A plate of uniform areal density is bounded by the four curves: where and are in meters. Point has coordinates and . What is the moment of inertia of the plate about point

Answers

Answer 1

The question is incomplete. The complete question is :

A plate of uniform areal density [tex]$\rho = 2 \ kg/m^2$[/tex] is bounded by the four curves:

[tex]$y = -x^2+4x-5m$[/tex]

[tex]$y = x^2+4x+6m$[/tex]

[tex]$x=1 \ m$[/tex]

[tex]$x=2 \ m$[/tex]

where x and y are in meters. Point [tex]$P$[/tex] has coordinates [tex]$P_x=1 \ m$[/tex] and [tex]$P_y=-2 \ m$[/tex]. What is the moment of inertia [tex]$I_P$[/tex] of the plate about the point [tex]$P$[/tex] ?

Solution :

Given :

[tex]$y = -x^2+4x-5$[/tex]

[tex]$y = x^2+4x+6$[/tex]

[tex]$x=1 $[/tex]

[tex]$x=2 $[/tex]

and [tex]$\rho = 2 \ kg/m^2$[/tex] , [tex]$P_x=1 \ $[/tex] , [tex]$P_y=-2 \ $[/tex].

So,

[tex]$dI = dmr^2$[/tex]

[tex]$dI = \rho \ dA \ r^2$[/tex]  ,           [tex]$r=\sqrt{(x-1)^2+(y+2)^2}$[/tex]

[tex]$dI = (\rho)((x-1)^2+(y+2)^2)dx \ dy$[/tex]

[tex]$I= 2 \int_1^2 \int_{-x^2+4x-5}^{x^2+4x+6}((x-1)^2+(y+2)^2) dy \ dx$[/tex]

[tex]$I= 2 \int_1^2 \int_{-x^2+4x-5}^{x^2+4x+6}(x-1)^2+(y+2)^2 \ dy \ dx$[/tex]

[tex]$I=2 \int_1^2 \left( \left[ (x-1)^2y+\frac{(y+2)^3}{3}\right]_{-x^2+4x-5}^{x^2+4x+6}\right) \ dx$[/tex]

[tex]$I=2 \int_1^2 (x-1)^2 (2x^2+11)+\frac{1}{3}\left((x^2+4x+6+2)^3-(-x^2+4x-5+2)^3 \ dx$[/tex]

[tex]$I=\frac{32027}{21} \times 2$[/tex]

  [tex]$= 3050.19 \ kg \ m^2$[/tex]

So the moment of inertia is  [tex]$3050.19 \ kg \ m^2$[/tex].

A Plate Of Uniform Areal Density Is Bounded By The Four Curves: Where And Are In Meters. Point Has Coordinates

Related Questions

Average speed is the rate at which an object is moving at a given instant. True or False.

Answers

Answer:

True

Explanation:

Average speed is the rate at which an object is moving at a given instant in time.

Answer: false.

Explanation: i’m pretty sure that’s instantaneous speed.

How does Mountaineering help to improve our lifestyle?​

Answers

Answer:There are numerous benefits to mountaineering. The most obvious benefits are improving both your physical fitness and cardiovascular fitness levels as well as reducing body fat through aerobic exercise.

Explanation: trust

Answer:

Lower your risk of heart disease. Improve your blood pressure and blood sugar levels. Boost bone density, since walking is a weight-bearing exercise.

What is the Tesla? How is it defined? Mention any other unit for the magnetic field.

Answers

Answer:

Tesla is name of a car

uu the way to go back and said that

IF I CRASH THIS CAR ON A GLIDE DONT WORRY BOUT UR CAR GETTINH DENTED

19
What is the mass of a ball that is traveling 30 m/s and has 4.5 J of kinetic energy?
ave a GPF of 35512

Answers

Answer: The mass of ball is 10 grams.

Explanation:

Given : Kinetic energy = 4.5 J

Velocity = 30 m/s

The formula for Kinetic energy is as follows.

[tex]K.E = \frac{1}{2}mv^{2}[/tex]

where,

K.E = Kinetic energy

m = mass

v = velocity

Substitute the values into above formula as follows.

[tex]K.E = \frac{1}{2}mv^{2}\\4.5 J = \frac{1}{2} \times m \times (30 m/s)^{2}\\m = \frac{4.5 J \times 2}{900 m^2/s^2} (1 Js^{2} = kg m^{2})\\= 0.01 kg (1 kg = 1000 g)\\= 10 g[/tex]

Thus, we can conclude that the mass of ball is 10 grams.

Will give brainliest!!

Adding a solute to a solvent ________ the boiling point of the solvent.

lowers

does not change

raises

doubles

Answers

Answer:

lowers :)

Explanation:

If a car travels 300 kilometers in 3 hours, its average speed is 100 km/hr.

O True
O False

Answers

Answer:

True

Explanation:

300/3=100km/hr

hope it helps. Plz mark me as brainliest.

Answer:

True

hope it helps u

thanks

50POINTS PLEASE HELP SPACE QUESTION
Explain how and why seasons vary in the Northern and Southern Hemispheres.

Answers

Regardless of the time of year, the northern and southern hemispheres always experience opposite seasons. This is because during summer or winter, one part of the planet is more directly exposed to the rays of the Sun than the other, and this exposure alternates as the Earth revolves in its orbit.

The seasons in the Northern Hemisphere are the opposite of those in the Southern Hemisphere. Seasons occur because Earth is tilted on its axis relative to the orbital plane, the invisible, flat disc where most objects in the solar system orbit the sun.

A rectangular copper strip 1.5cm wide and 0.10cn thick carries a current of 5.0A. Find the Hall voltage for a 1.2T magnetic field applied in a direction perpendicular to the loop

Answers

Answer:

4.4345× 10^-7V

Explanation:

The computation of the half voltage for a 1.2T magnetic field applied is shown below

The volume of one mole of copper is

v = m ÷p

= 63.5 ÷ 8.92

= 7.12cm

Now the density of free electrons in copper is

n = Na ÷ V

= 6.02 × 10^23 ÷ 7.12

= 8.456× 10^28/m^3

Now the half voltage is

= IB ÷ nqt

= (5 × 1.20) ÷ (8.456× 10^28 × 1.6 × 10^-19 × 0.1× 10^-2)

= 4.4345× 10^-7V

Which form of energy is responsible for the change of state here?

Answers

Answer:

d

Explanation:

space question 50 points
Explain how sun angle and seasons vary as you move away from the equator.

Answers

Seasonal change in the angle of sunlight, caused by the tilt of the Earth's axis, is the basic mechanism that results both in warmth of the weather and in length of the day.

Find the frequency and wavelength of the wave below, assuming it has a speed of 30 m/s

Answers

100m/s divided by 40 Hz (cycles)=2.5 meters per cycle

plz help

In a pot of boiling water, what happens to the hot water at the bottom of the pot? What happens to the cold water at the top of the pot?​

Answers

Explanation:

First, the liquid on the bottom of the pot closest to the heat source starts to get hot; as it does, it rises. The rising hot water is replaced by the cooler, more dense water molecules. The water molecules in your pot continually exchange in this way, thanks to gravity, eventually warming the entire pot of liquid.

The water at the bottom of the pot becomes hot and it’s density decreases.Cold water could become water vapor.

Why would ash from a volcano make the temperature drop?

Answers

First, volcanic eruptions produce major quantities of carbon dioxide (CO2), a gas known to contribute to the greenhouse effect. ... The small ash particles decrease the amount of sunlight reaching the surface of the earth and lower average global temperatures.

A man kicks the 150-g ball such that it leaves the ground at an angle of 60° and strikes the ground at the same elevation a distance of 12 m away (14 points). Determine: (a). The velocity of the ball instantly after the man kicks the ball; (6 points) (b). Determine the impulse of his foot on the ball at A. (8 points) Neglect the impulse caused by the ball’s weight while it’s being kicked.

Answers

Answer:

[tex]313.92\ \text{m/s}[/tex]

[tex]47.088\ \text{kg m/s}[/tex]

Explanation:

m = Mass of ball = 150 g

[tex]\theta[/tex] = Angle of kick = [tex]60^{\circ}[/tex]

[tex]x[/tex] = Displacement of ball in x direction = 12 m

Range of projectile is given by

[tex]x=\dfrac{u\sin^2\theta}{2g}\\\Rightarrow u=\dfrac{2xg}{\sin^2\theta}\\\Rightarrow u=\dfrac{2\times 12\times 9.81}{\sin^260^{\circ}}\\\Rightarrow u=313.92\ \text{m/s}[/tex]

The velocity of the ball instantly after the man kicks the ball is [tex]313.92\ \text{m/s}[/tex]

Impulse is given by

[tex]J=mu\\\Rightarrow J=0.15\times 313.92\\\Rightarrow J=47.088\ \text{kg m/s}[/tex]

The impulse of his foot on the ball is [tex]47.088\ \text{kg m/s}[/tex].

To obtain maximum Electromotive force (EMF), you should connect the batteries in

Answers

Answer:

Series

Cells in Series connection.In series, cells are joined end to end so that the same current flows through each cell. In case if the cells are connected in series the emf of the battery connected to the sum of the emf of the individual cell,If E is the overall emf of the battery combined with n number cells and E1, E2,......Em is the EMFs of individual cell.

Then   

E= E1+E2+...............+Em.

A car goes 20 mph to 10 mph in five seconds find its acceleration

Answers

C.-2 miles per hour per second
Explanation;
Acceleration = change in velocity / time
Acceleration = (final velocity - initial velocity )/time
Acceleration = (v - u)/t
Given: u = 20 miles per hour, v = 10 miles per hour
t = 5 seconds
Acceleration = (10 - 20)/5
Acceleration = -10/5
Acceleration = -2 miles per hour per second

a wave raises a buoy twice every second and the crests of the incoming waves are 4m apart
what is the wavelength in meters?

Answers

You just said that the crests of the incoming waves are 4m apart.

That's it ! That's the wavelength. The distance between crests. It doesn't matter how often they sail past you.

The question I was expecting here: How fast are the waves traveling ?

That's (frequency)x(wavelength). 8 m/s.

Do anyone know this ?

Answers

Answer:

Distance is 100m, displacement is 0m

Explanation:

Distance is how much you travelled in total (100m)

Displacement is when you compare your final and initial positions.

It is usually Final position - Initial position.

Since you start and finish at the same point, it would be 0 - 0 = 0m

So the displacement is 0m.

Distance is 100 and displacement is 0

Which of the following is an example of a noncontrolled substance?
A. Sleeping pills
B. Coffee
C. Pain medications
D. Cough medications
SUBMIT

Answers

An example of noncontrolled substance from the option is Cough medications.

What are Noncontrolled substances?

Noncontrolled substances are substances that are prescribed by medical personnel or pharmaceutical professionals for treatment of a disorder or ailments that is affecting a person.

Noncontrolled substances include medications that are majorly prescribed for treatment of medical conditions like high blood pressure, diabetes, and bacterial infections.

Therefore, An example of noncontrolled substance from the option is Cough medications.

Learn more about noncontrolled substances below.

https://brainly.com/question/5349491

a large heavy truck and a baby carriage roll down a hill. Neglecting friction, at the bottom of the hill, the baby carriage will likely have A. less momentum, B. about the same momentum, C. more momentum or D. double the momentum of the truck​

Answers

Answer:

please give me brainlist and follow

Explanation:

At the bottom of the hill, the baby carriage will likely have less momentum Therefore, option D is correct. Solution: ... Therefore, at the bottom of the hill, the heavy truck will have more momentum and baby carriage will have less momentum.

Compare the kinetic and potential energies of a 400 kg box being moved
horizontally by a forklift at a speed of 5 m/s. The box is at a height of 1 m.

Answers

Answer:

Kinetic energy is greater than the potential energy.

Explanation:

The potential energy stays constant because the height is not changing.  Potential energy = MGH, where m is the mass (400 kg), g is the acceleration due to gravity (9.8 m / sec2), and H is the height (1 m).  So the result is 400 * 9.8 * 1 = 3920 J

 

The kinetic energy = 1/2 mv2 = 0.5  * 400 kg * (5 m/sec)2 = 5000 J.  It also stays constant because the speed is not changing.

 

Therefore, the kinetic energy is greater than the potential energy.

The elastic force acting on a 0.60 kg object on a spring is 1.2 N. If the distortion of the object is 0.025 m to the right, what is the spring constant?​

Answers

Answer:

Spring constant = 48 N/m

Explanation:

Given the following data;

Mass = 0.60 kg

Force = 1.2 N

Distortion = 0.025 m

To find the spring constant;

Mathematically, the force exerted on a spring to cause a distortion or an extension is given by the formula;

Force = spring constant * distortion

Substituting into the formula, we have;

1.2 = spring constant * 0.025

Spring constant = 1.2/0.025

Spring constant = 48 N/m

Which situation will change the direction of the bicycle?
A. An added force of 20 N down the hill
B. Added forces of 30 N up the hill and 30 N down the hill
C. An added force of 20 N to the side of the hill
D. Added forces of 10 N up the hill and 30 N down the hill

Answers

Answer:

Dont know if this is right but i say C

Explanation:

Answer:

C. an added force of 20 N toward one side of the hill

Explanation:

I just took the quiz and got it correct./

. A convertible moves toward you and then passes you; all the while, its loudspeakers are producing a sound. The speed of the car is a constant 9.30 m/s, and the speed of sound is 342 m/s. What is the ratio of the frequency you hear while the car is approaching to the frequency you hear while the car is moving away

Answers

Answer:

[tex]1.056[/tex]

Explanation:

v = Velocity of sound = 342 m/s

[tex]v_s[/tex] = Velocity of source of sound = 9.3 m/s

[tex]f_a[/tex] = Frequency when car is approaching

[tex]f_m[/tex] = Frequency when car is moving away

[tex]f_s[/tex] = Frequecy of source of sound

The required ratio is

[tex]\dfrac{f_a}{f_m}=\dfrac{\dfrac{v}{v-v_s}f_s}{\dfrac{v}{v+v_s}f_s}\\\Rightarrow \dfrac{f_a}{f_m}=\dfrac{v+v_s}{v-v_s}\\\Rightarrow \dfrac{f_a}{f_m}=\dfrac{342+9.3}{342-9.3}\\\Rightarrow \dfrac{f_a}{f_m}=1.056[/tex]

The ratio of the frequency you hear while the car is approaching to the frequency you hear while the car is moving away is [tex]1.056[/tex]

Someone please help me! And I will mark you as brainlist!!

1) A ball with a mass of 2.0 kg is thrown upward 1.2m calculate its gravitational potential energy into two significant figures. Gravity = 9.8 N/kg

• 2.4 J
• 1.4 J
• 120 J
• 24 J


2) Translation kinetic energy is defined as the energy of a system due to the motion of the system’s...

• center of mass
• axis of symmetry
• molecules
• rotational movement

PLEASE HELP!!

Answers

Answer:

1. G.P.E = 24 J

2. center of mass

Explanation:

Given the following data;

Mass = 2kg

Height, h = 1.2m

Acceleration due to gravity = 9.8 N/kg or m/s².

To find the gravitational potential energy;

Gravitational potential energy (GPE) is an energy possessed by an object or body due to its position above the earth.

Mathematically, gravitational potential energy is given by the formula;

[tex] G.P.E = mgh[/tex]

Where;

G.P.E represents potential energy measured in Joules.m represents the mass of an object. g represents acceleration due to gravity measured in meters per seconds square. h represents the height measured in meters.

Substituting into the formula, we have;

[tex] G.P.E = 2*1.2*9.8 [/tex]

G.P.E = 23.52 to 2 S.F = 24 Joules.

Translation kinetic energy is defined as the energy of a system due to the motion of the system’s center of mass. The center of mass is typically where the mass of the object or particle is concentrated.

A wave travels 1.5 m/s with a frequency of 0.45 Hz. What is the wavelength of the wave?

Answers

Answer:

3.33m

Explanation:

λ = C/f

Where,

λ (Lambda) = Wavelength in meters

c = velocity=1.5m/s

f = Frequency=0.45

λ = 1.5/0.45

=3.33m.

Suppose that a particle accelerator is used to move two beams of particles in opposite directions. In a particular region, electrons move to the right at 4910 m/s and protons move to the left at 2583 m/s. The particles are evenly spaced with 0.0758 m between electrons and 0.0577 m between protons. Assuming that there are no collisions and that the interactions between the particles are negligible, what is the magnitude of the average current in this region

Answers

Answer:

The answer is "[tex]17.28 \times 10^{-14}\ A[/tex]"

Explanation:

Calculating the number of electrons passing in per second:

[tex]\to n_e = \frac{4910}{0.0758} = 6.4 \times 10^5[/tex]

Calculating the current in electron:

[tex]\to I_e = 6.4 \times 10^5 \times 1.6 \times 10^{-19} = 10.24 \times 10^{-14}\ A[/tex]

Calculating the number of protons passing in per second:

[tex]\to n_p = \frac{2583}{0.0577} = 4.4 \times 10^{4}[/tex]

Calculating the current in proton:

[tex]\to I_p = 4.4 \times 10^{4} \times 1.6 x 10^{-19} = 7.04 \times 10^{-14} \ A[/tex]

Calculating the total current:

[tex]\to I = I_p + I_e = 17.28 \times 10^{-14}\ A[/tex]

a student throws a coin vertically downward frok the top of a building. the coin leaves the throwers hand with a speed of 15.0m/s. what is its speed after falling freely for 2.00s?​

Answers

Answer:

Final speed after 2 seconds = 34.6 m/s

Explanation:

Given:

Initial speed of coin (u) = 15 m/s

Time taken = 2 seconds

Find:

Final speed after 2 seconds

Computation:

Gravitational acceleration of earth = 9.8 m/s²

Using first equation of motion;

v = u + at

or

v = u + gt

where,

v = final velocity

u = initial velocity

g = Gravitational acceleration

t = time taken

v = 15 + 9.8(2)

v = 15 + 19.6

Final speed after 2 seconds = 34.6 m/s

A 10 g bullet moving horizontally with a speed of 2000 m/s strikes and passes through a 4.0 kg block moving with a speed of 4.2 m/s in the opposite direction on a horizontal frictionless surface. If the block is brought to rest by the collision, what is the kinetic energy of the bullet as it emerges from the block. Round off your answer to zero decimal places.

Answers

Answer:

The answer is "512 J".

Explanation:

bullet mass [tex]m_1 = 10 g= 10^{-2} \ kg\\\\[/tex]

initial speed [tex]u_1 = 2\ \frac{Km}{s}= 2000\ \frac{m}{s}\\\\[/tex]

block mass [tex]m_2 = 4\ Kg[/tex]

initial speed [tex]v_2 =-4.2 \frac{m}{s}[/tex]

final speed [tex]v_2= 0[/tex]

Let [tex]v_1[/tex] will be the bullet speed after collision:

throughout the consevation the linear moemuntum

[tex]\to M_1V_1+m_2v_2=M_1U_1+m_2u_2\\\\\to (10^{-2} kg) V_1 +0 = (10^{-2} kg)(2000 \frac{m}{s}) + (4 \ kg)(-4.2 \frac{m}{s}) \\\\\ \to 10^{-2} v_1 = 20 -16.8\\\\[/tex]

                [tex]= 320 \frac{m}{s}[/tex]

The kinetic energy of the bullet in its emerges from the block

[tex]k=\frac{1}{2} m_1 v_1^2[/tex]

   [tex]=\frac{1}{2} \times 10^{-2} \times 320\\\\=512 \ J[/tex]

if you travel at a constant velocity what happens to the time it takes to travel you need to travel a longer distance ?

Answers

velocity-time. The relation between velocity and time is a simple one during uniformly accelerated, straight-line motion. The longer the acceleration, the greater the change in velocity. Change in velocity is directly proportional to time when acceleration is constant. Here is the formula for this for extra information VT=D. Hope this helps! Mark brainly please!
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Given z, find lzl.Z = 10iIzI = [?] Brian is 6 feet tall and cast a 12 foot shadow. At the same time, Shirley casts a 9 foot shadow. How tall is shirley? A former sells 9.4 kilograms of pears and apples at the farmers market. 4/5 of this weight is pears and the rest is apples. How many kilograms of apples did she sell at the farmers market PLEASE HELP THIS ASSINGMENT IS LATE Describe one way that a natural event can cause a decline in biodiversity. Please tell me please Swimming burns more calories per hour than aerobics and cycling. T or F? In a math class, the teacher always calls on the males, being sure to give them more wait time than the females. When male students get the answer correct, they receive specific, targeted praise, while the girls receive generic, one-word feedback. All of the posters in the room reference men who have done great things with mathematics, while there are no references to females who use math in society. By the end of the year, both the males and the females believe that "math is for boys and not for girls." Such a lesson would be part of the ___________. Advanced Products Corporation has supplied the following data from its activity-based costing system:Overhed CostsWages and salaries $300,000 Other overhead costs 100,000 Total overhead costs $400,000 Activity Cost Pool Activity Measure Total Activity for the Year Supporting direct labor Number of direct labor-hours 20,000 DLHs Order processing Number of customer orders 400 orders Customer support Number of customers 200 customers Other This is an organization- sustaining activity Not applicable Distribution of Resource Consumption Across Activities Supporting Direct Order Customer Other Total Labor Processing SupportWages and salaries 40% 30% 20% 10% 100% Other overhead costs 30% 10% 20% 40% 100% During the year, Advanced Products completed one order for a new customer, Shenzhen Enterprises. This customer did not order any other products during the year. Data concerning that order follow: Data Concerning the Shenzhen Enterprises Order Units ordered 10 units Direct labor-hours 2 DLHs per unit Selling price $300 per unit Direct materials $180 per unit Direct labor $50 per unit1. Using Exhibit, prepare a report showing the first-stage allocations of overhead costs to the activity cost pools.2. Using Exhibit, compute the activity rates for the activity cost pools.3. Prepare a report showing the overhead costs for the order from Shenzhen Enterprises including customer support costs.4. Using Exhibit, prepare a report showing the customer margin for ShenzhenEnterprises. You purchase a new car for $24,000. If you obtain a 5 year bank loan at 2.75% compounded monthly, what is your monthly loan payment? PLEASE HELP I WILL GIVE BRAINLIEST due today please helpp A stone is thrown horizantally with a velocity of 50 m/s from the top of a building. Find its velocity after 2 seconds. What value of n makes the equation true ? Show your work. Which of the following describes the importance of the University of Michigan to the 1960s antiwar movement? The Gulf of Tonkin Resolution was passed there. It was the location of a three-day counterculture music festival. It was where the Students for a Democratic Society was established. Students from that university wrote Catch-22. How does the poem's use of repetition contribute to the tone of the poem? Sonnet 43 Select all the statements that describe the expression 5 + 2x. *The expression represents 5 plus 2 plus x.The expression represents 5 plus 2 times xThe expression represents 5 plus x plus x.The expression represents 5 plus x times x.The expression represents the sum of 5 and 2xThe expression represents the product of 5 and 2x. A bag has 2 mint cookies, 1 donut, and 4 wafer cookies. Two items are drawn one at a time without replacement. What is the probability of first drawing 1 donut, and next drawing 1 mint cookie? Grasses mice cat coyote A natural disaster of a fire has occurred what could happen to this food chain? The grasses will be gone and all of the consumers will be able to leave. The grasses will be gone and some of the mice will die but the number of cats and coyotes will remain the same. The grasses will be gone but the number of consumers will all stay the same. The grasses will be gone and any surviving consumers will have to look for new resources in that environment. Nothing will happen to this food chain. [15 POINTS!!]The diagram below shows a food web.How would the removal of the rabbit population affect the other populations in the ecosystem?A. The field mouse population will decrease.B. The snake population will increaseC. The lizard population will increase.D. The tree population will decrease Can you help thanks!