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
kherson [118]
3 years ago
13

You have an evacuated, iron spherical shell and want to know how thick the shell wall is. However, you cannot cut open the iron

shell to measure the thickness of the wall. The ball just floats once completely submerged in water, and you measure the outer diameter to be 58.7 cm. If the density of iron is 7.87 g/cm3, what is the thickness of the wall?
Physics
1 answer:
AlladinOne [14]3 years ago
7 0

Answer:

26 cm

Explanation:

V = Volume

R = Outer radius of the shell = 58.7 cm

r = Inner radius of the shell

g = Acceleration due to gravity = 9.81 m/s²

\rho = Density

As the shell is completely submerged

Force on shell

F=v\rho g\\\Rightarrow F=\frac{4}{3}\pi R^3\times 1000g

Weight of the shell

W=\frac{4}{3}\pi (R^3-r^3)\times 7870g

Equating the two equations as the forces are conserved

\frac{4}{3}\pi R^3\times 1000g=\frac{4}{3}\pi (R^3-r^3)\times 7870g\\\Rightarrow R^3\times 1000=(R^3-r^3)\times 7870\\\Rightarrow R^3=(R^3-r^3)\frac{7870}{1000}\\\Rightarrow R^3=(R^3-r^3)7.87\\\Rightarrow 6.87R^3=r^37.87\\\Rightarrow r=\left(\frac{6.87}{7.87}\times0.587^3\right )^{\frac{1}{3}}\\\Rightarrow r=0.561\ m

Inner radius of the shell is 0.561 m

The thickness of the wall is 0.587-0.561 = 0.026 m = 26 cm

You might be interested in
In which phase of mitosis are chromosome first seen as a result of chromatin coiling?
Kruka [31]
<span>Mitosis is a a means for cells to split and produce exact copies of themselves. The process produces two identical copies of the original cell and occurs throughout the human body. Mitosis is divided up into four main phases known as prophase, metaphase, anaphase and telophase. The chromosomes first become visible in early prophase.</span>
7 0
3 years ago
Find :
Pepsi [2]

Answer:

Explanation:

b) Gravity reduces the initial upward velocity to zero in a time of

t = v/g = 40/10 = 4 s

a) h =  v₀t + ½gt² = 40(4) +  ½(-10)4² = 80 m

or

v² = u² + 2as

h = (0² - 40²) / 2(-10) = 80 m

8 0
2 years ago
How do dog whistles work?
Alchen [17]

<em>The sound it emits comes from what is known as the ultrasonic range, a pitch that is so high humans can't hear it. Dogs can hear these sounds, however, as can cats and other animals. Because of this, the dog whistle is a favored training tool, though it may not be for every dog parent.</em>

7 0
2 years ago
A dragster starts from rest and travels 1/4 mi in 6.80 s with constant acceleration. What is its velocity when it crosses the fi
Ahat [919]
<h2>Its velocity when it crosses the finish line is 117.65 m/s</h2>

Explanation:

We have equation of motion s = ut + 0.5 at²

        Initial velocity, u = 0 m/s

        Acceleration, a = ?

        Time, t = 6.8 s    

        Displacement, s = 1/4 mi =    400 meters

     Substituting

                      s = ut + 0.5 at²

                      400 = 0 x 6.8 + 0.5 x a x 6.8²

                      a = 17.30 m/s²

Now we have equation of motion v = u + at

     Initial velocity, u = 0 m/s

     Final velocity, v = ?

     Time, t = 6.8 s

      Acceleration, a = 17.30 m/s²

     Substituting

                      v = u + at  

                      v = 0 + 17.30 x 6.8

                      v = 117.65 m/s

Its velocity when it crosses the finish line is 117.65 m/s

6 0
3 years ago
Bill is farsighted and has a near point located 121 cm from his eyes. Anne is also farsighted, but her near point is 74.0 cm fro
Arada [10]

Answer:

Explanation:

The lens equation is

1 / f = 1 / di + 1 / do

Where

f is focal length

di is the image distance

do is the object distance

Both Annie and Billy use a glass whose near point is 25cm

Then, the object distance is

do = 25 - 2 = 23cm

The have the same object distance.

Let find the vocal length of bills eye

Given that,

Bill near point is 121cm and distance of the glass from the eye is 2cm

Then,

Image distance of bill is

di_B = -(121-2) = -119cm

object distance do = 23cm

Then,

1 / f_B = 1 / di_B + 1 / do

1 / f_B = -1 / 119 + 1 / 23

1 / f_B = -119^-1 + 23^-1

1 / f_B = 0.0351

Then, f_B = 28.51 cm

Also, let find Annie focal length

Given that,

Annie near point is 74 cm and distance of the glass from the eye is 2cm

Then,

Image distance of Annie is

di_A = -(74-2) = -72cm

object distance do = 23cm

Then,

1 / f_A = 1 / di_A + 1 / do

1 / f_A = -1 / 72 + 1 / 23

1 / f_A = -72^-1 + 23^-1

1 / f_A = 0.02959

Then, f_A = 33.8 cm

Distance of object from the lens when Annie uses Billy glass

Then,

1 / f_B = 1 / di_A + 1 / do

1 / 28.51 = -1 / 72 + 1 / do

28.51^-1 = -72^-1 + do^-1

do^-1 = 28.51^-1 + 72^-1

do^-1 = 0.048964

do = 20.42 cm

Then, the object location from the eye will be, the eye is 2cm from the glass. Then,

do_A = 20.42 + 2 = 22.42cm

do_A = 22.42 cm

Distance of object from the lens when Billy uses Annie glass

Then,

1 / f_A = 1 / di_B + 1 / do

1 / 33.8 = -1 / 119 + 1 / do

33.8^-1 = -119^-1 + do^-1

do^-1 = 33.8^-1 + 119^-1

do^-1 = 0.03799

do = 26.32 cm

Then, the object location from the eye will be, the eye is 2cm from the glass. Then,

do_B = 26.32 + 2 = 28.32 cm

do_B = 28.32 cm

7 0
3 years ago
Other questions:
  • A wheel moves in the xy plane in such a way that the location of its center is given by the equations xo = 12t3 and yo = R = 2,
    6·1 answer
  • What is meant by 'wasted energy'?
    14·2 answers
  • Which statement best defines an electric field?
    5·1 answer
  • I need help like right now!!!!! please
    14·1 answer
  • Which of the following are metric units? gallons kilograms pounds inches
    14·2 answers
  • The velocity versus time graph of particle A is tangent to the velocity versus time graph for particle B at point O. What is the
    11·1 answer
  • What was so significant about dalton discoveries
    12·1 answer
  • What is velocity and speed
    7·2 answers
  • A car climbs 10.0 kilometers up a hill that inclines 8.0 degrees. What is the car's vertical displacement?
    14·1 answer
  • Calculate the electric current that flows through a electric heater of power 1000watt when collected with 220 volt ac supply
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!