Expert answer:Lap report, paraphrasing and inclusion help
Answer & Explanation:1. Did the period of the pendulum swing
depend on the mass of the bob? On the length of the string? On the
displacement? How does your data relate to the pendulum equation? You need not
include your data tables and graphs, but you should explain your answer based
on the information in your data tables and graphs.
Answer: Observing
the data from the lab and the tables, I can say that as the mass of the bob
increased, so did the period of the pendulums swing. The graph for part 1 of this lab shows that
as the mass of the bob increased from 50g to 400g, the average of the period
also increased very gradually with each weight that was added despite the angle
of the angle of the string being the same and also the length of the string
being the same. However the average of the period that increased with each mass
was very little and can be negotiated as the mass of the bob did not really
affect the swing of the pendulum much and any data that shows that the mass
does effect the period of pendulum can be explained through either human or experimental
errors.
In the data from the 3rd part of
the lab and graph we can see that the length of the string also caused a
difference in the average period of the pendulum swing. In the 3rd
part I test to see if the same mass and same angle but changing the length of
the string would make a difference in the period of the pendulum swing. The
results confirm that the length of the string also affects the period of
pendulum. The length of string differed fro 0.10m to 0.40m. In each case where
a length was added to the string, it tool longer for each path of periodic
motion, which further resulted in longer length of string more period of
pendulum. The longer the string will result in longer period of the swing as
the length the period has to travel increases.
In the second part of the lab we tested if the displacement
affects the period of the pendulum swing. I tested the different angular
displacements along with the period of the pendulum. Looking at the table I can
say that the displacement does affect the period of the pendulum. The angular
displacements tested were 45°-15° and what can be observed is that as the
angular displacement increased the period of the pendulum also increased.
And so the greater the displacement, the greater the period
of pendulum, as the higher the arc at which the bob was released, the more time
it will take for the bob to travel the distance it has to travel .
(6 points)
Score
2. Calculate the slope of the line
in your graph of the square of the period of the pendulum vs. length of the
string [slope = (y2 – y1)/(x2 – x1)].
Galileo figured out the equation that describes the behavior of a pendulum. If
you square both sides of the equation, you will find that the slope of the line
is related to the acceleration due to gravity (g). Specifically, slope = 4p2/g. Use your data to calculate g.
How does it compare with the accepted value of 9.807 m/s2?
Calculate the percent error and show your work.
Answer:
Firstly
let the 2 points on the graph be (0.1,0.9) and (0.4,1.7)
Slope
= (y2 – y1)/(x2 – x1)]
Therefor (1.7-0.9) / (0.4-0.1) = 2.67 is the
slope of the line of my graph
To be able
to get an answer we need to alter the formula slope = 4p2/g to g
= 4π² / slope to be able to substitute it with values I already have.
g=4π² / slope
g=4π² / 2.67 = 14.79 m/s2
Percent error = (experimental value – theoretical
value / theoretical value)*100
(14.79-9.807/9.807)*100 =50.81% error
The value I received for gravity after calculation
is higher than the acceptable value of gravity, which is 9.807 m/s2,
which resulted in a percentage error of 50.81%.
(6 points)
Score
3. Did the period of the spring
swing depend on the length of the displacement? On the mass? Explain your
answer using your data. How do your findings relate to the spring equation?
Answer:
T=2p √m/k
F=1/T
Observing the data collecting during the
lab and looking at the graph, I can say that as the length of the displacement
was increased from 0.05m-0.20m, the average period of the spring also increased
but the increase was not significant What we need to remember is that a 200 g
mass was hung on the other end of the spring. Also looking at my data and lab,
I see that the affects of the length of displacement were rather gradual on the
average period. The change, which was seen, can be negotiated as the difference
and increase was very minor.
In the last part of the lab, difference
masses were attached to the spring to observe how the mass would affect the
period of the spring swing. According to my observations, mass plays a role in
the period of the spring, as the mass increased from 0.10kg-0.40kg, the period
average of the spring also increased.
My observation
and testing confirms that the period of the spring depends on the mass on the
spring and also that the period does not necessarily depend on
the amplitude of motion, however human errors or experimental errors could
create a false image of showing a correlation between the amplitude and the
period of spring.
When comparing to the spring formula,
we can see that amplitude does not have any significant affects on the period
of spring, rather the 2 factors that the period of spring is dependent upon is
the K which is the spring contact and m which is the mass on the spring. The
frequency is also important as when conducting the lab we calculated the time
for 10 swings.
(6 points)
Score
4. Calculate the slope of the line
in your graph of the square of the period of the spring vs. mass
[slope = (y2 – y1)/(x2 – x1)].
Robert Hooke figured out the equation that describes the periodic motion of the
spring. If you square both sides of the equation, you will find that the slope
of the line is related to the spring constant (k). Specifically, slope = 4p2/k. Use your data to calculate the k of your spring.
Answer: Let the 2 points on the graph be (0.10,0.09)
and (0.40,0.24)
Slope
= (y2 – y1)/(x2 – x1)].
Therefor
(0.25-0.09)/(0.40-0.10) = 0.53
To be able to get an answer we need to alter the
formula slope = 4p2/k to k = 4π² / slope to be able to substitute it with
values I already have.
k=4π² / slope
slope =0.53
The k of the spring is equal to 74.49 N/m
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