Answers
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].
Related Questions
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.
Find the frequency and wavelength of the wave below, assuming it has a speed of 30 m/s
Answers
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.
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 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
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
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.
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
Why would ash from a volcano make the temperature drop?
Answers
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.
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
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]
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.
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:
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.
50POINTS PLEASE HELP SPACE QUESTION
Explain how and why seasons vary in the Northern and Southern Hemispheres.
Answers
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.
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.
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.
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.
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.
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].
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
if you travel at a constant velocity what happens to the time it takes to travel you need to travel a longer distance ?
Answers
. 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]
A car goes 20 mph to 10 mph in five seconds find its acceleration
Answers
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
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 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]
Which form of energy is responsible for the change of state here?
Answers
Answer:
d
Explanation:
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
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.