Concept explainers
The equilibrium readings of both upper and lower scales.
Answer to Problem 71AP
The lower scale reading is
Explanation of Solution
The weight of the iron block is balanced by the sum of tension on spring and the buoyant force exerted on iron block by the oil when viewed from the upper part of the scale.
Here,
Write the expression for density of iron block.
Here,
Rearrange equation (II) to find
By Archimedes law, volume of iron block dipped in oil is equal to the volume of oil displaced from the jar.
Here,
Write the expression for the buoyant force exerted by the oil on the iron block.
Here,
Rearrange equation (I) to find
Use expression (V) in (VI) to find
Write the expression for force of gravity on iron block.
Here,
Use expression (VIII) in (VII).
Use expression (III) in (IX) to find
Now observe the system from the bottom side of scale. Let
Write the sum of all the vertical forces acting on the system.
Here,
At equilibrium the sum of all vertical forces is equal to zero.
Write the expression for
Here,
Write the expression for
Here,
Use expressions (XIV), (XIII), and (VIII) in expression (XII) and solve for
Conclusion:
Substitute
Substitute
Therefore, the lower scale reading is
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Chapter 14 Solutions
Physics: for Science.. With Modern. -Update (Looseleaf)
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