A platinum sphere with radius 0.0179 m is totally immersed in mercury. Find the weight of the sphere, the buoyant force acting on the sphere, and the sphere's apparent weight. The densities of platinum and mercury are 2.14 x 10ª kg/m³ and 1.36 x 104 kg/m², respectively.

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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### Problem Description

A platinum sphere with a radius of 0.0179 m is totally immersed in mercury. Determine the following:

1. The weight of the sphere.
2. The buoyant force acting on the sphere.
3. The sphere's apparent weight.

### Given Data

- **Radius of the sphere:** 0.0179 m
- **Density of platinum:** \(2.14 \times 10^4 \, \text{kg/m}^3\)
- **Density of mercury:** \(1.36 \times 10^4 \, \text{kg/m}^3\)

### Variables

- **Weight:** [Input Box] N
- **Buoyant Force:** [Input Box] N
- **Apparent Weight:** [Input Box] N

### Explanation

This problem involves calculating the weight and buoyant force of a submerged object, as well as its apparent weight. The weight of the sphere is the gravitational force, found using the sphere's volume and density. The buoyant force is the force exerted by the fluid (mercury) on the sphere, calculated using Archimedes’ principle. The apparent weight is the actual weight minus the buoyant force.

### Note

Remember to use the formula for the volume of a sphere and apply the principles of buoyancy to solve this problem.
Transcribed Image Text:### Problem Description A platinum sphere with a radius of 0.0179 m is totally immersed in mercury. Determine the following: 1. The weight of the sphere. 2. The buoyant force acting on the sphere. 3. The sphere's apparent weight. ### Given Data - **Radius of the sphere:** 0.0179 m - **Density of platinum:** \(2.14 \times 10^4 \, \text{kg/m}^3\) - **Density of mercury:** \(1.36 \times 10^4 \, \text{kg/m}^3\) ### Variables - **Weight:** [Input Box] N - **Buoyant Force:** [Input Box] N - **Apparent Weight:** [Input Box] N ### Explanation This problem involves calculating the weight and buoyant force of a submerged object, as well as its apparent weight. The weight of the sphere is the gravitational force, found using the sphere's volume and density. The buoyant force is the force exerted by the fluid (mercury) on the sphere, calculated using Archimedes’ principle. The apparent weight is the actual weight minus the buoyant force. ### Note Remember to use the formula for the volume of a sphere and apply the principles of buoyancy to solve this problem.
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