Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

The roof over a $9.0-\mathrm{m} \times 10.0-\mathrm{m}$ room in a school has a totalmass of $13,600 \mathrm{kg} .$ The roof is to be supported by vertical wooden $" 2 \times 4 \mathrm{s}^{\prime \prime}$ (actually about 4.0 $\mathrm{cm} \times 9.0 \mathrm{cm} )$ equallyspaced along the 10.0 -m sides. How many supports are required on each side, and how far apart must they be?Consider only compression, and assume a safety factor of $12 .$

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Jayashree Behera

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Physics 101 Mechanics

Chapter 12

Static Equilibrium; Elasticity and Fracture

Equilibrium and Elasticity

University of Michigan - Ann Arbor

Hope College

McMaster University

Lectures

04:12

In physics, potential energy is the energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors. The unit for energy in the International System of Units is the joule (J). One joule can be defined as the work required to produce one newton of force, or one newton times one metre. Potential energy is the energy of an object. It is the energy by virtue of an object's position relative to other objects. Potential energy is associated with restoring forces such as a spring or the force of gravity. The action of stretching the spring or lifting the mass is performed by a force which works against the force field of the potential. The potential energy of an object is the energy it possesses due to its position relative to other objects. It is said to be stored in the field. For example, a book lying on a table has a large amount of potential energy (it is said to be at a high potential energy) relative to the ground, which has a much lower potential energy. The book will gain potential energy if it is lifted off the table and held above the ground. The same book has less potential energy when on the ground than it did while on the table. If the book is dropped from a height, it gains kinetic energy, but loses a larger amount of potential energy, as it is now at a lower potential energy than before it was dropped.

04:17

09:35

The roof over a 9.0-m $\ti…

02:49

A tunnel of length $L=200 …

08:23

A tunnel of length $L=150 …

04:06

A tunnel $150 \mathrm{~m}…

03:38

05:01

Roof of house in wind The …

03:07

The mass of the roof of a …

01:58

A bronze rod fixed to a ce…

02:25

The construction of a flat…

full boost. So we know that stress is equal to the force which is here. The Lord force over area and hit here. Idiom ins Video on this is equal to compressive strength over the safety factor and since the Lord force only guns from the weight off the roof so we substitute wait here in place off force. The weight is mass times gravity on area is basically the my application off the dimensions which are Siegel Point. It's just rated area for now began substitute That may lose later on DDE. Look a lot more. Think that area is area off all the supports, which means that the total area will be equal to number off supports. It's calling. It's been ordered by this hash sign. Dines idea for one support. So this is the total area that is equal to the town here. This means that number off supports is equal. Do the week it is mg times 60 factor over complicity Strength gyn's You need a sorry area par support, which is 1/4 e one. Now let's plug the values into the secretion, so we have mg. With this mass times, gravity is amasses 1.36 Time tempted by four Katie gravity is 9.8. Meet up. A second Scotch safety factor is given to be 12 years. The compressive strength is 35 dimes tend to the bar, six Neutron bomb meter squared and then we have area for one support, which is my application off. Their dimensions with is equal to 0.4 meter times. Cedar 0.9 meters actually convert the units in tow meters to be consistent with the units. Now we solve this to find the number off supports, which comes out to be 12.69 now. This is strange because in number should not be affection are there should not be any decimal point here. So since there are, these are more than 12 supports and to have since there are to be more than 12 supports and to have the same same number off supports on each side, so there will be 14 supports. This means that there are seven supports on each side for some board on eat side this equal toe seven. Therefore, there will be six support to support spans, support to support spans, and each off these will be given by spacing. It's will equal do then May does or were the gaps It is six. Therefore, this is equal door 1.66 meters. That's right, Old gap. So the spacing is 1.66 meter. What gap? Let me just repeat how they arrived from here to here. So we know that there should be more than 12 supports on. If you look at this value, this is more than to us, but not hurting. So if we let's take a round off off this and we say that this is equal to 30. But this is aren't on dhe. One more condition is that we should have the same number off supports on either side. Therefore instead off approximately two tarting it will not be a good idea. The approximate to 14. Now, this is even on this will work. And this one gave us seven supports on each side. So that's how we arrive at ah, for David and crying in the doll gap. Well, uh, the spacing. Oh, here

View More Answers From This Book

Find Another Textbook

00:59

true or false converging continental crust or plates result in collision zon…

02:07

how do you compare the action and reactions forces in termsof magnitude and …

01:34

how does a players discussion making affect the success of any game or sport…

03:03

how can you say that a person is physical fit?

00:43

write 3 things that you want to know more about sports

02:16

Which pair refers to the deformation of two blocks that tend to pull apart?A…

02:39

Plants make food by absorbing water and carbon dioxide. Which of the followi…

02:03

How many joules of work are done on an object when a force of 10 N pushes it…

01:41

1. What do you think will happen when ions of opposite charge(s) are attract…