1. A hollow glass-stopper was found to weigh 27.5g in air and 14.7g in
paraffin oil. What is the volume of cavity?
(Relative density: glass-2.5, paraffin oil-0.8)
(Answer: 5 cm^3)
2. A piece of copper of mass 0.2kg and a piece of iron are fastened to the
ends of a string passing over a pulley and hang in equilibrium when both are
completely immersed in water. Find the weight of the piece of the iron.
(Relative density of copper:8.9, Relative density of water :7.2)
(Answer: 0.262 kg)
Please show me the full steps of calculation. Answers are attached for
reference. Thx.
Physics--principle of archimedes
2008-11-17 3:06 am
回答 (2)
2008-11-17 5:51 am
✔ 最佳答案
1. Upthrust acting on the glass-stopper = (27.5-14.7) gf = 12.8 gf[gf denotes gram-force, i.e. the weight given by a mass of 1 gram]
Weight of paraffin oil displaced = 12.8 gf
Mass of paraffin oil displaced = 12.8 g
Volume of paraffin oil displace = 12.8/0.8 cm3 = 16 cm3
Since volume of glass in the stopper = 27.5/2.5 cm3 = 11 cm3
(2.5 g/cm3 is the density for crown glass)
Volume of cavity in the glass stopper = (16-11) cm3 = 5 cm3
2. Volume of copper piece = 200/8.9 cm3 = 22.472 cm3
Upthrust acting on the copper piece = (200/8.9) x 1 = 22.472 gf
hence, apparent weight of copper piece = (200 - 22.472) gf = 177.528 gf
Thus, the apparent weight of iron piece must be equal to the apparent weight of the copper in order to attain equilibrium
i.e. apparent weight of iron piece = 177.528 gf
Let M be the mass of the iron piece
volume of iron piece = M/7.2 cm3
upthrust acting on the iron piece = M/7.2 gf
apparent weight of iron piece = (M-M/7.2) gf = 0.8611M gf
hence, 177.528 = 0.8611M
M = 206 g
Upthrust acting on the iron piece =
2008-11-17 5:30 am
1. Let V = volume of glass-stopper
upward thrust = vol of paraffin oil displaced = 0.8 xV
upward thrust + wt in oil = wt in air
0.8V+14.7=27.5
V=16cc
Actual vol of pure glass w/o cavity = 27.5/2.5 = 11 cc
vol of cavity=16-11= 5 cc
2. relative density of water = 1, iron = 7.2
vol copper = 200/8.9 cc
wt of water displaces by copper = 22.47g
force on pulley by copper = 200 - 22.47 =177.53g
Let mass of iron = m
vol iron = m/7.2 cc
wt of water displaces by iron = m/7.2 g
force on pulley by iron = m-m/7.2 g
hang in equilibrium --> m- m/7.2 = 177.53
m = 206.1 g = 0.206 kg
upward thrust = vol of paraffin oil displaced = 0.8 xV
upward thrust + wt in oil = wt in air
0.8V+14.7=27.5
V=16cc
Actual vol of pure glass w/o cavity = 27.5/2.5 = 11 cc
vol of cavity=16-11= 5 cc
2. relative density of water = 1, iron = 7.2
vol copper = 200/8.9 cc
wt of water displaces by copper = 22.47g
force on pulley by copper = 200 - 22.47 =177.53g
Let mass of iron = m
vol iron = m/7.2 cc
wt of water displaces by iron = m/7.2 g
force on pulley by iron = m-m/7.2 g
hang in equilibrium --> m- m/7.2 = 177.53
m = 206.1 g = 0.206 kg
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