Module'1'–'Fluids:'Quiz'2a'
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A!cork!has!a!volume!of!4.25!cm3.!!!The!density!of!cork!is!207!kg/m3.!!!
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a. Draw!a!FBD!to!show!the!forces!acting!on!the!cork.!
!
b. What!volume!of!the!cork!is!beneath!the!surface!when!the!cork!floats!in!
water?!!!
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c. What!downward!force!is!needed!to!completely!submerge!the!cork?!
!
!
!
!
Answer:!
!
!
!
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!
!
FB
a. !
w
F
b. The!floating!cork!will!displace!a!volume!of!water!equal!to!its!own!weight.!!We!can!use!the!
density!of!the!cork!to!find!its!weight.!!With!the!weight,!we!can!then!calculate!the!volume!of!
water!displaced.!
w = ρVg
!
⎛
kg ⎞
= ⎜ 207 3 ⎟ 4.25 x 10−6 m 3
m ⎠
⎝
(
FB = ρVg
V=
FB
ρg
)⎛⎜⎝ 9.8 sm ⎞⎟⎠
= 8620 x 10−6 N
2
= 8.62 x 10−3 N !
⎛
⎞
⎜
⎟
kg m ⎜
1
⎟
= 8.62 x 10−3
m ⎞ ⎟!
s2 ⎜
3 kg ⎛
⎜ 1.00 x 10 3 ⎜ 9.8 2 ⎟ ⎟
m ⎝
s ⎠⎠
⎝
!
V = 0.880 x 10−6 m3
=
8.80 x 10−7 m3
FB − F − w = 0
F = FB − w
!
c. The!sum!of!the!forces!must!be!zero:!
!
!
!
We’ve!already!calculated!the!weight!of!the!cork,!w.!
!
FB = ρVg
= 1.0 x 104
(
)
kg
m
−6
3 ⎛
4.25
x
10
m
9.8
⎜
m3
s2
⎝
'
!
!
FB = 41.6 x 10−2 N = 4.16 x 10−2 N
⎞
⎟
⎠
!
Now'we'can'find'the'force'
F = FB − w = 4.16 x 10−2 N − 8.62 x 10−3 N !
F = 4.16 x 10−2 N − 0.862 x 10−2 N
=
3.30 x 10−2 N
!