Calculating the acceleration of gravity using a ticker tape.

[lolbits]

Homework Statement

It was an experiment we did at school. We placed a tape through a vibrator that leaves a black dot on a tape for every 1/100 s. We dropped the tape and registered many dots. We have narrowed the experiment down to 10 dots. So we chose a dot, and registered the length between the dot before it, and after it to calculate the velocity at that dot. We did this to a dot 10 dots further down to find the velocity at that dot, so we could use the difference in distance / difference in time. This is our measurements:

L_A = 0.036 m
L_B = 0.044 m

We "know" the time it takes for the vibrator to leave 10 dots is 10*1/100= 1/10=0.1, therefore the distance between the three dots is 0.02s. We get

(0.044/0.02)-(0.036/0.02) = 0.4

0.4/0.1= 4m/s^2 = g.

Thats very wrong!
Any suggestions?

 

[Heimisson]

This way of calculating gives you average velocity. use s=0.5*g*t^2 that is g=2s/t^2.

 

[lolbits]

This way of calculating gives you average velocity. use s=0.5*g*t^2 that is g=2s/t^2.

Hello,

Thank you for replying.

I still can not figure out how that formula will help me. That would give me the acceleration at one given point, right? And not the "avarage" acceleration for all the points, because that's what I am after.

Because the formula gives me: 0.8/0.1^2 = 80m/s^2, which obviously is way too high.

Please do correct me if I am wrong.

 

[Heimisson]

No this should be more like 0.08m from the data you are showing.
s is not velocity but position.

There are several different ways of getting some numerical value from a collection of data. What would be most professional is to make a graph of s as a function of t^2 (which should be linear), the slope of the best line through the points should give you 0.5*g. However your teacher should have thought you the proper way to get a average value from the data.

You can do this in a several different ways. If the instruction don't give you some specific way to do this, just do what you think is best.

 

[rwisz]

First, it's important to clarify that the acceleration of gravity cannot be calculated using a ticker tape. The acceleration of gravity, denoted by g, is a constant value that is determined by the mass and distance between two objects, specifically the Earth and an object falling towards its surface.

What you have calculated is the average velocity of the object at two different points on the tape, using the distance and time measurements. This average velocity can then be used to estimate the acceleration of the object, but it is not a direct calculation of g.

To improve the accuracy of your experiment, you could increase the number of dots you measure and calculate the average velocity at each point. This will give you a better estimate of the object's acceleration over a longer distance. Additionally, you could also consider measuring the distance and time for more than just two points on the tape, which will give you a more precise average velocity.

It's also important to note that there may be other factors at play that could affect the accuracy of your results, such as air resistance or the accuracy of the ticker tape machine. Therefore, it's important to repeat the experiment multiple times and take an average of your results to minimize any errors.

Overall, while your method may not provide an exact calculation of the acceleration of gravity, it is a good way to estimate it and gain a better understanding of the relationship between distance, time, and velocity for a falling object.