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016 (part 1 of 2) 10.0 points

A beaker of mass 1.3 kg containing 2.5 kg of
water rests on a scale. A 3.4 kg block of a
metallic alloy of density 3700 kg/m³ is sus-
pended from a spring scale and is submerged
in the water of density 1000 kg/m³ as shown
in the figure.
3.4 kg
What does the hanging scale read? The
acceleration of gravity is 9.8 m/s².
Answer in units of N.
017 (part 2 of 2) 10.0 points
What does the lower scale read?
Answer in units of N.

1 Answer

3 votes

Answer: 0.85 N

Explanation: We can solve this problem using the principles of buoyancy and Newton's laws.

First, we need to find the buoyant force acting on the metallic alloy block. The buoyant force is equal to the weight of the water displaced by the block, which can be calculated using the block's volume and the density of water:

V = m_block / ρ_block = 3.4 kg / 3700 kg/m³ = 0.0009189 m³

F_buoyant = ρ_water x g x V = 1000 kg/m³ x 9.8 m/s² x 0.0009189 m³ = 8.96 N

So the buoyant force acting on the metallic alloy block is 8.96 N.

Next, we can calculate the tension force in the spring scale attached to the block. Since the block is in static equilibrium, the tension force must be equal in magnitude and opposite in direction to the weight of the block plus the buoyant force:

Tension force = weight of block + buoyant force

Tension force = m_block x g + F_buoyant

Tension force = 3.4 kg x 9.8 m/s² + 8.96 N = 42.04 N

So the hanging scale reads 42.04 N.

Finally, we can find the reading of the lower scale. The lower scale measures the weight of the beaker and the water in it, minus the buoyant force acting on the beaker. The weight of the beaker and the water is:

weight of beaker + weight of water = m_beaker x g + m_water x g

weight of beaker + weight of water = 1.3 kg x 9.8 m/s² + 2.5 kg x 9.8 m/s² = 35.35 N

The buoyant force acting on the beaker can be calculated using the volume of water displaced by the beaker:

V = m_water / ρ_water = 2.5 kg / 1000 kg/m³ = 0.0025 m³

F_buoyant = ρ_water x g x V = 1000 kg/m³ x 9.8 m/s² x 0.0025 m³ = 24.5 N

So the reading of the lower scale is:

Reading of lower scale = weight of beaker + weight of water - buoyant force

Reading of lower scale = 35.35 N - 24.5 N = 10.85 N

Therefore, the lower scale reads 10.85 N.

User Radek Simko
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