/*! 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 92 A block of wood, with density \(... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 92

A block of wood, with density \(780 \mathrm{kg} / \mathrm{m}^{3},\) has a cubic shape with sides \(0.330 \mathrm{m}\) long. A rope of negligible mass is used to tie a piece of lead to the bottom of the wood. The lead pulls the wood into the water until it is just completely covered with water. What is the mass of the lead? [Hint: Don't forget to consider the buoyant force on both the wood and the lead.]

Short Answer

Expert verified
Answer: The mass of the lead is approximately 8.238 kg.

Step by step solution

01

Calculate the volume and mass of the wooden cube.

First, we need to calculate the volume of the wooden cube. The wooden cube has a side length of 0.330 m. Therefore, the volume (V_wood) of the wooden cube can be calculated as: V_wood = \(0.330^3\) = \((0.330\,\mathrm{m})^3\) = \(0.035937\,\mathrm{m^3}\) Next, we will calculate the mass of the wooden cube using the density. The mass (m_wood) of the wooden cube can be calculated as: m_wood = density_wood 脳 V_wood = \(780\,\mathrm{kg/m^3} \times 0.035937\,\mathrm{m^3}\) = \(28.03086\,\mathrm{kg}\)
02

Calculate the total buoyant force.

As the wooden cube is fully submerged in water, the buoyant force (F_B) will be equal to the weight of the displaced water. We know that the buoyant force is given by F_B = m_water 脳 g, where m_water is the mass of the displaced water and g is the acceleration due to gravity (approximately \(9.81\,\mathrm{m/s^2}\)). The density of water (蟻_water) is \(1000\,\mathrm{kg/m^3}\), so we can calculate the mass of the displaced water (m_water) as: m_water = 蟻_water 脳 V_wood = \(1000\,\mathrm{kg/m^3} \times 0.035937\,\mathrm{m^3}\) = \(35.937\,\mathrm{kg}\) Now, we can calculate the total buoyant force (F_B) as: F_B = m_water 脳 g = \(35.937\,\mathrm{kg} \times 9.81\,\mathrm{m/s^2}\) = \(352.5933\,\mathrm{N}\)
03

Calculate the weight of the lead.

As the wooden cube and lead are in equilibrium, the total downward force (weight of the wooden cube and lead) must be equal to the total upward force (buoyant force). Therefore, we can write the equation as: W_wood + W_lead = F_B Where W_wood is the weight of the wooden cube given by m_wood 脳 g and W_lead is the weight of lead that we are looking for. Now, we can solve for W_lead as: W_lead = F_B - W_wood = \(352.5933\,\mathrm{N} - (28.03086\,\mathrm{kg} \times 9.81\,\mathrm{m/s^2})\) = \(80.81861\,\mathrm{N}\)
04

Calculate the mass of the lead.

Finally, we can determine the mass of the lead (m_lead) using the weight calculated in the previous step. As weight = mass 脳 gravity, we can write: m_lead = W_lead / g = \(80.81861\,\mathrm{N} / 9.81\,\mathrm{m/s^2}\) = \(8.238\,\mathrm{kg}\) The mass of the lead is approximately 8.238 kg.

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

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 \(W / F_{\mathrm{a}}\).
If the average volume flow of blood through the aorta is $8.5 \times 10^{-5} \mathrm{m}^{3} / \mathrm{s}\( and the cross-sectional area of the aorta is \)3.0 \times 10^{-4} \mathrm{m}^{2},$ what is the average speed of blood in the aorta?
An air bubble of 1.0 -mm radius is rising in a container with vegetable oil of specific gravity 0.85 and viscosity \(0.12 \mathrm{Pa} \cdot \mathrm{s} .\) The container of oil and the air bubble are at \(20^{\circ} \mathrm{C} .\) What is its terminal velocity?
The diameter of a certain artery has decreased by \(25 \%\) due to arteriosclerosis. (a) If the same amount of blood flows through it per unit time as when it was unobstructed, by what percentage has the blood pressure difference between its ends increased? (b) If, instead, the pressure drop across the artery stays the same, by what factor does the blood flow rate through it decrease? (In reality we are likely to see a combination of some pressure increase with some reduction in flow.)

Estimate the average blood pressure in a person's foot, if the foot is \(1.37 \mathrm{m}\) below the aorta, where the average blood pressure is 104 mm Hg. For the purposes of this estimate, assume the blood isn't flowing.
See all solutions

Recommended explanations on Physics Textbooks

Solid State Physics

Read Explanation

Engineering Physics

Read Explanation

Kinematics Physics

Read Explanation

Rotational Dynamics

Read Explanation

Turning Points in Physics

Read Explanation

Geometrical and Physical Optics

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.