Chapter 12: Problem 30
You are preparing some apparatus for a visit to a newly discovered planet Caasi having oceans of glycerine and a surface acceleration due to gravity of 5.40 m/s\(^2\). If your apparatus floats in the oceans on earth with 25.0% of its volume submerged, what percentage will be submerged in the glycerine oceans of Caasi?
Short Answer
Step by step solution
Understand Archimedes' Principle
Calculate Submersion on Earth
Expression for Weight of Apparatus
Calculate Submersion on Caasi
Final Calculation
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Buoyancy and Its Role in Floating
According to Archimedes' Principle, the buoyant force on an object submerged in fluid is equal to the weight of the fluid that the object displaces. If an object is partially submerged, it means that it displaces a volume of fluid whose weight equals the object's weight.
This principle helps us calculate how much of an object remains underwater based on its density and the fluid's density. If the buoyant force is greater than the object's weight, it will float. If lesser, it will sink. It’s fascinating to see how this principle applies to different fluids and gravitational conditions – like in the scenario with the planet Caasi.
Understanding Fluid Displacement
To determine how much of an object is submerged, you must consider the object's weight and the fluid's density. On Earth, the apparatus displaced enough water such that 25% of its volume was submerged, revealing the exact point where the force of gravity and the buoyancy force balance out.
- Denser objects displace more fluid to achieve buoyancy.
- If the fluid is denser, less volume needs to be displaced to equal the object's weight.
- This concept is crucial when calculating submersion percentages in different fluids or planets.
Gravity Effects on Buoyancy
The surface gravity on planets affects how objects float, as seen in the planet Caasi with a lower gravity than Earth (5.4 m/s\(^2\) compared to 9.81 m/s\(^2\)). This lower gravitational pull means that objects need to displace a relatively smaller volume of more dense fluid, like glycerine, to balance their weight.
- Stronger gravity would require more displaced volume to achieve buoyancy.
- The relationship between gravity and buoyancy forces determines submersion levels.
- Understanding these gravity effects helps in predicting how objects behave in different environments.