Mark Riley 3107631608
RESULTS/CALULATIONS PAGE3
TABLE1a.
Maximum extension of spring when a 1.00kg weight was added -
Extension of spring when a 9.81N force is applied Force applied Fw = (1.00x9.81) = 9.81N
1st Trial 2nd Trial 3rd Trial 4th Trial 5th Trial 6th Trial 7th Trial 8th Trial 9th Trial 10th Trial
0.505m 0.505m 0.500m 0.500m 0.510m 0.508m 0.510m 0.512m 0.510m 0.510m
TABLE2a.
Extension of spring (x) versus Mass (m) and Force Applied (Fw)
Extension (m) 0.000m 0.000m 0.010m 0.046m 0.090m 0.111m 0.145m 0.181m 0.216m 0.251m
Mass (kg) 0.100kg 0.200kg 0.300kg 0.400kg 0.500kg 0.600kg 0.700kg 0.800kg 0.900kg 1.00kg
Force Applied 0.981N 1.96N 2.94N 3.92N 4.91N 5.88N 6.86N 7.84N 8.83N 9.81N
LIMITATIONS OF THE EQUIPMENT MUST BE TAKEN INTO CONSIDERATION FOR ALL MEASUREMENTS OF
EXTENSION AND MASS IN TABLE 1A. AND 2A.
PRECISION OF RULER 1mm โด ยฑ0.5mm PRECISION OF MASS 1gram โด ยฑ0.5g
GRAPH A.
y = 31.98x + 2.0376
0.000
2.000
4.000
6.000
8.000
10.000
12.000
0.000 0.050 0.100 0.150 0.200 0.250 0.300
Forc
e (N
)
Extension (m)
Force versus Extension
Mark Riley 3107631608
RESULTS/CALULATIONS PAGE4
GRAPH B.
Blue values represent data that was disregarded when plotting the trend line
TABLE3b.
Extension (m x 10-2) Force (N)
0.00 0.981
0.00 1.96
1.00 2.94
4.60 3.92
9.00 4.91
11.1 5.89
14.5 6.87
18.1 7.85
21.6 8.83
25.1 9.81
y = 28.901x + 2.5832
0.000
2.000
4.000
6.000
8.000
10.000
12.000
0.000 0.050 0.100 0.150 0.200 0.250 0.300
Forc
e (N
)
Extension (m )
Force versus Extension
Mark Riley 3107631608
RESULTS/CALULATIONS PAGE5
CALC1a. The average maximum extension (x) of 1kg weight using values from TABLE1a.
๐๐.๐๐๐ + ๐๐.๐๐๐ + ๐๐.๐๐๐ + ๐๐.๐๐๐ + ๐๐.๐๐๐ + ๐๐. ๐๐๐ + ๐๐.๐๐๐ + ๐๐.๐๐๐ + ๐๐.๐๐๐ + ๐๐.๐๐๐
๐ต๐๐๐๐๐ ๐๐ ๐๐๐๐๐๐ ๐๐.๐
๐๐๐๐๐
๐๐.๐= ๐๐.๐๐๐ = ๐. ๐๐๐๐๐๐๐๐๐ ๐๐ ๐.๐๐๐ฑ๐๐โ๐๐๐๐๐๐๐
CALC1b. Uncertainty in the measure of extension(x) for the 1kg weight
50.7 โ 50.5 = ๐. ๐ 50.7 โ 50.5 = ๐.๐ 50.7 โ 50 = ๐. ๐ 50.7 โ 50 = ๐. ๐
51.0 โ 50.7 = ๐. ๐ 50.8 โ 50.7 = ๐.๐ 51.0 โ 50.7 = ๐. ๐ 51.2 โ 50.7 = ๐.๐
51.0 โ 50.7 = ๐. ๐ 51 โ 50.7 = ๐. ๐
๐.๐๐๐ + ๐.๐๐๐ + ๐.๐๐๐ + ๐.๐๐๐ + ๐. ๐๐๐ + ๐. ๐๐๐ + ๐. ๐๐๐ + ๐. ๐๐๐ + ๐.๐๐๐ + ๐.๐๐๐
๐ต๐๐๐๐๐ ๐๐ ๐๐๐๐๐๐ ๐๐
๐.๐๐๐
๐๐= ๐. ๐๐๐๐ = ๐.๐๐๐๐๐๐๐๐๐๐ ๐๐ ๐.๐๐ฑ๐๐โ๐๐๐๐๐๐๐
โx = ยฑ 3.6mm
CALC1c. Express this uncertainty as a percentage
๐. ๐๐๐๐
๐๐.๐๐๐ ๐ฑ ๐๐๐ = ๐. ๐๐%
Mark Riley 3107631608
RESULTS/CALULATIONS PAGE6
CALC3a. Spring constant = the gradient of a Force applied vs extension graph. Using the two
points that best fit the trend line in respect to GRAPH B.
๐๐โ ๐๐
๐๐โ ๐๐ โด
๐.๐๐ โ ๐.๐๐
๐.๐๐๐โ๐.๐๐ ๐= ๐๐.๐ ๐ = ๐๐.๐ ๐
CALC4a. Loss of Gravitation Potential Energy (GPE) using height (x) value from CALC1a. All
GPE is transferred at the relative height of zero.
๐ฎ๐ท๐ฌ = ๐๐๐ ๐ = ๐๐๐๐ ๐ = ๐๐๐๐๐๐๐ (๐.๐๐) h=height (extension in this case)
๐ฎ๐ท๐ฌ ๐๐๐๐๐๐๐๐๐๐๐ = ๐.๐๐๐๐ ๐ฑ ๐.๐๐ ๐ฑ ๐.๐๐๐๐ = ๐.๐๐ ๐ฑ
CALC4b. Gain in Elastic Potential Energy (EPE) using K value from CALC3a. and the X value
from CALC1a.
๐ฌ๐ท๐ฌ = ๐
๐๐๐๐ ๐ = ๐๐๐๐๐๐ ๐๐๐๐๐๐๐๐ ๐ = ๐๐๐๐๐๐๐๐๐
๐ฌ๐ท๐ฌ ๐๐๐๐๐๐ =๐
๐ ๐ฑ ๐๐.๐ ๐ฑ ๐.๐๐๐๐ = ๐.๐๐ ๐ฑ
CALC5a. Difference between loss of GPE and gain of EPE using values from CALC4a. &
CALC4b.
๐ฎ๐ท๐ฌโ ๐ฌ๐ท๐ฌ = ๐ซ๐ฐ๐ญ๐ญ๐ฌ๐น๐ฌ๐ต๐ช๐ฌ ๐.๐๐๐ฑโ ๐.๐๐๐ฑ = ๐.๐๐๐ฑ
Mark Riley 3107631608
RESULTS/CALCULATIONS PAGE7
CALC5b. Difference between the two energies as a percentage in relation to GPE
๐. ๐๐
๐. ๐๐ ๐ฑ ๐๐๐ = ๐๐.๐%
REF6a. Comparison between CALC5b. and CALC1c.
๐๐.๐% ๐๐๐๐๐๐ ๐.๐๐%
CALC7a. Area underneath a Force vs Extension graph should equal the work done.
Work done in respect to GRAPH B
2.58 x 0.251 = ๐.๐๐๐
9.81 โ 2.58 x0.251
2= ๐.๐๐๐
๐พ๐๐๐ ๐ ๐๐๐ = ๐. ๐๐๐ + ๐. ๐๐๐ = ๐.๐๐๐ฑ
CALC7b. The actual Relationship between Force applied and Extension. Refer to the
equation to the trend line in GRAPH B. F = kx + F0
๐ = ๐๐ + ๐ ๐๐ ๐ญ = ๐๐ + ๐ญ๐
๐ญ = ๐๐.๐๐ + ๐. ๐๐
Mark Riley 3107631608
RESULTS/CALCULATIONS PAGE8
CALC9a. The actual relationship between F and x for this spring was found in the previous
calculation CALC7b. Express this relationship in terms of area and substitute into
the expression EPE = ยฝkx2 . Where x will be the best estimate of the maximum
extension of the falling 1kg mass.
๐ฌ๐ท๐ฌ = ๐
๐๐๐๐ + ๐ญ๐๐ โด
๐
๐๐๐.๐๐ฑ๐.๐๐๐๐ + ๐.๐๐๐ฑ๐.๐๐๐ = ๐.๐๐๐ฑ
CAL9b. Compare this energy to the Energy calculated for the loss of GPE CALC4a.
๐ฌ๐ท๐ฌ ๐๐ ๐ฎ๐ท๐ฌ ๐.๐๐๐ฑ ๐๐ ๐.๐๐๐ฑ
4.97J โ 5.02J = -0.051
Difference between values = 0.051J
CALC9c. Express the difference found in the previous calculation as a percentage in respect
to GPE.
๐. ๐๐๐
๐. ๐๐ ๐ ๐๐๐ = ๐. ๐๐%
CALC9d. Compare this percentage difference to the percentage uncertainty in the
measurement of distance/extension value for x which is 0.71% CALC1c.
๐. ๐๐% ๐๐ ๐.๐๐%
This time the percentage uncertainty for measurement of the extension can pretty
much account for the error in calculation of EPE using the equation from CALC9c.
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