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A beaker of mass 1 kg containing 2.6 kg of water rests on a scale. A 3 kg block of a metallic

alloy of density 4500 kg/m3
is suspended from
a spring scale and is submerged in the water
of density 1000 kg/m3
as shown in the figure.
3 kg
What does the hanging scale read? The
acceleration of gravity is 9.8 m/s
2
.
Answer in units of N.
017 (part 2 of 2) 10.0 points
What does the lower scale read?
Answer in units of N.

User Mbenhalima
by
7.4k points

1 Answer

5 votes

Answer:

We need to find the force exerted by the water on the beaker,

This force will be subtracted from the reading of the top scale and be added to the force on the bottom scale - this is the buoyant force.

That is, the bottom scale will support an additional weight equal to the weight of the water displaced by the block and this force will then be subtracted from the top spring scale,

ρ = 1000 kg/m^3 is the mass density of the water

Mb = ρb Vb for the mass of the block

Vb = 3 kg / 4500 kg/m^3 = 6.67E-4 m^3 for the volume of the block

Mw = 1000 kg/m^3 * 6.67E-4 m^3 = .667 kg for the mass of the water displaced

Ww = .667 kg * 9.80 m/s^2 = 6.64 N weight of water displaced

Wo = 3 kg * 9.80 m/s^2 = 29.4 N original reading of spring scale

29.4 - 6.64 = 22.8 N weight of spring scale after immersion

Wbo = (1 + 2.6) kg * 9.80 m/s^2 = 35.3 N original weight on bottom scale

Wbf = (35.3 + 6.64) N = 41.9 N weight on bottom scale after providing support for metal block

User Babul
by
6.4k points