Lab_0
New Problems
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Make sure to calculate your answers in SI units unless specified otherwise .
1) You measure a distance as ( +- )
m
. What is the relative error ? (See
equation (2) in "Error and Uncertainty" ("EU").
) Indicate with a positive (negative) sign whether the relative error is (not) equal to the percentage error.
2) You have measured the 5 time (
t
) values , , , 5.8 and 7.4
seconds
. Calculate the absolute error of the average time.(See
equations (5) and (5") in "EU"
.)
3) You measure the width
w
and length
l
of a rectangle to be
w
= ( +- )
cm
and
l
= ( +-0.11)
cm
. Calculate the relative errror of the perimeter of the rectangle. (Hint: write down the formula for half of the circumference (
C
) in terms of
w
and
l
, 1/2
C
=
w + l
and use
equation (6) in "EU"
to calculate the absolute error of 1/2
C.
Then use
equation (2) in "EU"
to convert to the relative error of 1/2
C
, which is asked for.
Equation (3) in "EU"
tells you that the relative error of 1/2
C
and
C
are the same, since
C
is multiplied by the constant factor 1/2.) Indicate with a positive (negative) sign whether the abslolute error on twice the perimeter is (twice) as large as the absolute error on the perimeter.
4) Assume that the error in the quantity
B
is the fraction of the error in
A
. You have a derived quantity
S=A+B
and want to calculate its error
D
S
. You reason that, since the error in
B
is only a fraction of the error in
A
, you simply neglect the error in
B
. By how much deviates the error
D
S,
calculated with this neglection, from the correctly calculated error
D
S
? Give your answer in the form of the fraction |Correct-approximate|/Correct, that is the deviation given as a fraction of the correctly calculated error
D
S
. (Hint: you don't need to know the value of
D
A
, since it will drop out in the ratio. Use
equation (6) in "EU"
to write the absolute error of
S
in terms of the absolute errors
D
A
and
D
B. Substitute for
D
B the given fraction times
D
A
. Calcultae the ratio (Correct-approximate)/Correct. Indicate with a positive (negative) sign whether the fraction you calculated is less (greater) than the given fraction above.
5) You measure the width
w
and length
l
of a rectangle to be
w
= ( +- )
cm
and
l
= ( +-0.11)
cm
. Calculate the absolute errror of the area of the rectangle in
cm
2
. (Hint: write down the formula for the area (
A
) in terms of
w
and
l
,
A = w * l
and use
equation (7) in "EU"
to calculate the relative error of the area
A
. Then use
equation (4) in "EU"
to convert to the absolute error of
A
, which is asked for.) Indicate with a positive (negative) sign whether the relative error on twice the area is twice as large as the (equal to the ) relative error on the area.
6) You measure a time (
t
) value of ( +- )
s
. You need to evaluate the error of the quantity 3
t
. Calulate its absolute error. (Hint: Use
equation (8) in "EU"
to calculate the relative error of
t
.
Equation (3)
in "EU"
tells you that the relative error of
t
is equal to the relative error of 3
t
. use
equation (2) in "EU"
to convert to the absolute error of 3
t
.)
Once you have submitted your answers for grading by clicking the grade button, you
cannot resubmit answers
for the same Problem Set--you must use the 'New Problems' button first.
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