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A spherical shell rolls without sliding along the floor. The ratio of its rotational kinetic energy (about an axis through its center of mass) to its translational kinetic energy is:

Answers

Answer 1

Answer:

Answer:

The ratio is $(RE)/(TE) = (2)/(3)$

Explanation:

Generally the Moment of inertia of a spherical object (shell) is mathematically represented as

$I = (2)/(3) * m r^2$

Where m is the mass of the spherical object

and r is the radius

Now the the rotational kinetic energy can be mathematically represented as

$RE = (1)/(2)* I * w^2$

Where $w$ is the angular velocity which is mathematically represented as

$w = (v)/(r)$

=> $w^2 = [(v)/(r)] ^2$

$RE = (1)/(2)* [(2)/(3) *mr^2] * [(v)/(r) ]^2$

$RE = (1)/(3) * mv^2$

Generally the transnational kinetic energy of this motion is mathematically represented as

$TE = (1)/(2) mv^2$

$(RE)/(TE) = ((1)/(3) * mv^2)/((1)/(2) * m*v^2)$

$(RE)/(TE) = (2)/(3)$

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A uniform piece of wire, 20 cm long, is bent in a right angle in the center to give it an L-shape. How far from the bend is the center of mass of the bent wire?

Answers

Answer:TL;DR: 3.535 cm

Explanation:

Xcm = ΣxMoments/ΣMasses = (10*0 + 10*5)/(10+10) = 50/20 = 2.5 cm

by symmetry,

Ycm = 2.5 cm

The distance D from the point Xcm,Ycm to the origin is D = √(2.5²+2.5²) = 3.535 cm

Final answer:

The center of mass of the bent wire is approximately 11.18 cm from the bend.

Explanation:

In order to find the center of mass of the bent wire, we need to divide it into two segments: the horizontal segment and the vertical segment. The length of each segment is half of the total length of the wire, which is 20 cm, so each segment is 10 cm long.

The center of mass of the horizontal segment is located exactly at its middle point, which is 5 cm from the corner. The center of mass of the vertical segment is also located at its middle point, which is 10 cm from the corner. Since the horizontal and vertical segments are orthogonal, the distance from the bend to the center of mass of the bent wire is the hypotenuse of a right triangle with legs of length 5 cm and 10 cm. Using the Pythagorean theorem, we can calculate the distance:

d = sqrt(5^2 + 10^2) = sqrt(25 + 100) = sqrt(125) = 11.18 cm

Therefore, the center of mass of the bent wire is approximately 11.18 cm from the bend.

A Venturi tube may be used as the inlet to an automobile carburetor. If an inlet pipe with a diameter of 2.0 cm diameter narrows to diameter of 1.0 cm, determine the pressure drop in the constricted section for an initial airflow of 3.0 m/s in the 2-cm section? (Assume air density is 1.25 kg/m

Answers

The pressure drop is equal to 80.99 Pa

Given information:

d1 = 2 cm = 0.02 m

d2 = 1 cm = 0.01 m

v = 3 m/s

p = 1.25 kg/m^3

Here we use Bernoulli's principle for the Venturi Tube:

Calculation of pressure drop:

$P1 - P2 = ((v^2* p)/ 2)* ((A1^2/ A2^2)-1)\n\nP1 - P2 = \Delta P = ((v1^2* p)/ 2)* ((A1^2/ A2^2)-1)$

Now the following formula for area calculation should be used:

$A1 = (\pi* d1^2)/ 4 = (\pi* (0.02 m)^2)/ 4 = 0.00031 m^2\n\nA2 = (\pi* (0.01 m)^2)/ 4 = 0.000079 m^2\n\n\Delta P = ((3 m/s)^2 *1.25 kg/m^3)/ 2) * ((0.00031 m^2)^2/(0.000079 m^2)^2)-1)$

= 80.99

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Answer:

the pressure drop is equal to 80.99 Pa

Explanation:

we have the following data:

d1 = 2 cm = 0.02 m

d2 = 1 cm = 0.01 m

v = 3 m/s

p = 1.25 kg/m^3

ΔP = ?

For the calculation of the pressure drop we will use Bernoulli's principle for the Venturi Tube:

P1 - P2 = ((v^2*p)/2)*((A1^2/A2^2)-1)

where A = area

P1 - P2 = ΔP = ((v1^2*p)/2)*((A1^2/A2^2)-1)

for the calculation of the areas we will use the following formula:

A1 = (pi*d1^2)/4 = (pi*(0.02 m)^2)/4 = 0.00031 m^2

A2 = (pi*(0.01 m)^2)/4 = 0.000079 m^2

ΔP = ((3 m/s)^2*1.25 kg/m^3)/2)*((0.00031 m^2)^2/(0.000079 m^2)^2)-1) = 80.99 N/m^2 = Pa

Why are certain things obligations of citizenship instead of responsibilities? atleast 5 sentences please

Answers

Answer:

Please find the answer in the explanation

Explanation:

Responsibilities of citizens are those things citizens are to take care of.

While obligations are those things that are compulsory for the citizens to observe and adhere to.

Why are certain things obligations of citizenship instead of responsibilities?

1.) Because of law and order of the community. It is mandatory for all citizens to obey the law of the land.

2.) Because of the progress and peaceful coexistence of the citizens in the community.

3.) Because of the protection of constitution of the land

4.) To support and defend the constitution

5.) To maintain orderliness and eschew violence.

The pendulum consists of two slender rods AB and OC which have a mass of 3 kg/m. The thin plate has a mass of 12 kg/m2 . a) Determine the location ӯ of the center of mass G of the pendulum, then calculate the mass moment of inertia of the pendulum about z axis passing through G. b) Calculate the mass moment of inertia about z axis passing the rotation center O.

Answers

Answer:

The answer is below

Explanation:

a) The location ӯ of the center of mass G of the pendulum is given as:

$y=(0+(\pi*(0.3\ m) ^2*12kg/m^2*1.8\ m-\pi*(0.1\ m) ^2*12kg/m^2*1.8\ m)+0.75\ m*1.5\ m *3\ kg/m)/((\pi*(0.3\ m) ^2*12kg/m^2-\pi*(0.1\ m) ^2*12kg/m^2)+3\ kg/m^2*0.8\ m+3\ kg/m^2*1.5\ m) \n\ny=0.88\ m$

b) the mass moment of inertia about z axis passing the rotation center O is:

$I_G=(1)/(12)*3(0.8)(0.8)^2+ 3(0.8)(0.888)^2-(1)/(2)*(12)(\pi)(0.1)^2(0.1)^2 -(12)(\pi)(0.1)^2(1.8-\n0.888)^2+(1)/(2)*(12)(\pi)(0.3)^2(0.3)^2 +(12)(\pi)(0.3)^2(1.8-0.888)^2+(1)/(12)*3(1.5)(1.5)^2+\n3(1.5)(0.888-0.75)^2\n\nI_G=13.4\ kgm^2$

c) The mass moment of inertia about z axis passing the rotation center O is:

$I_o=(1)/(12)*3(0.8)(0.8)^2+ (1)/(3)* 3(1.5)(1.5)^2+(1)/(2)*(12)(\pi)(0.3)^2(0.3)^2 +(12)(\pi)(0.3)^2(1.8)^2-\n(1)/(2)*(12)(\pi)(0.1)^2(0.1)^2 -(12)(\pi)(0.1)^2(1.8)^2\n\nI_o=13.4\ kgm^2$

Final answer:

To solve this problem, calculate the mass of each element of the pendulum, use that information to determine the center of mass, and then apply the parallel axis theorem to calculate the two moments of inertia.

Explanation:

To determine the center of mass and the mass moment of inertia of the pendulum, first we calculate the individual masses of the rods: AB and OC, and the plate. Each rod has a mass of 2 kg (given mass per unit length is 3kg/m and length of each rod is 1 m from the first reference paragraph).

The center of mass ӯ can be determined using the formula for center of mass, averaging distances to each mass element weighted by their individual masses. The mass moment of inertia, also known as the angular mass, for rotation about the z axis through G is determined using the parallel axis theorem, which states that the moment of inertia about an axis parallel to and a distance D away from an axis through the center of mass is the sum of the moment of inertia for rotation about the center of mass and the total mass of the body times D squared.

Finally, the moment of inertia about the z axis passing through the center of rotation O can be calculated again using the parallel axis theorem, with distance d being the distance between points G and O.

Learn more about Mass Moment of Inertia here:

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A 55-liter tank is full and contains 40kg of fuel. Find using Sl units: • Density p. • Specific Weight y • Specific Gravity Answer tolerance = 1%. Be sure to include units. The sign of the answers will not be graded, use a positive value for your answer. Your answers: p= (Enter a positive value) y = (Enter a positive value) SG = (Enter a positive value)

Answers

Answer:

Density of the fuel is 727.3 kilograms per cubic meter.

Specific weight of the fuel is 7127.3 Newtons per cubic meter.

Specific gravity of the fuel is 0,727.

Explanation:

In order to use SI units, we have to convert liters to cubic meters. Knowing that a liter is a cubic decimeter and a cubic decimeter is $1*10^(-3)$ cubic meters, we know that the tank has 0,055 cubic meters of fuel (because it is full).

Now that we have things in SI units, we calculate density:

$p_(fuel)= (mass)/(volume) = (40 kg)/(0.055 m^(3) ) =727.3 (kg )/(m^(3) )$

Knowing the mass per unit of volume, we can calculate weight per unit of volume thanks to Newton's second law (mass times acceleration, g in this case, equals force (weight)), i.e. specific weight:

$y=p*g=727,3 (kg)/(m^(3))*9.8(m )/(s^(2))=7127,3 (N)/(m^(3))$

With density we can also calculate how dense the fuel is related to a reference (water), i.e. specific gravity. SG is a dimensionless number that tell us how much denser (SG>1) or lighter per unit of volume (SG<1) a substance is than water. We use water as a reference because it is one of the most used substances in our life, and it is a standard density (1000 kg per cubic meter at 4°C and 1 atm).

$SG=(p_(fuel) )/(p_(water) ) =(727.3 (kg )/(m^(3) ))/(1000 (kg )/(m^(3) )) =0,727$

Chuck wants to investigate how gas moleculesmove in a container. Which model would be most
helpful to represent this motion?
A. stacking blocks to build a tower
B. freezing water in an ice cube tray
C. bouncing elastic balls off of each other and
the walls of a room
D. placing a closed, water-filled plastic bag in
the sun and watching condensation form

Answers

The answers C the molecules in gas move rapidly and all around they are spread out and bounce off each-other

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