How can you determine the acceleration rate of an object using a ticker-tape wth dots on it? Any advice?

Answer 1

If the tape represented a displacement and one can be place a dot in equal interval's of time you would have a record of displacement, velocity and acceleration as a function of time.

I'm supposing that at least in one of the arrangements the the tape is dragged frictionlessly along the path through a time marking device, which places a dot on the tape.

For example By measuring S3 , S2, and S1
Average velocity between S2 and S1 is
V1=(S2-S1)/t
V2=(S3-S2)/t
t- time interval the timing device is set to

Acceleration a between V1 and V2 is
a=(V2-V1)t

I hope it helps

Answer 2

first, the dots are at a constant time interval t. you need to know what that is. ie is it 60 dots per second? or 1/60 of a second between dots? you can find that by using a stopwatch, having the object accelerate then stopping the watch and counting the dots between start and stop. then calculate the time between dots.

Second measure the total distance from stating point to each dot. then calculate the delta distance between dots. velocity = distance / time. so velocity of each interval = delta distance / time

third. calculate delta velocity / time = acceleration....

usually students doing this setup a table like this for example...

first say you have 60 dots per second....

t = time = 1/60 sec
d (t) = change in time = .02 sec
x = total distance from start to dot.
d (x) = change in distance per time interval
v = velocity = d (x) / d (t)
d (v) = change in velocity / change in time interval
acc = acceleration = d (v) / d (t)

sorry the tables a bit scewed due to cut and paste here...


t,d (t), x,d (x),v,d (v),acc

0, 0
1/60, 0.02, 3, 3, 150
2/60, 0.02, 9, 6, 300, 150, 7500
3/60, 0.02, 18, 9, 450, 150, 7500
4/60, 0.02, 30, 12, 600, 150, 7500
5/60, 0.02, 45, 15, 750, 150, 7500

Answer 3

We did this in class (a LONG time ago!). A small disk with a sharp exterior edge falls down a guide wire. A paper tape is aligned with the wire and backed up by a metal bar located close to the disk edge. A high voltage 60Hz potential is created between the wire and bar. Each 1/120 sec, the potential is enough to cause a spark to jump between the wire, disk and bar, thus putting a small burn hole in the paper. Measuring the distances between the holes and knowing the time interval gives both v and a at any point along the travel of the disk.

Answer 4

The dots measure change in position. Presumably, you know the time between dots. So the distance between 2 dots divided by that time is the average velocity. The difference in velocities between adjacent pairs divided by that time is the average acceleration. If you plot velocities vs. time, it should be a linear relationship (if acceleration is constant). The slope of the line will be the acceleration.