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
lesya692 [45]
3 years ago
10

A rod of length L and mass M has a nonuniform mass distribution. The linear mass density (mass per length) is λ=cx2, where x is

measured from the center of the rod and c is a constant.A. What are the units of c?Mastering physics says the answer is: kg/m^3 but i don't understand where they got this answer.B. Find the expression for c.Mastering physics says the answer is 12M/L^3 --> No clue where they got this answer!C. Find the expression for the moment of inertia of the rod for rotation about an axis through the center.
Physics
1 answer:
grigory [225]3 years ago
4 0

Answer:

Explanation:

λ=c x²

c = λ / x²

λ is mass / length

so its dimensional formula is ML⁻¹

x is length so its dimensional formula is L

c = λ / x²

= ML⁻¹ / L²

= ML⁻³

B )

We shall find out the mass of the rod with the help of given expression of mass per unit length and equate it with given mass that is M

The mass in the rod is symmetrically distributed on both side of middle point.

we consider a small strip of rod of length dx at x distance away from middle point

its mass dm = λdx = cx² dx

By integrating it from -L to +L we can calculate mass of whole rod , that is

M = ∫cx² dx

= [c x³ / 3] from -L/2 to +L/2

= c/3 [ L³/8 + L³/8]

M = c L³/12

c = 12 M L⁻³

C ) Moment of inertia of rod

∫dmx²

= ∫λdxx²

= ∫cx²dxx²

= ∫cx⁴dx

= c x⁵ / 5 from - L/2 to L/2

= c / 5 ( L⁵/ 32 +L⁵/ 32)

= (2c / 160)L⁵

= (c / 80) L⁵

= (12 M L⁻³/80)L⁵

= 3/20 ML²

=

=

You might be interested in
A 15-ft3 tank contains oxygen initially at 14.7 psia and 80°F. A paddle wheel within the tank is rotated until the pressure insi
Nikolay [14]

Explanation:

Equation for energy balance will be as follows.

         \Delta E_{system} = E_{in} - E_{out}

        \Delta U = W_{in} - Q_{out}

Hence,    W_{in} = Q_{out} + mC_{v} (T_{2} - T_{1})

Therefore, we will calculate the final temperature as follows.

            \frac{P_{1}V}{T_{1}} = \frac{P_{2}V}{T_{2}}

       T_{2} = \frac{20 psia}{14.7}(638 R)

                   = 868.03 R

Now, we will calculate the mass as follows.

             m = \frac{P_{1}V}{RT_{1}}

                 = \frac{14.7 psia \times 15 ft^{3}}{0.3353 psi ft^{3}/lbm R \times 638 R}

                 = 1.031 lbm

Hence,

        W_{in} = Q_{out} + mC_{v} (T_{2} - T_{1})

Putting the values into the above equation as follows.

            W_{in} = Q_{out} + mC_{v} (T_{2} - T_{1})

    W_{in} = 20 Btu + 1.031 lbm (\frac{0.160 Btu}{lbm R})(735 - 540)R

            W_{in} = 655.2 Btu

Thus, we can conclude that work done by paddle wheel is 655.2 Btu.

6 0
3 years ago
Pls help. This is about heat. I got the answer, just need the working
Mars2501 [29]

Answer:

See below

Explanation:

You have to heat the calorimeter to 100 C  from 20 C

  this will take   .20 kg *    390 j /kg-C   *  80 C = <u>6240 j</u>

You have to heat the mass of water to boiling point (100 C ) from 20C

this will take    

    .50 kg * 4182 j/kg-C  * 80 = <u>167,280 j </u>

AND you have to add enough heat to boil off  .03 kg of water:

   .03 kg * (2260000 j/kg-C )  =<u> 67,800 j</u>

<u />

Power = joules / sec =  (6240 + 167280 + 67800) / 274.8 =<u> 878 watts </u>

<u />

<u>Your answer may differ just a bit for slightly different or rounded values of specific heat or heat of fusion for water .....</u>

7 0
2 years ago
What is similar about analogical and symbolic representations?
ICE Princess25 [194]
Symbolic representations are mental pictures that have no direct relationship to the actual object you are thinking about. Instead, these mental pictures are connected by themes that are meaningful to you. Anytime you think of words and descriptions for one main concept, you're thinking symbolically. Analogical representations are mental pictures that have a direct relationship to the actual object you are thinking about. Do cows have their ears on the top or side of their heads? Rather than thinking symbolically about a cow and his ears (tiny, smelly, leather), analogical representations of the cow's ears involve thinking of an actual cow in your head.
3 0
3 years ago
Read 2 more answers
A circuit is set up such that it has a current of 8 A. What would be the new current if the resistance was increased by a factor
RUDIKE [14]

Answer:

4 A

Explanation:

The relationship between current, voltage and resistance in a circuit is given by Ohm's law:

V=RI

where

V is the voltage

R is the resistance

I is the current

The equation can also be rewritten as

I=\frac{V}{R}

from which we see that the current is inversely proportional to the resistance, R.

In this problem, the initial current is I = 8 A. Then the resistance is doubled:

R ' = 2R

So the new current is

I'=\frac{V}{R'}=\frac{V}{2R}=\frac{1}{2}(\frac{V}{R})=\frac{I}{2}=4 A

so the current is halved.

7 0
3 years ago
P14.003A spherical gas-storage tank with an inside diameter of 8.1 m is being constructed to store gas under an internal pressur
Artist 52 [7]

Answer:

The minimum wall thickness required for the spherical tank is 0.0189 m

Explanation:

Given data:

d = inside diameter = 8.1 m

P = internal pressure = 1.26 MPa

σ = 270 MPa

factor of safety = 2

Question: Determine the minimum wall thickness required for the spherical tank, tmin = ?

The allow factor of safety:

\sigma _{a}  =\frac{\sigma }{factor-of-safety} =\frac{270}{2} =135MPa

The minimun wall thickness:

t=\frac{Pd}{4\sigma _{a} } =\frac{1.26*8.1}{4*135} =0.0189m

3 0
2 years ago
Other questions:
  • A cube is 4.4 cm on a side, with one corner at the origin. Part 1 (a) What is the unit vector pointing from the origin to the di
    11·1 answer
  • What is the ratio of the gravitational force on an astronaut when he is in a space satellite in a circular orbit 315 km above th
    14·1 answer
  • A pendulum is swinging back and forth with a period of 2.0 seconds here on Earth. This pendulum is then brought to the Moon, whe
    8·1 answer
  • Calculate the amount of work done to draw a current of 8A from a point at 100V to a point at 120V in 2 seconds?
    13·1 answer
  • Write three example for types of energy​
    6·2 answers
  • All organisms in Kingdom Animalia are multicellular, meaning their bodies are composed of more than one cell. Which other charac
    8·2 answers
  • The Earth belongs to the group of rocky planets that orbits between the sun and the asteroid belt. Place these planets in order,
    15·2 answers
  • A child and sled with a combined mass of 54.8
    11·1 answer
  • 8. The mass of the sun is 1.99 x 1030 kilograms and its distance from Earth is 150 million kilometers (150 x 109 meters). What i
    12·1 answer
  • Need help pls and explain also
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!