How do I calculate the acceleration of falling dominoes in a domino run.?

Question

Ok so I have done an experiment for my physics AS level. It is to investigate what variables will increase the speed of a domino run.
I've been noticing that the domino run accelerates towards the end of the run, obviously due to extra weight and force etc. But I'm having a really hard time trying to calculate the acceleration:

I have taken the speed of the dominoes from domino 1>4 then 4>8 then 8>12 etc throughout my 20domino run. So as expected the first four dominos took longer to fully topple than the last four did due to the acceleration. So now I have a set a time results and speed results.
Time Speed
0.33 0.18
0.16 0.36
0.08 0.73
0.05 1.16
0.02 2.90
But now I'm stuck. How do I use this data to calculate the acceleration. The graph gives a negative curve so I'm really quite confused as to what to do next.
Can anyone help me?

Answer 1

distance = intitial speed + (acceleration x time)



make sure your not pushing the first domino just setting it very slightly off balance, then you can say the intial speed at the start is 0.

instead of measuring distance in metres, we'll measure it in dominos



so the equation from domino 1>4 would look like this:



4 = 0 + (acceleration x time from 1-4)



you don't measure the next section on its own. you calculate from the first domino to the 8th domino: +



8 = 0 + (acceleration + time from 1-8)



this gives you two simultanious equations.



remember that your answer will be in dominos per second



EDIT: oh ya. this would give you a constant acceleration if you repeated it the whole way to domino 20. so this time use dominos 5>8 for the first equation and 5>12 for the second. this will give you a new acceleration. this time, however, you need to work out the initial speed of domino 5.



easy peasy. use the first acceleration you worked out



1>4

initial speed = 0

acceleration = whatever you calculated

time = whatever you recorded

distance = 4 dominos

final velocity = the initial velocity of domino 5



use the formula:



final velocity = (initial velocity x time) + 1/2(acceleration x time^2)

Answer 2

I don't believe that there is any acceleration. I believe that not counting the first domino, each domino falls at the same rate as the one before. The reason is that a domino falls because of gravitational effect rather than being forced downward by the impact of the prior domino. Each domino's balance is upset far enough from the vertical that there is more mass on the leading side of the balance point than on the trailing side. Therefore, the gravitational force pulling down on the leading side of the domino has a greater effect than the gravitational force pulling down on the trailing side. The sideways force of the prior domino is sufficient to cause the impacted domino to move through it's balance point over the leading edge. But that impact force ends and gravity takes over. Since gravity is constant and each domino has the same mass, there would be no acceleration.



I suggest that the way to prove me right or wrong would be to increase your test quantity. I suggest you start with 220 dominos. Don't time the first 19 because the timing can be messed up by the starter. The starter can take a long time to get the first domino to fall or can hit the first one with unnecessary force. Start the timer on number 20 and stop on number 120. That hundred is the first timed group. At the same time you stop the timer on number 120, start another timer. End the second timer on the fall of number 220. Then compare the two times. I believe there will be no significant difference between the times.



A more accurate test of acceleration would be to use 1000 dominos. You would time the total sequence and time the final hundred. If the time to complete the final hundred is exactly one tenth of the total sequence, that proves that there has been no acceleration.



Mayan

Answer 3

acceleration is the change in velocity over the change in time.

so, get acceleration by getting any two time intervals say ..

0.33 and 0.16 there equivalent speeds are 0.18 and 0.36.



so acceleration of your domino run during 0.16 and 0.33 seconds will be (0.18 - 0.36) / (0.33 - 0.16) .



Now this gives a negative value. Which means the velocity is slowing down (which is true from your data) or the dominoes are moving back.



And since you said that the dominoes are accelerating, your data should be - " as time increases, speed also increases" which is not the case.



So, it is also probable that you might have measured your speeds in the wrong way. Another very probably reason is that your run is too short and the margins of error in gathering your data will be very big. Try using more dominoes.



Now, assessing your experiment in terms of energy. The kinetic energy that you used to topple your first domino would be transferred to the next one, etc. In effect, the last domino would have the same energy as the first. Simply said, the last domino will fall at the same rate that your first domino fell, or no acceleration in your domino run.



Great work btw :)