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Karolina [17]
2 years ago
12

Pls need an answer asap

Physics
1 answer:
Andrei [34K]2 years ago
3 0

c] Electrons

Electron gets transferred

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Find the mass and center of mass of the solid E with the given density function ρ. E lies under the plane z = 3 + x + y and abov
makvit [3.9K]

Answer:

The mass of the solid is 16 units.

The center of mass of the solid lies at (0.6875, 0.3542, 2.021)

Work:

Density function: ρ(x, y, z) = 8

x-bounds: [0, 1], y-bounds: [0, x], z-bounds: [0, x+y+3]

The mass M of the solid is given by:

M = ∫∫∫ρ(dV) = ∫∫∫ρ(dx)(dy)(dz) = ∫∫∫8(dx)(dy)(dz)

First integrate with respect to z:

∫∫8z(dx)(dy), evaluate z from 0 to x+y+3

= ∫∫[8x+8y+24](dx)(dy)

Then integrate with respect to y:

∫[8xy+4y²+24y]dx, evaluate y from 0 to x

= ∫[8x²+4x²+24x]dx

Finally integrate with respect to x:

[8x³/3+4x³/3+12x²], evaluate x from 0 to 1

= 8/3+4/3+12

= 16

The mass of the solid is 16 units.

Now we have to find the center of mass of the solid which requires calculating the center of mass in the x, y, and z dimensions.

The z-coordinate of the center of mass Z is given by:

Z = (1/M)∫∫∫ρz(dV) = (1/16)∫∫∫8z(dx)(dy)(dz)

<em>Calculate the integral then divide the result by 16.</em>

First integrate with respect to z:

∫∫4z²(dx)(dy), evaluate z from 0 to x+y+3

= ∫∫[4(x+y+3)²](dx)(dy)

= ∫∫[4x²+24x+8xy+4y²+24y+36](dx)(dy)

Then integrate with respect to y:

∫[4x²y+24xy+4xy²+4y³/3+12y²+36y]dx, evaluate y from 0 to x

= ∫[28x³/3+36x²+36x]dx

Finally integrate with respect to x:

[7x⁴/3+12x³+18x²], evaluate x from 0 to 1

= 7/3+12+18

Z = (7/3+12+18)/16 = <u>2.021</u>

The y-coordinate of the center of mass Y is given by:

Y = (1/M)∫∫∫ρy(dV) = (1/16)∫∫∫8y(dx)(dy)(dz)

<em>Calculate the integral then divide the result by 16.</em>

First integrate with respect to z:

∫∫8yz(dx)(dy), evaluate z from 0 to x+y+3

= ∫∫[8xy+8y²+24y](dx)(dy)

Then integrate with respect to y:

∫[4xy²+8y³/3+12y²]dx, evaluate y from 0 to x

= ∫[20x³/3+12x²]dx

Finally integrate with respect to x:

[5x⁴/3+4x³], evaluate x from 0 to 1

= 5/3+4

Y = (5/3+4)/16 = <u>0.3542</u>

<u />

The x-coordinate of the center of mass X is given by:

X = (1/M)∫∫∫ρx(dV) = (1/16)∫∫∫8x(dx)(dy)(dz)

<em>Calculate the integral then divide the result by 16.</em>

First integrate with respect to z:

∫∫8xz(dx)(dy), evaluate z from 0 to x+y+3

= ∫∫[8x²+8xy+24x](dx)(dy)

Then integrate with respect to y:

∫[8x²y+4xy²+24xy]dx, evaluate y from 0 to x

= ∫[12x³+24x²]dx

Finally integrate with respect to x:

[3x⁴+8x³], evaluate x from 0 to 1

= 3+8 = 11

X = 11/16 = <u>0.6875</u>

<u />

The center of mass of the solid lies at (0.6875, 0.3542, 2.021)

4 0
2 years ago
The main difference between turbojets and rocket engines is the fact that
mafiozo [28]

Answer;

D. rocket engines are not dependent on oxygen from the air.

Explanation;

-Jet engines and rockets work on the same principle. They produce thrust through an internal pressure difference and, as explained by Newton’s Third Law of Motion, eject exhaust gases in an equal and opposite direction.

-The main difference between them is that jets get the oxygen to burn fuel from the air and rockets carry their own oxygen, which allows them to operate in space.

Additionally, Jet engines have two openings (an intake and an exhaust nozzle). Rocket engines only have one opening (an exhaust nozzle).

5 0
3 years ago
Read 2 more answers
A dump truck contains a load of soil. Which action will leave the dump truck's
soldier1979 [14.2K]

Answer:

D

Explanation:

This will not change the weight and therefore not change the inertia

3 0
2 years ago
Read 2 more answers
If a migrating loon flies at an average speed of 19 m/s, what is its average speed in mi/hr?
zlopas [31]

Unit conversion is a way of converting some common units into another without changing their real value. The average speed of the migrating loon flies is 45.5019 miles/hr.

<h3>What is Unit conversion?</h3>

Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimeter is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.

Given that migrating loon flies at an average speed of 19 m/s. Now, since 1 meter is equal to (1/1609.34) miles and 1 second is equal to (1/3600) seconds. Therefore, we can write the speed as,

\rm Speed = 19\ \dfrac{meter}{second}\\

         =19 \times \dfrac{\frac{1}{1609.34}\rm\ miles}{\frac{1}{3600} \rm\ hours}

         = 19 × (3600/1609.34) miles/hr

         = 42.5019 miles/ hr

Hence, the average speed of the migrating loon flies is 45.5019 miles/hr.

Learn more about Units conversion here:

brainly.com/question/4736731

#SPJ4

4 0
11 months ago
A soccer ball with a mass of 0.60 kg travels toward a soccer goalie at
Deffense [45]

Assuming constant acceleration, the goalie slows the ball from 18 m/s to rest in 0.035 s, so that the acceleration felt by the ball is

a_{\rm ave} = a = \dfrac{18\frac{\rm m}{\rm s}-0}{0.035\,\mathrm s} \approx \boxed{510\dfrac{\rm m}{\mathrm s^2}}

7 0
2 years ago
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