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PHYSICS 1
FAP0015
Questions & Answers to Physics I Assignments Chapter 1
11. What, roughly, is the percent uncertainty in the volume of a spherical beach ball whose radius is r = 2.86 ± 0.09 m? Answer: To find the approximate uncertainty in the volume, calculate the volume for the specified radius, the minimum radius, and the maximum radius. Subtract the extreme volumes. The uncertainty in the volume is then half this variation in volume.
3 Vspecified = 4 π rspecified = 4 π ( 2.86 m ) = 9.80 × 101 m3 3 3 3 3 Vmin = 4 π rmin = 4 π ( 2.77 m ) = 8.903 × 101 m3 3 3 3 3 4 4 Vmax = 3 π rmax = 3 π ( 2.95 m ) = 10.754 × 101 m3 3
ΔV =
1 2
(Vmax − Vmin ) = 12 (10.754 × 101 m3 − 8.903 × 101 m3 ) = 0.926 × 101 m3
ΔV Vspecified = 0.926 × 101 m 3 9.80 × 101 m 3 × 100 = 9.418 ≈ 9 %
The percent uncertainty is
19. Express the following sum 1.80 m + 142.5 cm + 5.34 × 10 5 μm. Answer:
with
the
correct
number
of
significant
figures:
To add values with significant figures, adjust all values so that their units are all the same.
1.80 m + 142.5 cm + 5.34 × 105 μ m = 1.80 m + 1.425 m + 0.534 m = 3.759 m = 3.76 m
When adding, the final result is to be no more accurate than the least accurate number used. In this case, that is the first measurement, which is accurate to the hundredths place.
27. Estimate how long it would take one person to mow a football field using an ordinary home lawn mower. Assume the mower moves with a 1 km h speed, and has a 0.5 m width. Answer: The dimension of a football field (FIFA specification) is 64 meters by 100 meters. The mower has a cutting width of 0.5 meters. Thus the distance the mower has to move is
d=
Area of field 6400 m 2 = = 12800 m = 12.8 km Width of mower 0.5 m
At a speed of 1 km/hr, then it will take about 12.8 h to mow the field.
51. The diameter of the Moon is 3480 km. What is the volume of the Moon? How many Moons would be needed to create a volume equal to that of Earth?
FAP0015
Questions & Answers to Physics I Assignments Chapter 1
11. What, roughly, is the percent uncertainty in the volume of a spherical beach ball whose radius is r = 2.86 ± 0.09 m? Answer: To find the approximate uncertainty in the volume, calculate the volume for the specified radius, the minimum radius, and the maximum radius. Subtract the extreme volumes. The uncertainty in the volume is then half this variation in volume.
3 Vspecified = 4 π rspecified = 4 π ( 2.86 m ) = 9.80 × 101 m3 3 3 3 3 Vmin = 4 π rmin = 4 π ( 2.77 m ) = 8.903 × 101 m3 3 3 3 3 4 4 Vmax = 3 π rmax = 3 π ( 2.95 m ) = 10.754 × 101 m3 3
ΔV =
1 2
(Vmax − Vmin ) = 12 (10.754 × 101 m3 − 8.903 × 101 m3 ) = 0.926 × 101 m3
ΔV Vspecified = 0.926 × 101 m 3 9.80 × 101 m 3 × 100 = 9.418 ≈ 9 %
The percent uncertainty is
19. Express the following sum 1.80 m + 142.5 cm + 5.34 × 10 5 μm. Answer:
with
the
correct
number
of
significant
figures:
To add values with significant figures, adjust all values so that their units are all the same.
1.80 m + 142.5 cm + 5.34 × 105 μ m = 1.80 m + 1.425 m + 0.534 m = 3.759 m = 3.76 m
When adding, the final result is to be no more accurate than the least accurate number used. In this case, that is the first measurement, which is accurate to the hundredths place.
27. Estimate how long it would take one person to mow a football field using an ordinary home lawn mower. Assume the mower moves with a 1 km h speed, and has a 0.5 m width. Answer: The dimension of a football field (FIFA specification) is 64 meters by 100 meters. The mower has a cutting width of 0.5 meters. Thus the distance the mower has to move is
d=
Area of field 6400 m 2 = = 12800 m = 12.8 km Width of mower 0.5 m
At a speed of 1 km/hr, then it will take about 12.8 h to mow the field.
51. The diameter of the Moon is 3480 km. What is the volume of the Moon? How many Moons would be needed to create a volume equal to that of Earth?