10293-2-3QC
AID: 1825 | 22/11/2013
(a)
Compute mass of ice
m2 m1
and uncertainty.
Denote the measurements of mass of cup and water by
of cup, water, and ice by
m2
m1
and the measurements of mass
.
The two measurements are as follows:
m1 203 2 grams
m2 246
10293-2-13P
AID: 1825 | 22/11/2013
Find the best estimate for the total mass
M m
.
The standard form of M is stated as below:
(1)
M best M
The standard form of m is stated as below:
(2)
mbest m
The best estimate for M is
M best
and the best estimate for
10293-2-12P
AID: 1825 | 22/11/2013
Compute the discrepancy and its uncertainty for the measured and expected accelerations.
Trial
numbe
r
Acceleration
a m s2
Expected
acceleration
g sin m s
2
Discrepancy
a g sin
Uncertainty
1
2.04 0.04
2.36 0.1
2.04 2.36
10293-2-19P
AID: 1825 | 29/11/2013
(a)
Draw the graph for Period (T) against Amplitude (A):
Use MINITAB and draw the graph for Period (T) against Amplitude (A) as in Figure (1).
MINITAB procedure:
Step 1: Choose Graph > Scatterplot.
Step 2: Choose With Re
10293-2-20P
AID: 1825 | 22/11/2013
(a)
Compute the percentage uncertainty for height (h).
Fractional uncertainty
Substitute 5.03 for
hbest
h
hbest
and 0.04 for
in the above equation.
h
0.04
5.03
0.0079
Since height = 5.03 0.04 m
Fractional uncertainty
10293-2-21P
AID: 1825 | 22/11/2013
(a)
Compute the percentage uncertainty for x.
The formula for fractional error is given below:
(1)
x
Fractional uncertainty
xbest
Substitute 3.3 for
xbest
and 1.4 for
x
in Equation (1).
1.4
3.3
0.4
Since x 3.323 1.4
10293-2-22P
AID: 1825 | 29/11/2013
(a)
Let x be
543.2 m 4%
.
Use the below rules and rewrite the given measurements.
Rule for uncertainty:
The uncertainties should always be rounded off to one significant figure.
Rule for stating answer:
The last signific
10293-2-15P
AID: 1825 | 29/11/2013
The following table represents the pressure (P) and temperature (K) of a gas.
Temperature
(K)
100
150
200
250
300
Pressure
(P)
0.36
0.46
0.71
0.83
1.04
The graph of pressure (P) against temperature (K) is shown in Figure
10293-2-7P
AID: 1825 | 22/11/2013
(a)
Find the best estimate and its uncertainty.
Use MINITAB to calculate the mean and standard deviation.
MINITAB procedure:
Step1: Choose Stat > Basic Statistics > Display Descriptive Statistics.
Step2: In Variables, ent
10293-2-11P
AID: 1825 | 29/11/2013
Let L denote the initial angular momentum of a rotating system and
angular momentum of a rotating system.
L
be the final
The result of the initial angular momentum L is stated as follows:
Lbest L
where
L
denotes the unce
10293-2-8P
AID: 1825 | 29/11/2013
The two measurements of the electron charge are as follows:
Group A:
Group B:
e 1.75 0.04 1019 C
e 1.62 0.04 1019 C
Compute the discrepancy between the two measurements as given below:
discrepancy 1.75 1.62
0.13C
Thus, t
10293-2-3P
AID: 1825 | 29/11/2013
(a)
Let the
measured height = 5.03 0.04329 m
Use the below rules and rewrite the given measurements.
Rule for uncertainty:
The uncertainties should always be rounded off to one significant figure.
Rule for stating answer:
10293-2-4P
AID: 1825 | 29/11/2013
(a)
Let x be
3.323 1.4 mm
Use the below rules and rewrite x.
Rule for uncertainty:
The uncertainties should always be rounded off to one significant figure.
Rule for stating answer:
The last significant figure in any stat
10293-2-5P
AID: 1825 | 22/11/2013
Let the two measurements of the length of the same rod be A and B, that is,
A 135 3 mm
B 137 3 mm
The discrepancy between the two measurements is computed as follows:
discrepancy B A
137 135
2 mm
Thus, the discrepancy b
10293-2-5QC
AID: 1825 | 22/11/2013
(a)
Compute the percent uncertainty for l.
The formula for fractional error is given below:
(1)
x
Fractional uncertainty =
xbest
Substitute 9.1 for
xbest
and 0.1 for
Fractional uncertainty
x
in Equation (1).
0.1
9.1
0
10293-2-4QC
AID: 1825 | 22/11/2013
(a)
Compute the fractional and percent error.
The formula for fractional error is given below:
(1)
x
Fractional uncertainty =
xbest
Substitute 55 for
xbest
and 2 for
Fractional uncertainty
x
in Equation (1).
2
55
0.04
10293-2-6P
AID: 1825 | 29/11/2013
The two measurements of masses are as follows:
m1 7.8 0.1 1027 kg
m2 7.0 0.2 1027 kg
Compute the discrepancy between the two research groups as given below:
discrepancy 7.8 7.0 10 27
0.8 1027 kg
The discrepancy between t
10293-2-9P
AID: 1825 | 22/11/2013
Compute the length of the simple pendulum and its uncertainty:
Denote the distance from the top of the string to the bottom of the ball by x and the radius
of the ball by r. The two measurements are as follows:
x 95.8 0.1
10293-2-10P
AID: 1825 | 29/11/2013
Use the provisional rule to compute the uncertainty in the time for one revolution:
It is given that the uncertainty for the starting and stopping time is
1
.
Thus, the uncertainty in the time for one revolution is obtai
10293-2-14P
AID: 1825 | 29/11/2013
Let L denote the initial angular momentum of a rotating system.
Let
L
denote the final angular momentum of a rotating system.
Initial
L
Final
L'
3.0 0.3
2.7 0.6
2.7
3.3
2.1
3.3
7.4 0.5
8.0 1
6.9
7.9
7
9
14.3 1
16.5 1
13.
10293-2-18P
AID: 1825 | 29/11/2013
(a)
Draw the graph for speed
v
2
against height
h
as shown in Figure (1).
Figure (1)
Observation:
Figure (1) shows an error bar through each point to indicate the range in which it
probably lies. That is, the possible
10293-3-3P
AID: 1825 | 15/11/2013
The towns record of cancer cases for the past 4 years is 20.
Thus, the average number of cancer cases recorded (q) is obtained as follows:
q
20 20
20 4.5
It is almost equal to 16the expected number of cancers.
Hence, t
10293-3-3QC
It is given that the diameter of a circle is
AID: 1825 | 15/11/2013
d 5.0 0.1 cm
.
Then, the uncertainty in the circumference c is given below:
c d
22
0.1
7
3.143 0.1
0.3
The circumference c is computed as follows:
c d c
22
5 0.3
7
3.14 5
10293-3-2QC
AID: 1825 | 15/11/2013
The measure of the quantity x is given below:
x 8.0 0.2
Here, the uncertainty
.
x 0.2
The percentage of the uncertainty
x
is obtained as follows:
x 0.2
100
x 8.0
2.5%
The measure of the quantity y is given below:
y 5.
10293-3-4P
AID: 1825 | 29/11/2013
(a)
The average number of events in time t is calculated using the below formula.
Average number of events in time, t
where, the observed number is denoted as
BySquare-Root Rule for
Counting Experiments.
and the uncer
10293-3-14P
AID: 1825 | 15/11/2013
Let the time of fall of a stone in a well be
Let the depth of the well be
Suppose that
g 9.80 m/s 2
1
d gt 2
2
t 3.0 0.5 sec
.
.
.
The fractional uncertainty of time of fall is,
t 0.5
100
t
3
16.67%
Since
1
2
has no u
10293-3-15P
AID: 1825 | 15/11/2013
(a)
Student A watches the emission of alpha particles for 2 minutes and counts 32 particles.
The uncertainty in Student As measurements is
32 6
.
Thus, the average number of counts measured by Student A is
32 6
.
(b)
Stu
10293-3-18P
AID: 1825 | 15/11/2013
(a)
It is given that
m 18 1 gram
a 5 1 cm
,
b 18 2 cm
,
.
If the uncertainties are not independent,
q a b c
1 2 1
4
Thus,
q 5 18 12 4
35 4 cm
35 cm 10%
Therefore, the value of q is
35 cm 10%
.
If the uncertainties are