How Does Immersion Affect Spring Scale Readings?

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SUMMARY

The discussion centers on calculating the forces acting on a submerged metal block and the reading of a spring scale. A 10.5 kg block measuring 12 cm x 10 cm x 10 cm is submerged in water, with the top 5.25 cm below the surface. The force on the top of the block is calculated as 1.0181 kN, while the force on the bottom is 1.0299 kN. The reading of the spring scale is determined by the buoyant force, which equals the weight of the water displaced by the block.

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  • Understanding of fluid mechanics, specifically buoyancy principles.
  • Knowledge of pressure calculations in fluids.
  • Familiarity with the concept of forces acting on submerged objects.
  • Basic understanding of spring scale measurements.
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  • Learn about pressure variations in fluids, particularly in water.
  • Explore the calculation of buoyant force and its impact on submerged objects.
  • Investigate the relationship between mass, volume, and density in fluid contexts.
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This discussion is beneficial for physics students, engineers, and anyone involved in fluid dynamics or related fields, particularly those studying buoyancy and pressure in submerged objects.

jenha14
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A 10.5 kg block of metal measuring 12 cm 10 cm 10 cm is suspended from a scale and immersed in water. The 12.0 cm dimension is vertical and the top of the block is 5.25 cm below the surface of the water.
(a) What are the forces acting on the top and on the bottom of the block? (Use P0 = 1.0130 105 N/m2.)
(b) What is the reading of the spring scale?

ATTEMPT AT SOLUTION
(a) The forces acting on the top of the block is:
(0.1m)*(0.1m)*(P0+1000*9.8*0.0525 N/m^2)
= (1.0130e3+5.1)N = 1.0181e3 N
and on the bottom of the block is:
(0.1m)*(0.1m)*(P0+1000*9.8*0.1725 N/m^2)
= (1.0130e3+16.9)N = 1.0299e3 N

(b) I'm stuck on this one
 
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(b) The block displaces the mass of the water that would have taken that space. Start there.
 

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