Why did I find 9.41 and not 9.81 m/s² ?

[Ellio]

Homework Statement

"Calculate the acceleration of the falling object with your research."

Relevant Equations

slope = Δy/Δx
x = 1/2 × a × t²

Hello I hope you are all very well !
So I have a practical work in physics.
The experiment was to release a long tape with a mass of 40g at the end from a certain height. An instrument would hit the tape 50 times/s and put a mark each time. From that we had to do a graph x(t²) and a series of exercises.
1) The slope of the graph ≅ 4,707 (0,610/0,1296)
2) 4,707 = 1/2 × a × 1
<=> a = 9,414

It may sound like a stupid question but why is my result not equal to 9,81 ? 9,81m/s² is the acceleration of all object falling on the surface of the Earth right ?
What did cause this inequality of 4% ?

 

[PeroK]

Homework Statement: "Calculate the acceleration of the falling object with your research."
Homework Equations: slope = Δy/Δx
x = 1/2 × a × t²

Hello I hope you are all very well !
So I have a practical work in physics.
The experiment was to release a long tape with a mass of 40g at the end from a certain height. An instrument would hit the tape 50 times/s and put a mark each time. From that we had to do a graph x(t²) and a series of exercises.
1) The slope of the graph ≅ 4,707 (0,610/0,1296)
2) 4,707 = 1/2 × a × 1
<=> a = 9,414

It may sound like a stupid question but why is my result not equal to 9,81 ? 9,81m/s² is the acceleration of all object falling on the surface of the Earth right ?
What did cause this inequality of 4% ?

What do you think may be the factors?

 

[Ellio]

What do you think may be the factors?

The air surrounding the room, I presume.

 

[Orodruin]

There are also always measurement errors. How was your experiment set up? Did you do a proper error analysis?

 

[kuruman]

In addition to what @PeroK and @Orodruin mentioned, I want to place your question in a more general framework and ask you, why are you distrusting your measurements? If I asked you to measure the length of a table and came up with 2.65 m and I said, "No it's 2.45 m", would you say (a) "But I measured it and it's 2.65 m" or (b) "Yes, boss, whatever you say. I must have done something wrong." Are you results invalid just because someone you consider more authritative than you contradicts them? Are you the "boss" or not? It's tricky isn't it? At some point, when you do science, you have to trust yourself and call the shots the way you see them after you have eliminated all paths that might have led you astray.

 

[Orodruin]

If I asked you to measure the length of a table and came up with 2.65 m and I said, "No it's 2.45 m", would you say (a) "But I measured it and it's 2.65 m" or (b) "Yes, boss, whatever you say. I must have done something wrong."

I would say it depends on how much you trust your measurement in relation to the others. In the case of gravitational acceleration, students tend to expect 9.8-ish.

There is also significant bias in students presenting results. I had a high-school teacher tell me that if you make a histogram of student results for g, you typically get a very nice gaussian centered around 9.8 m/s^2 - except that it is cut-off at 10 m/s^2...

 

[kuruman]

I would say it depends on how much you trust your measurement in relation to the others. In the case of gravitational acceleration, students tend to expect 9.8-ish.

I agree.

There is also significant bias in students presenting results. I had a high-school teacher tell me that if you make a histogram of student results for g, you typically get a very nice gaussian centered around 9.8 m/s^2 - except that it is cut-off at 10 m/s^2...

I've had a related experience about 20 years ago with a class of about 220 students doing the g measurement. The students were split in groups of 3 so we are talking about 70 separate measurements. The average over all reported values came out to be 9.6 m/s² with a standard deviation of about 0.3 m/s². The outliers were were limited to no more than 10.4 m/s² but there was a remarkable but honest 2.4 m/s². After seeing the results, I decreed that from then and until the end of the semester the value of g is what the entire class thinks it is, 9.6 m/s², and that value should be used in all calculations where numerical answers are required. After the semester was over, students could use whatever value they wanted for g. Some students were disconcerted, "Can you do this?", to which I replied, "You and 220 of your peers measured came up with that average value. Which do you believe, your and your classmates or something printed in a book and why?". At the time I thought that it would be a worthwhile exercise, but the students hated using a value the "knew" to be wrong it so I didn't repeat the experiment.

 

[phyzguy]

@Ellio , let me ask you this. When the weight in your experiment was falling, was gravity the only force acting on it? Could there have been any other forces?

 

[haruspex]

An instrument would hit the tape 50 times/s and put a mark each time.

What held the tape in such a way that the instrument was able to mark it? Can a mark be made without hindering the tape at all? What other hindrance may affect the tape?

 

[Ellio]

In addition to what @PeroK and @Orodruin mentioned, I want to place your question in a more general framework and ask you, why are you distrusting your measurements? If I asked you to measure the length of a table and came up with 2.65 m and I said, "No it's 2.45 m", would you say (a) "But I measured it and it's 2.65 m" or (b) "Yes, boss, whatever you say. I must have done something wrong." Are you results invalid just because someone you consider more authritative than you contradicts them? Are you the "boss" or not? It's tricky isn't it? At some point, when you do science, you have to trust yourself and call the shots the way you see them after you have eliminated all paths that might have led you astray.

Well, thank you all for your answers. But I wasn't really claiming thay my measurement were 'wrong'. 4% of deviation is indeed nothing, I'm of course leaving my answer.
I just wanted to know by curiosity what are the factors that could cause this very slight deviation (atmosphere, ...).

 

[DaveC426913]

I just wanted to know by curiosity what are the factors that could cause this very slight deviation (atmosphere, ...).

Think more mechanically.
Could any forces be interfering with the free fall of the weight?

 

[Ellio]

Think more mechanically.
Could any forces be interfering with the free fall of the weight?

I think the two factors causing this deviation are the vibrator (hitting the tape 50 times/s) and the measurement of the distance between each mark with a ruler (±1mm of error)
But isn't there any other that I could have forgotten ?

 

[haruspex]

the measurement of the distance between each mark with a ruler (±1mm of error)

There may be that much error in individual marks but to affect your estimate of g what matters is the cumulative error along the tape. Could it have become stretched by 4%?

You previously mentioned air drag on the tape. You didn't answer my question re what holds the tape in place so that marks can be made on it... presumably some sort of guide.

 

[Ellio]

There may be that much error in individual marks but to affect your estimate of g what matters is the cumulative error along the tape. Could it have become stretched by 4%?

You previously mentioned air drag on the tape. You didn't answer my question re what holds the tape in place so that marks can be made on it... presumably some sort of guide.

This was the instrument. The band was held where there's the red circle. The yellow arrow shows the vibrator which hit the band 50 times/s.
(The tape was of course vertical in the experiment.)

 

[kuruman]

This was the instrument. The band was held where there's the red circle. The yellow arrow shows the vibrator which hit the band 50 times/s.
(The tape was of course vertical in the experiment.)

Is your setup as shown here? If so, note that the use of 200 g is recommended because "If the mass used is too small, it will not give accurate results because of air drag and friction on the paper tape." You used 40 g.

 

[Ellio]

Is your setup as shown here? If so, note that the use of 200 g is recommended because "If the mass used is too small, it will not give accurate results because of air drag and friction on the paper tape." You used 40 g.

Ok thank you very much ! (Yes it's the setup we used.)