#1. For each set of values below order them from largest to smallest:
• Convert all values to the units indicated with a “*” so that you can compare the values.
Show your work using the conversion factor method shown in class. Make sure that
you show your units and how they cancel.
• Give your answer to each part by ranking the values from the highest to the lowest.
Write all answers in scientific notation rounded to 2 significant figures.
a) 3.0 x 108 m/s, 89.6 km/min, 7.5 x 1020 nm/week and 9200 miles/hr (*mi/hr)
b) 1300 Newtons, 240 pounds (lb), 4.63 x 107 dynes (*N)
a) 3.00E+08 m/s
Largest
6.71E+08 mi/hr
7.50E+20 nm/wk
2.77E+06 mi/hr
9200 mi/hr
9.20E+03 mi/hr
Smallest
89.6
km/min
3.34E+03
mi/hr
b)
Largest
1300 N
1.30E+03 N
240 lb
1.07E+03 N
Smallest
4.63E+07
dynes
4.63E+02 N
23. One cubic centimeter (1.0 cm3) of water has a mass of 1.0 × 10–3 kg. (a) Determine the mass of 1.0 m3 of water. (b) Assuming that biological substances are 98% water, estimate the masses of a cell with a diameter of 1.0 μm, a human kidney, and a fly. Take a kidney to be roughly a sphere with a radius of 4.0 cm and a fly to be roughly a cylinder 4.0 mm long and 2.0 mm in diameter. 1.23
(a)
⎛ 1.0 ×10 −3 kg ⎞
3
mass = ( density )( volume ) = ⎜
⎟ (1.0 m )
3
1.0
cm
⎝
⎠
3
⎛ 10 2 cm ⎞
kg ⎞
⎛
3
= ⎜ 1.0 × 10 −3
1.0 m 3 ) ⎜
⎟ = 1.0 × 10 kg
3 ⎟(
cm ⎠
⎝
⎝ 1m ⎠
(b) As rough calculation, treat as if 100% water.
kg ⎞ 4
⎛
cell: mass = density × volume= ⎜ 103 3 ⎟ π 0.50 × 10−6 m
m ⎠3
⎝
(
)
3
= 5.2 × 10 −16 kg
kg ⎞ 4
⎛
kidney: mass = density × volume = ⎜ 103 3 ⎟ π 4.0 × 10−2 m
m ⎠3
⎝
(
(
fly: mass = density × volume = ( density ) π r 2 h
)
3
= 0.27 kg
)
2
kg ⎞
⎛
= ⎜ 103 3 ⎟ π (1.0 × 10−3 m ) ( 4.0 × 10−3 m ) = 1.3 × 10 −5 kg
m ⎠
⎝
38. A surveyor measures the distance across a straight river by the following method: Starting directly across from a tree on the opposite bank, he walks 100 m along the riverbank to establish a baseline. Then he sights across to the tree. The angle from his baseline to the tree is 35.0°. How wide is the river? 1.38
Using the sketch at the right:
w
= tan 35.0° , or
100 m
Tree
River
w
w = (100 m ) tan 35.0° = 70.0 m
100 m
35.0°