/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 31 (a) What is the buoyant force on... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 31

(a) What is the buoyant force on \(0.90 \mathrm{kg}\) of ice floating freely in liquid water? (b) What is the buoyant force on \(0.90 \mathrm{kg}\) of ice held completely submerged under water?

Short Answer

Expert verified
Q: Find the buoyant force acting on 0.90 kg of ice floating in liquid water and when the same ice is submerged completely underwater. A: The buoyant force acting on 0.90 kg of ice floating freely in liquid water and when the same ice is submerged completely underwater is the same and equal to the weight of the displaced water, which can be calculated using the steps provided in the solution.

Step by step solution

01

Calculate the volume of the ice

To calculate the volume of the ice, we can use its mass and density following the formula: Volume = Mass / Density The mass of the ice is \(0.90 \mathrm{kg}\), and the density of ice is \(920 \mathrm{kg/m^3}\). Therefore, the volume of the ice is: \(V_{ice} = \frac{0.90}{920} \mathrm{m^3}\)
02

Calculate the weight of the displaced water

Since the ice displaces an equal amount of water, we can now calculate the weight of the water displaced when submerged. To do this, we need to find the mass of the displaced water and then multiply by the acceleration due to gravity (\(g = 9.81 \mathrm{m/s^2}\)). We first find the mass of the displaced water by multiplying the volume of the ice by the density of the water: Mass of displaced water = Volume of ice 脳 Density of water \(M_{water} = V_{ice} 脳 1000 \mathrm{kg/m^3}\) Now, we can find the weight of the displaced water by multiplying the mass with the acceleration due to gravity: \(W_{water} = M_{water} 脳 9.81 \mathrm{N}\)
03

Find the buoyant force

According to Archimedes' principle, the buoyant force is equal to the weight of the displaced water. Thus: \(F_{buoyant} = W_{water}\) Now, we can calculate the buoyant force for both cases (a) and (b). Since the ice displaces an equal amount of water in both cases, the buoyant force will have the same value. Calculating: \(a)\) \(F_{buoyant\,a} = W_{water}\) \(b)\) \(F_{buoyant\,b} = W_{water}\) So the buoyant force acting on \(0.90 \mathrm{kg}\) of ice floating freely in liquid water and when the same ice is submerged completely underwater is the same and equal to the weight of the displaced water, which can be calculated using the steps provided.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A nozzle of inner radius \(1.00 \mathrm{mm}\) is connected to a hose of inner radius \(8.00 \mathrm{mm} .\) The nozzle shoots out water moving at $25.0 \mathrm{m} / \mathrm{s} .$ (a) At what speed is the water in the hose moving? (b) What is the volume flow rate? (c) What is the mass flow rate?
At the surface of a freshwater lake the air pressure is 1.0 atm. At what depth under water in the lake is the water pressure 4.0 atm?
A container is filled with gas at a pressure of $4.0 \times 10^{5} \mathrm{Pa}\( The container is a cube, \)0.10 \mathrm{m}$ on a side, with one side facing south. What is the magnitude and direction of the force on the south side of the container due to the gas inside?
In a hydraulic lift, the radii of the pistons are \(2.50 \mathrm{cm}\) and $10.0 \mathrm{cm} .\( A car weighing \)W=10.0 \mathrm{kN}$ is to be lifted by the force of the large piston. (a) What force \(F_{\mathrm{a}}\) must be applied to the small piston? (b) When the small piston is pushed in by $10.0 \mathrm{cm},$ how far is the car lifted?(c) Find the mechanical advantage of the lift, which is the ratio \(W / F_{\mathrm{a}}\).
A water tower supplies water through the plumbing in a house. A 2.54 -cm- diameter faucet in the house can fill a cylindrical container with a diameter of \(44 \mathrm{cm}\) and a height of \(52 \mathrm{cm}\) in 12 s. How high above the faucet is the top of the water in the tower? (Assume that the diameter of the tower is so large compared to that of the faucet that the water at the top of the tower does not move. \()\)
See all solutions

Recommended explanations on Physics Textbooks

Kinematics Physics

Read Explanation

Physics of Motion

Read Explanation

Electricity

Read Explanation

Astrophysics

Read Explanation

Fields in Physics

Read Explanation

Work Energy and Power

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.