Find an expression for the center of mass of a solid hemisphere, given as the distance R from the center of the flat part of the hemisphere. Express your answer in terms of R. Express the coefficients using three significant figures.

Answers

Answer 1

Answer:

z_c = ⅜R

Explanation:

If we assume that the hemisphere has uniform density, we can express the centre of mass as;

z_c = (ρ/M)∫∫∫ z•dV

We know that density(ρ) = mass(M)/volume(V)

Thus, Vρ = M

And volume of hemisphere = 2πr³/3

Thus;

2Vρπr³/3 = M

So;

z_c = (ρ/(2Vρπr³/3))∫∫∫ z•dV

Where r = R in this case.

ρ will cancel out to give;

z_c = (3/(2πr³))∫∫∫_V (z•dV)

In spherical coordinates,

r is radius

Φ = angle between the point and the z − axis

θ = azimuthal angle

Therefore, the integral becomes what it is in the attached image.

I've completed the explanation as well in the attachment.

Find An Expression For The Center Of Mass Of A Solid Hemisphere, Given As The Distance R From The Center

Related Questions

It will be easier to lift a load in wheel barrow if the load is moved
towards the wheel.why​

Answers

Answer:

the moment

Explanation:

the shorter the distance from the force, the lesser the torque acting on it

HELP ASAP!!!!!!!!!
Mark and Steven were conducting an investigation where they were measuring the energy of a glass marble as it rolled down a ramp. According to their calculations, the total energy of the marble decreased. Which statement below is the best explanation for the decrease in total energy?
A) It decreased because it was destroyed by the interaction with the ramp
B) The total energy always decreases in an energy conversion
C) They were incorrect; the energy totals should have been the same
D) The energy decreased because heat resulted from friction between the marble and the ramp

Answers

B) The total energy always decreases in an energy conversion,

This is because: Energy decreases as it moves up trophic levels because energy is lost as metabolic heat when the organisms from one trophic level are consumed by organisms from the next level. Trophic level transfer efficiency (TLTE) measures the amount of energy that is transferred between trophic levels

Hope this helps! ✨

A biker first accelerates from 0.0 m/s to 6.0 m/s in 6 s, then continues at this speed for 5 s. What is the total distance traveled by the biker?

100 m

80 m

30 m

48 m

PLZ heeeeelp ​

Answers

Answer:

48m

Explanation:

Given the following data;

Initial velocity = 0m/s

Final velocity = 6m/s

Time, t = 6 secs

Time, T2 = 5 secs

Mathematically, acceleration is given by the equation;

[tex]Acceleration (a) = \frac{final \; velocity - initial \; velocity}{time}[/tex]

Substituting into the equation;

[tex]a = \frac{6 - 0}{6}[/tex]

[tex]a = \frac{6}{6}[/tex]

Acceleration, a = 1m/s²

To find the distance covered in the first phase;

Solving for distance, we would use the second equation of motion;

[tex] S = ut + \frac {1}{2}at^{2}[/tex]

Substituting the values into the equation;

[tex] S = 0(6) + \frac {1}{2}*1*(6)^{2}[/tex]

[tex] S = 0 + \frac {1}{2}*1*36[/tex]

[tex] S = 0.5 *36[/tex]

Distance, S1 = 18m

For the second phase, time T2 = 5 secs;

Mathematically, speed is given by the equation;

[tex]Speed = \frac{distance}{time}[/tex]

Making distance the subject of formula, we have;

[tex]Distance, S = speed * time[/tex]

Substituting into the above equation;

[tex]Distance, S = 6 * 5[/tex]

Distance, S2 = 30m

Total distance = S1 + S2 = 18m + 30m = 48m

Total distance = 48m

Therefore, the total distance traveled by the biker is 48m.

A box with weight of magnitude F_G = 2.00 N is lowered by a rope down a smooth plane that is inclined at an angle φ = 30.0 degrees about ve the horizontal. The normal force acting on the box has a magnitude n = 1.73 N, the tension force is 1.00 N, and the displacement Δr of the box is 1.80 m down the cloned plane.

What is the work W_G done on the box by the gravity?

Answers

Answer:

1.8 J

Explanation:

I had this exact question today and found someone who had solved it before, this was their response to the work done by gravity. They used the name "physicsmom"

Vertical distance = 1.8 sin 30 = .9 m

W = 2 N * .9 m = 1.8J

Good luck! I hope this helps!

The work done on the box by the gravity is 0.072 J.

The given parameters;

weight of the box, [tex]F_g[/tex] = 2 Ninclination of the rope, φ = 30⁰normal force acting on the box, n = 1.73 Ntension on the rope, T = 1 Ndisplacement of the box, Δr = 1.8 m

The work done on the box by gravity is calculated as follows;

W = FΔr

where;

F is the net horizontal force on the block

The net horizontal force on the box  is calculated as follows;

[tex]\Sigma F_x = F_g sin(\theta ) - F_k\\\\ \Sigma F_x = F_g sin(\theta ) - \mu_k F_n \\\\ \Sigma F_x = 2 \times sin(30 ) - (tan \theta) \times F_n\\\\ \Sigma F_x = 1 - (tan\ 30) \times 1.73\\\\ \Sigma F_x = 0.04 \ N[/tex]

The work done on the box by gravity is calculated as;

W = 0.04 x 1.8

W = 0.072 J.

Thus, the work done on the box by the gravity is 0.072 J.

Learn more here: https://brainly.com/question/14945453

A car drives 150 km SE and then 50 km due N. What is the car's displacement?

Answers

Answer:

If the car travels 150 kilometers to the Southeast, and then 50 kilometers to the North, it is understood that the car does not travel the same way out as it does back. Therefore, the car's displacement will be the sum of both distances traveled, that is, 150 + 50, which is equal to 200. Therefore, the car traveled about 200 kilometers from its starting point.

An artery with cross sectional area of 1 cm2 branches into 20 smaller arteries each with 0.5 cm2 cross sectional area. If the velocity of blood in the thicker artery is v, what is the velocity of the blood in the thinner arteries

Answers

Answer:

The velocity of the blood in the thinner arteries is 0.1 times that of the thicker artery.

Explanation:

To find the velocity of the blood we need to use the continuity equation:

[tex] n_{1}A_{1}v_{1} = n_{2}A_{2}v_{2} [/tex]   (1)  

Where:

n: is the number of branches

A: is the cross-sectional area

v: is the velocity

For artery 1, we have:

n₁ = 1, A₁ = 1 cm², v₁ = v

For the 20 arteries (2), we have:

n₂ = 20, A₂ = 0.5 cm², v₂ =?

By using equation (1):

[tex] n_{1}A_{1}v_{1} = n_{2}A_{2}v_{2} [/tex]

[tex] 1 cm^{2}*v = 20*0.5 cm^{2}*v_{2} [/tex]

[tex] v_{2} = \frac{1 cm^{2}*v}{20*0.5 cm^{2}} = \frac{v}{10} = 0.1v [/tex]

Therefore, the velocity of the blood in the thinner arteries is 0.1 times that of the thicker artery.

I hope it helps you!      

When a balloon is rubbed on a surface and then touched to hair it will attract the hair, causing it to stick to the balloon. Explain why this happens.

Answers

Answer:

electricity

Explanation:

Answer:

This is called static electricity

Explanation:

The reasoning behind this is because the negative electrons in your hair are being transferred to the balloon, then when the balloon is removed it pulls on the hair with an attractive electric force.

things that affects the demand for electricity

Answers

New inventions like :
Solar panel
Wind mill
And etc .

What is precipitation and how does it affect weather? (20 points)

Answers

Precipitation is any liquid or frozen water that forms in the atmosphere and falls back to the earth. It comes in many forms like rain, sleet, and snow. Along with evaporation and condensation.

Answer:

precipitation is any frozen or liquid that forms in the atmosphere and falls back to Earth in the form of rain, hail, snow, or sleet.

Explanation:

precipitation can give an excessive amount of rainfall which will result in freezing crops andcold temperatures

What is the momentum of 100 kg running at 4m/s north?

Answers

The momentum is known as mass x velocity then u should say that it will be 400 kg m/s

Q17: The coefficient of linear expansion of steel is a = 11 x 10-6 / °C. A steel
ball has a volume of exactly 100 cm3 at 0°C. When heated to 100°C, its
volume becomes in (cm3):
A
B
D
E
100.33
100.11
100.0011
100.0033
None of them

Answers

Solution:

The coefficient of volume expansion

p = ΔV/V1Δt

3a = V2-V1/V1Δt

Given

a = = 11 x 10-6 / °C

V2 is the final volume

V1 is the initial volume = 100cm³

Δt = 100-0 = 100°C

Substitute

3(11 x 10-6) = V2-100/100(100)

33*10^-6 * 10000 = V2-100

33*10^-2 = V2-100

V2 = 100 + 0.33

V2 = 100.33

Hence the new volume is 100.33cm³

how can voltage be produced by magnetism and motion?​

Answers

Answer:

Electromagnetic Induction by a Moving Magnet

Then the action of moving a coil or loop of wire through a magnetic field induces a voltage in the coil with the magnitude of this induced voltage being proportional to the speed or velocity of the movement.

Explanation:

a neutral comb brushes

Answers

? What’s the question

Two masses are to collide directly with each other. One has a mass of 5 kg and a velocity of 2 m/s. The other has a mass of 3 kg and a velocity of 1 m/2. The collision is perfectly inelastic. Find the velocity of the masses after the collision.

Answers

Answer:

v₃ = 1.625 [m/s]

Explanation:

To solve this problem we must use the definition of linear momentum conservation, which tells us that momentum is conserved before and after a collision.

Since the collision is inelastic, the two bodies are joined after the collision.

P = m*v [kg*m/s]

m = mass [kg]

v = velocity [m/s]

where:

P = lineal momentum [kg*m/s]

Now, it is important to clarify that in the following equation we will take the left side of the equation as the momentum before the collision and the right side of the equal sign as the momentum after the collision.

Pbefore = Pafter

(m₁*v₁) + (m₂*v₂) = (m₁+m₂)*v₃

where:

m₁ = mass one = 5 [kg]

v₁ = velocity of the mass one = 2 [m/s]

m₂ = mass two = 3 [kg]

v₂ = velocity of the mass two = 1 [m/s]

v₃ = velocity of the combined masses after the collision [m/s]

Now replacing we have:

(5*2) + (3*1) = (5 + 3)*v₃

10 + 3 = 8*v₃

v₃ = 13/8

v₃ = 1.625 [m/s]

If the jet is moving at a speed of 1140 km/h at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g's.

Answers

Answer:

The radius is  [tex]r =1705.44 \ m[/tex]

Explanation:

From the question we are told that

   The speed is [tex]v = 1140 \ km /h = \frac{1140 * 1000}{3600} = 316.67 \ m/s[/tex]

   The centripetal acceleration is  [tex]a = 6 g's = 6 * 9.8 = 58.8 \ m/s^2[/tex]

Generally the centripetal force acting on the jet is mathematically represented as  

        [tex]F_c = \frac{m * v^2 }{r}[/tex]

Generally this centripetal force is equal to the net force acting which according to Newton's third law is mathematically  represented as

      [tex]F = m * a[/tex]

So

      [tex]\frac{m * v^2 }{r} = ma[/tex]

=>   [tex]\frac{ v^2 }{r} = a[/tex]

=>  [tex]r = \frac{v^2}{a}[/tex]

=>  [tex]r = \frac{316.67^2}{58.8}[/tex]

=>  [tex]r =1705.44 \ m[/tex]

The first group of planets that are made of rock and closest to the sun

Answers

Answer:

A terrestrial planet, telluric planet, or rocky planet is a planet that is composed primarily of silicate rocks or metals. Within the Solar System, the terrestrial planets are the inner planets closest to the Sun

Can someone please help me with this problem. I’ve tried but I can’t seem to figure it out.

Answers

The last one, Tension = 30N, Normal force = 20 N

Rosa eats a peanut butter sandwich for lunch. Peanut butter contains a lot
of protein, and bread is mostly starch. Rosa plans to go for a run later this
afternoon. Rosa is breathing normally.

Answers

Cmndkdkkdnd djnd dhdbhd s ahah who w baggage wbhebwnwh

Full moon is located______

a. farthest from the Sun

b. at a 90 degree angle with the Sun and Earth

c. closest to the Sun

Answers

Answer:

Im going to take an educated guess and say its B.

Explanation:

A Full moon is located farthest from the Sun. Thus, the correct option for this question is A.

What is a Full moon?

A full moon may be defined as one of the types of lunar phases when the Moon significantly appears fully illuminated from Earth's perspective. This event typically occurred when Earth is located between the Sun and the Moon.

When the earth is located between the sum and the moon, it is the time when the moon is located farthest from the sun. And it directs to an event of a full moon. The average time duration of the full moon and the repetition of the same phase normally requires 29.53 days.

Therefore, the Full moon is located farthest from the Sun. Thus, the correct option for this question is A.

To learn more about the Full moon, refer to the link:

https://brainly.com/question/15032553

#SPJ2

Which form of energy has the most potential globally

a) Solar energy

b) Bio energy

c) Wind energy

d) Geothermal energy

Answers

Answer:

i think the answer is solar,

Explanation:

because it is a natural resource im sorry if im wrong

What is a young lady in a binkini I pictures help me understand the must :)

Answers

Uhhh.. creep. Can you like..not?

Answer: Lol what the heck I never heard this type of question. but I mean you see it when you go to the beach so yeah that's all I'm telling you U-U

An electron (restricted to one dimension) is trapped between two rigid walls 1.40 nm apart. The electron's energy is approximately 19 eV. (a) What is the quantum number n for the energy state that the electron occupies? (b) Based on the quantum number you found in part (a), calculate a more precise value for the electron's energy in eV), expressed to at least three significant figures. (Use any physical constants or unit conversions to at least four significant figures in your calculations.) _________ eV

Answers

Answer:

a)    n = 9.9       b)      E₁₀ = 19.25 eV

Explanation:

Solving the Scrodinger equation for the electronegative box we get

         Eₙ = (h² / 8m L²2) n²

where l is the distance L = 1.40 nm = 1.40 10⁻⁹ m and n the quantum number

 In this case En = 19 eV let us reduce to the SI system

          En = 19 eV (1.6 10⁻¹⁹ J / 1 eV) = 30.4 10⁻¹⁹ J

          n = √ (In 8 m L² / h²)

let's calculate

          n = √ (8  9.1 10⁻³¹ (1.4 10⁻⁹)²  30.4 10⁻¹⁹ / (6.63 10⁻³⁴)²

          n = √ (98)            n = 9.9

since n must be an integer, we approximate them to 10

b) We substitute for the calculation of energy

        In = (h² / 8mL2² n²

        In = (6.63 10⁻³⁴) 2 / (8 9.1 10⁻³¹  (1.4 10⁻⁹)² 10²

        E₁₀ = 3.08 10⁻¹⁸ J

we reduce eV

      E₁₀ = 3.08 10⁻¹⁸ j (1ev / 1.6 10⁻¹⁹J)

      E₁₀ = 1.925 101 eV

      E₁₀ = 19.25 eV

the result with significant figures is

        E₁₀ = 19.25 eV

A ball is thrown straight up from the ground with an unknown velocity. It reaches its highest point after 5.5 s. With what velocity did it leave the ground?

Answers

v = u + at
0 = u -9.8 x 5.5
u = 9.8 x 5.5 = 53.9 m/s

Bicyclist travels at an average velocity of 11.2 km/h [W]. How far will the bicyclist travel in 175 minutes?

Answers

Answer:

32.67km

Explanation:

~= round off

11.2km/h~3.11m/s

175minutes=10500s

10500*3.11~32, 666.67m

=32.66667km

~ 32.67km

In general, how do you find the average velocity of any object falling in a vacuum?

Answers

In general, how do you find the average velocity of any object falling in a vacuum? (Assume you know the final velocity.) Multiply the final velocity by final time. 3. Calculate : Distance, average velocity, and time are related by the equation, d = v • t A

The measurement of length and time is calculated the average speed with the expression

         [tex]v_{avg} = \frac{\Delta x}{\Delta t}[/tex]

Average velocity is defined as the change in displacement between the interval time

      [tex]v_{avg} = \frac{\Delta x}{\Delta t}[/tex]

where [tex]v_{avg}[/tex] is the average velocity, Δx is the displacement in the interval, and Δt the time.

To carry out this measurement, it must be taken into account that the velocity is a vector, for which we define a reference system, it can be a vertical axis with the upward direction as positive, therefore the downward displacement is negative.

A tape measure is placed and the interval during which the scalar distance measurement is performed is defined, the most as is to use time as an independent variable (controlled by the researcher) that is measured with a stopwatch.

The displacement is measured for each given time interval and these two quantities are divided. The sign of the velocity is negative because it goes down

Using the measurements of length and time, the average velocity is calculated with the expression

         [tex]v_{avg} = \frac{\Delta x}{\Delta t}[/tex]t

learn more about average speed here:  brainly.com/question/17277454

Moderate injuries are generally __________.
A.
life-threatening
B.
soft tissue injuries
C.
bumps and bruises
D.
too serious for first aid


Please select the best answer from the choices provided.

A
B
C
D

Answers

Answer:

B. soft tissue injuries

Explanation:

i took the test on edge and its really the only one that would make sense if you payed attention to the lesson  :)

Need help ASAP please help

Answers

Answer:

.....

Explanation:

Walking down a pebble beach becomes less painful as you enter the sea. Explain why.

Answers

Answer:Since pressure = force/area, the same force on a smaller area means more pressure. When you are walking on sand, the force being applied by your body is spread out over the entire surface of your foot. ... So, more pressure applied on a given area of your foot causes more pain.

Explanation:

Good Question

pls answer this
quick as possible

Answers

Answer:

The answer is the 4th one

Explanation:

Good luck man

How many bonds can antimony form?

Answers

Answer:

An antimony can form 3 bonds

Let me know if this helps

Thanks!

:)

Explanation:

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