1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lisov135 [29]
3 years ago
5

A 12.0-cm long cylindrical rod has a uniform cross-sectional area A = 5.00 cm2. However, its density increases linearly from 2.6

0 g/cm3 at one end to 18.5 g/cm3 at the other end. This linearly increasing density can be described using the equation ???? = B + Cx. (a) Find the constants B and C required for this rod, assuming the low-density end is placed at x = 0 cm and the high-density end is at x = 12 cm. (b) The mass of the rod can be found using:m=dV=Adx=(B+Cx)Adx
Physics
1 answer:
andriy [413]3 years ago
7 0

Answer:

(a) The constants required describing the rod's density are B=2.6 and C=1.325.

(b) The mass of the road can be found using A\int_0^{12}\left(B+Cx)dx

Explanation:

(a) Since the density variation is linear and the coordinate x begins at the low-density end of the rod, we have a density given by

2.6\frac{g}{cm^3}+\frac{18.5\frac{g}{cm^3}-2.6\frac{g}{cm^3}}{12 cm}x = 2.6\frac{g}{cm^3}+1.325x\frac{g}{cm^2}

recalling that the coordinate x is measured in centimeters.

(b) The mass of the rod can be found by having into account the density, which is x-dependent, and the volume differential for the rod:

m=\int\rho dv=\int\left(B+Cx\right)Adx=5\int_0^{12}\left(2.6+1.325x\right)dx=126.6,

hence, the mass of the rod is 126.6 g.

You might be interested in
How are humans able to perceive light waves? Sound waves?
Vesna [10]
Sound and light are similar in that both are forms of energy that travel in waves. They both have properties of wavelength, freqency and amplitude. ... Sound is a form of mechanical energy caused by vibrations of matter. Light is electromagnetic energy caused by interacting electric and magnetic fields.
7 0
3 years ago
Easy chemical formula question (9th grade)
kogti [31]

Silver and Silver (II) are different because silver (II) has more than 1 electric charge. It has 2! lol

4 0
3 years ago
A 3-m-high, 7-m-wide rectangular gate is hinged at the top edge and is restrained by a fixed ridge. Determine the hydrostatic fo
Shalnov [3]

Answer:

The Hydrostatic force is   F  =  137.2 kN

The location of pressure center is  Z  = 1.333 \ m  

Explanation:

From the question we are told that

   The height of the gate is  h =  3 \ m

     The weight of the gate is  w =  7 \  m

      The height of the water is  h_w  =  2 \ m

       The density of water is \rho_w  =  1000 \ kg/m^3

Note used h_w for height of water and height of gate immersed by water since both have the same value

The area of the gate immersed in water  is mathematically represented as

         A =  h_w  * w

substituting values

         A =  2*  7

         A =  14  \ m^2

The hydrostatic force is mathematically represented as

          F  =  \rho_w * g * h_f * A

Where

            h_f =h-  h_w

           h_f =3 -2

           h_f = 1\ m  

So  

              F  =  1000 * 9.8 * 1 * 14

            F  =  137.2 kN

The center of pressure is mathematically represented as

        Z  =  h_f + \frac{I_g}{h_f * A}

Where I_g is the moment of inertia of the gate which mathematically represented as

            I_g =  \frac{w * h_w^2}{12}

The h_w is the height of gate immersed in water

            I_g =  \frac{7  * 2^2 }{12}

             I_g = 4.667\ kg  m^2

Thus  

        Z  = 1  + \frac{4.66}{1 * 14}

        Z  = 1.333 \ m

3 0
3 years ago
A water balloon is hovering directly above the line join points ANB which are 4.6 km apart if the angles of elevation to the bal
Anna35 [415]

Answer:

Drawing the triangle:

H / x = tan 52.2 = 1.29

H / (4.6 - x) = tan 28.8 = .550

H = 1.29 x

H = .55 * 4.6 - .55 x

1.84 x = 2.53        combining equations

x = 1.38

4.6 - 1.38 = 3.22

Total base of triangle = 1.38 + 3.22 = 4.6

H / x = tan 52,2 = 1.29

H = 1.29 * 1.38 = 1.78 height of triangle

Check:

1.78 / 3.22 = tan 28.9    

This agrees with the given value of 28.8

7 0
2 years ago
How to do this question
mestny [16]

thanks again and have to go to the store and get some rest I will be there at puno my phone is not working and I have a few questions about the week and I have a few questions about the week and I have a few questions about the week and I have a few questions about the week and I have a few questions about the week and I have a few questions about the week and I have a few questions about the week and I have a few questions about the week and I have a few questions about the week and I have a few questions about you

4 0
3 years ago
Other questions:
  • The picture below shows an asteroid and a comet.
    9·1 answer
  • A hill that has a 33.9% grade is one that rises 33.9 m vertically for every 100.0m of distance in the horizontal direction. At w
    10·2 answers
  • The nucleus of the atom contains 8 protons and 9 neutrons. The atom is electrically
    10·1 answer
  • Balance these equations:
    10·1 answer
  • What is the difference between an energy pyramid and a biomass pyramid?
    8·1 answer
  • Distance and ___ are really the same quantity. A. length b. direction c. speed d. displacement​
    15·1 answer
  • What quantity measures the amount of space an object occupies?
    7·1 answer
  • Why does the Earth exert a gravitational force on objects on its surface?
    15·1 answer
  • Two planes approach each other head on. Each has a speed of 721km/h and they spot each other when they are initially 14.7km apar
    11·1 answer
  • On being introduced to the laws of thermodynamics, a student retorted, “When the brakes of a moving car are applied, the kinetic
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!