5) A solid aluminum block weighs 79 N in air. a) What is its volume? b) The bloc
ID: 1285468 • Letter: 5
Question
5) A solid aluminum block weighs 79 N in air.
a) What is its volume?
b) The block is suspended from a rope and totally immersed in water. What is the tension in the rope, which is the apparent weight of the block in water?
6) A rock is suspended by a light string. When the rock is in air, the tension in the string is 39.2 N. When the rock is totally immersed in water, the tension is 28.4 N. When the rock is totally immersed in an unknown liquid, the tension is 18.6 N. What is the density of the unknown liquid?
7) A cube of wood of side 25.0 cm and density 625 kg/m3 floats on water.
a) What is the distance from the horizontal top surface of the cube to the water level?
b) What mass of lead should be placed on top of the cube so that the top of the cube will be just level with the water surface?
Explanation / Answer
1)
Weight of aluminum ingot(in air) =W=72 N
Density of aluminum = d =2700 kg/m^3
Mass = m =weight (W) /acceleration of gravity(g)
m=W/g
Volume= v = mass (m) / density(d)=m/d
Volume= v = W/gd = 72/9.8*2700
Volume= v = 0.0027 m^3
Volume of aluminum ingot is 0.0027 m^3
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the tension in the rope (the apparent weight of the ingot in water = T = wt of ingot in air - buoyant force(upthrust)
the tension in the rope = T = wt in air - wt of equal volume of water
T =W - vpg
where p is density of water , p = 1000 kg/m^3
T =72 -0.0027*1000*9.8=72 - 26.46=45.54 N
The tension in the rope (the apparent weight of the ingot in water) is 45.54 N
2)
From the first two you can get the volume of the rock. The weight is 39.2 N, ignoring the buoyancy of air.
The buoyancy is 39.2
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