who pushed the domino should immediately signal the other person to begin timing. Once the final domino makes contact with the bench surface, the person with the stopwatch should stop timing. Repeat steps 1-5 twice more with d = 0.5cm. Repeat steps 1-6 with different values for d (namely 1.0cm, 1.5cm, 2.0cm, 2.5cm and 3.0cm) Eliminate any outliers (data values that significantly deviate from other data values), and then take an average of the time taken for each value of d.
Assuming no outliers, the average is calculated using the equation below:
Average=(time_1+time_2+time_3)/3
Fill in a table resembling the one below:
Separation of dominoes (cm) Time taken, trial 1 (s) Time taken, trial 2 (s) Time taken, trial 3 (s) Average time taken (s)
0.5
1.0
1.5
2.0
2.5
3.0 Plot a graph of t against d and draw a line of best fit using Microsoft Excel. Hence, determine the relationship between d and t.
Data processing
Qualitative observations
During the setting up of the dominoes, it was difficult to set them up exactly in a straight line. Some of the dominoes were at slight angles to each other. This problem was alleviated to some extent by having two parallel metre-length rulers on both sides of the dominoes to act as guides. Unfortunately this did not completely eliminate the issue thus small angles were still present. This may have caused some discrepancies in the results, as each trial used chains of 40 dominoes (meaning that if each one was affected by this, then the overall result would be somewhat noticeable). Additionally, the distance between dominoes was slightly difficult to measure due to some slight parallax error.
The initial force applied to the first domino was applied solely through human action. This meant that there was room for some random error as it is very difficult for humans to perfectly replicate the force they apply to an object. This means that there is likely to be some random error present due to the means of starting the domino effect.
After having delivered the ‘gentle push’ to the first domino to start the domino effect, the other dominoes fell very quickly. This made it difficult to measure the time taken for the dominoes to fall over. This was especially true for lower distances between dominoes, as all of the dominoes fell over even more quickly.
Raw Data
Distance between dominoes (cm) (±0.1cm) (Trial 1)Time taken for dominoes to fall (s)
(±0.4s) (Trial 2) Time taken for dominoes to fall (s)
(±0.4s) (Trial 3) Time taken for dominoes to fall (s)
(±0.4s)
0.5 1.14 1.17 1.08
1.0 1.16 1.32 1.24
1.5 1.29 1.33 1.25
2.0 1.46 1.48 1.51
2.5 1.63 1.63 1.67
3.0 1.82 1.85 1.79
Calculation of uncertainties
Distance between dominoes: A 30cm ruler was used to measure the distance between dominoes. This ruler was able to measure to the nearest millimetre, thus its uncertainty is ±0.05cm (half of the smallest measurable unit). However, for each domino, the ruler was used to measure between two points (the ‘0’ point on the ruler and the point where d is equal to the desired amount). Consequently, the uncertainty of the ruler must be doubled to ±0.1cm. There was also some very slight parallax error, but it was most likely negligible (at worst, error of a fraction of a millimetre).
Time taken for dominoes to fall: A stopwatch was used to measure the time taken to fall. The stopwatch was able to measure to the hundredth of a second, thus its uncertainty is ±0.005s. However, as a human was operating the stopwatch, there is also an uncertainty associated with reaction times. The uncertainty associated with human reaction time is approximately ±0.2s, but since reaction time affected the starting and the stopping of the watch, the uncertainty must be doubled to ±0.4s. The uncertainty due to the instrument is negligible when compared to the uncertainty due to human reaction time.
Processed Data
Average time taken to fall
This was calculated by summing the times of the three trials for that specific value of d, and then dividing the sum by 3.
For example for d = 0.5cm:
Average time taken=(1.14+1.17+1.08)/3=1.13s
Since the times used in the calculation of the average time taken had uncertainties, the average time taken also has an uncertainty, which is equal to the uncertainty of each of the trials, ±0.4s (as each trial has the same uncertainty). Overall, for d = 0.5cm, the time taken was 1.1±0.4s (the time has been rounded off to one decimal place to agree with the uncertainty).
This was done for other values of d as well.
In the table below, all units have been converted to the appropriate SI units. d, Distance between dominoes (cm) ±0.001m t, Average time taken (s) ±0.4s
0.005 1.1
0.010 1.2
0.015 1.3
0.020 1.5
0.025 1.6
0.030 1.8
Graphs
The effect of distance between dominoes and time taken to fall
Introduction
By collecting data whilst keeping all variables constant apart from the independent and dependent variables of an experiment, it is possible to determine a relationship between them. One relationship that can be observed in a laboratory is the relationship between the distance (denoted by symbol d) of separation of dominoes in a domino chain and the time taken (denoted by symbol t) for all dominoes to fall over.
It is expected that greater distances of separation will result in greater time taken for all dominoes to fall over. This is due to the fact that when they are separated by greater distances, the dominoes will have to cover more distance (and …show more content…
consequently fall for a longer period of time) before they hit the subsequent dominoes.
In this practical, dominoes will be allowed to fall over (after being supplied a very small force [outlined in Variables and Method section]) with various distances of separation. The time taken for each value of d will be observed and recorded. Once these data have been obtained, the relationship between d and t will be determined through the use of Microsoft Excel.
Research question (aim)
Given that the dimensions, mass and arrangement of the dominoes are kept constant in addition to the initial force applied to the first domino in the domino chain, what is the relationship (e.g.
d∝t,d∝1/t,d∝√t,d∝t^2) between the distance (d) of the separation between each domino and the time taken (t) for all of the dominoes to fall over?
Variables
Independent variable: The distance between each domino. This will be changed by moving the dominoes. The distance will be measured using a 30cm ruler. The distances being used in this experiment: 0.5cm, 1.0cm, 1.5cm, 2.0cm, 2.5cm, 3.0cm.
Distances greater than 3.0cm are not used as the dominoes would fall over without making contact with each other if the distance between them is greater than 3.0cm. Likewise, a distance of 0.0cm is not used as the ‘domino effect’ would not occur since the force applied to the subsequent dominoes as a result of the ‘gentle push’ (outlined in the Variables and Method sections) applied to the first domino would not be great enough.
Dependent variable: The time taken for all 40 dominoes to fall over. This will be measured through the use of a stopwatch.
Controlled …show more content…
variables:
Variable Significance of controlling Method of controlling
Experimental surface The surface that the dominoes are placed on must be kept constant as the material of the surface they are placed on will have varying friction, which will slightly influence falling times of the dominoes.
Furthermore, the surface must be uniform (i.e. flat). If it is not, then for each trial, dominoes will be inclined at different angles (e.g. some will be leaning over a bit more than others, this will cause their falling times to be slightly lower). Overall, if the surface is not kept constant, then random error will result. All trials will be done on the same surface (a bench in the
laboratory).
Force applied to first domino If the force being applied to the first domino is not kept constant, there will be random error. This is due to the fact that if the first domino is pushed with a greater force, then it will fall over faster, thereby decreasing the time taken for all 40 dominoes to fall over. If a large force is only applied to some of the trials, then there will be imprecision of the data.
The aim of the experiment is to observe the effect of only changing the distance between dominoes, thus this variable must be kept constant. This variable is slightly difficult to manage, but it will be kept as constant as possible by starting each ‘domino effect’ by carefully and gently pushing the first domino until it just begins to fall over.
Properties of the dominoes The properties of the dominoes, namely their dimensions (length, width, height) and their masses should be kept constant as they are likely to have an effect on the falling time of the dominoes. Variation in these properties should result in random error. For instance, a more massive domino should apply a greater force to the subsequent domino (due to the relationship: force = mass × acceleration due to gravity, [F=mg]). If very massive dominoes are used in one trial but not another, then there will be an imprecision in the data as the mass of the dominoes will be affecting the falling times in addition to the change in distance. The same dominoes will be used for all trials.
Pattern of placement of dominoes
(does not include distance between dominoes) The pattern of placement (e.g. in a straight line, in a spiral pattern) of the dominoes must be kept constant as different arrangements of the dominoes should affect the time taken for the dominoes to fall over. For instance, if dominoes are falling onto each other at 45o angles in one trial but at 0o angles (i.e. in a perfectly straight line) in another trial, the dominoes in the straight line will fall over more quickly. This is because in the trial with the straight line arrangement, all of the force being applied to subsequent dominoes is acting in the same direction that the subsequent dominoes are facing. This means that they will fall over more quickly. Conversely, in the trial where the dominoes are arranged at 45o angles to each other, the force imparted on subsequent dominoes is only partially acting upon the direction that the subsequent dominoes are facing. This is a source of random error if it is not kept constant. For each trial, the dominoes will be arranged in a straight line. This will be managed by placing two one metre rulers alongside the dominoes as they are being set up (the rulers will act as a guide for laying out the dominoes in a straight line)
Start and end points of experiment The start and end points of each trial should be clearly defined and kept constant for each trial. If the stopwatch is started and stopped at different points in time for different trials, then there will be imprecision in the data. This change in time taken will not only be due to the change in distance between dominoes.
For instance, if in one trial the experiment was deemed to be finished when the final domino began to fall over, while in another trial the stopwatch was stopped when the final domino finished falling over, then there would be a discrepancy. The start point will be defined as the point in time when the first domino just makes contact with the second domino. The end point will be defined as the point in time when the final domino hits the surface (i.e. finishes falling over).
Environmental conditions (i.e. wind conditions) If the experiment is undertaken in a windy environment for one trial but in a windless environment for another, then there will be random error. This is because the wind in the trial undertaken in windy conditions will give the dominoes some initial velocity, which should slightly affect the time taken for the dominoes to fall over. The experiment will be undertaken in the laboratory with the air conditioner turned off and windows shut for all trials.
Apparatus
40 identical dominoes Stopwatch (±0.005s) 30cm ruler (±0.05cm) 2 one metre rulers
Method
Before starting, ensure that all windows are shut and that the air conditioner is turned off. Find a flat bench that is at least 2m in length. Place the two one-metre-length rulers side by side on the bench, separating them by a width slightly greater than the width of the dominoes. Ensure that they are parallel. Set up the 40 dominoes as shown in the diagram below (a side view is given of the experimental setup):
NB Use the two metre-length rulers as guides to ensure that the dominoes are aligned in a straight line. Set the value of d to 0.5cm by using the 30cm ruler to measure the distance between dominoes. Have one person hold the stopwatch and stand at one end of the chain of dominoes, and another person (without the stopwatch) at the other end. Have the person without the stopwatch gently push the first domino until it just begins to fall over. As soon as the first domino makes contact with the second domino, the person who pushed the domino should immediately signal the other person to begin timing. Once the final domino makes contact with the bench surface, the person with the stopwatch should stop timing. Repeat steps 1-5 twice more with d = 0.5cm. Repeat steps 1-6 with different values for d (namely 1.0cm, 1.5cm, 2.0cm, 2.5cm and 3.0cm) Eliminate any outliers (data values that significantly deviate from other data values), and then take an average of the time taken for each value of d.
Assuming no outliers, the average is calculated using the equation below:
Average=(time_1+time_2+time_3)/3
Fill in a table resembling the one below:
Separation of dominoes (cm) Time taken, trial 1 (s) Time taken, trial 2 (s) Time taken, trial 3 (s) Average time taken (s)
0.5
1.0
1.5
2.0
2.5
3.0 Plot a graph of t against d and draw a line of best fit using Microsoft Excel. Hence, determine the relationship between d and t.
Data processing
Qualitative observations
During the setting up of the dominoes, it was difficult to set them up exactly in a straight line. Some of the dominoes were at slight angles to each other. This problem was alleviated to some extent by having two parallel metre-length rulers on both sides of the dominoes to act as guides. Unfortunately this did not completely eliminate the issue thus small angles were still present. This may have caused some discrepancies in the results, as each trial used chains of 40 dominoes (meaning that if each one was affected by this, then the overall result would be somewhat noticeable). Additionally, the distance between dominoes was slightly difficult to measure due to some slight parallax error.
The initial force applied to the first domino was applied solely through human action. This meant that there was room for some random error as it is very difficult for humans to perfectly replicate the force they apply to an object. This means that there is likely to be some random error present due to the means of starting the domino effect.
After having delivered the ‘gentle push’ to the first domino to start the domino effect, the other dominoes fell very quickly. This made it difficult to measure the time taken for the dominoes to fall over. This was especially true for lower distances between dominoes, as all of the dominoes fell over even more quickly.
Raw Data
Distance between dominoes (cm) (±0.1cm) (Trial 1)Time taken for dominoes to fall (s)
(±0.4s) (Trial 2) Time taken for dominoes to fall (s)
(±0.4s) (Trial 3) Time taken for dominoes to fall (s)
(±0.4s)
0.5 1.14 1.17 1.08
1.0 1.16 1.32 1.24
1.5 1.29 1.33 1.25
2.0 1.46 1.48 1.51
2.5 1.63 1.63 1.67
3.0 1.82 1.85 1.79
Calculation of uncertainties
Distance between dominoes: A 30cm ruler was used to measure the distance between dominoes. This ruler was able to measure to the nearest millimetre, thus its uncertainty is ±0.05cm (half of the smallest measurable unit). However, for each domino, the ruler was used to measure between two points (the ‘0’ point on the ruler and the point where d is equal to the desired amount). Consequently, the uncertainty of the ruler must be doubled to ±0.1cm. There was also some very slight parallax error, but it was most likely negligible (at worst, error of a fraction of a millimetre).
Time taken for dominoes to fall: A stopwatch was used to measure the time taken to fall. The stopwatch was able to measure to the hundredth of a second, thus its uncertainty is ±0.005s. However, as a human was operating the stopwatch, there is also an uncertainty associated with reaction times. The uncertainty associated with human reaction time is approximately ±0.2s, but since reaction time affected the starting and the stopping of the watch, the uncertainty must be doubled to ±0.4s. The uncertainty due to the instrument is negligible when compared to the uncertainty due to human reaction time.
Processed Data
Average time taken to fall
This was calculated by summing the times of the three trials for that specific value of d, and then dividing the sum by 3.
For example for d = 0.5cm:
Average time taken=(1.14+1.17+1.08)/3=1.13s
Since the times used in the calculation of the average time taken had uncertainties, the average time taken also has an uncertainty, which is equal to the uncertainty of each of the trials, ±0.4s (as each trial has the same uncertainty). Overall, for d = 0.5cm, the time taken was 1.1±0.4s (the time has been rounded off to one decimal place to agree with the uncertainty).
This was done for other values of d as well.
In the table below, all units have been converted to the appropriate SI units. d, Distance between dominoes (cm) ±0.001m t, Average time taken (s) ±0.4s
0.005 1.1
0.010 1.2
0.015 1.3
0.020 1.5
0.025 1.6
0.030 1.8
Graphs