Answer:
Semen is the most important thing in the life cycle of life
It is a “new moon” (the Moon is totally dark in the sky). Using the masses of the Earth, Sun, and Moon and the average distances between the Earth-Moon and Earth-Sun, find the net gravitational force on the Earth from the Sun and the Moon combined.
Find also distance when it is full moon
It is a “new moon” (the Moon is totally dark in the sky). The gravitational force between the Earth and the Moon is:
2.9 x 10^20 N3.5 x 10^22 N3.5 x 10^22 NWhat is gravitational force?Generally, The gravitational force between two objects is given by the equation:
force = G * (mass1 * mass2) / distance^2
Where G is the gravitational constant (6.67 x 10^-11 N*(m/kg)^2), mass1 and mass2 are the masses of the two objects, and distance is the distance between the two objects.
The mass of the Earth is 5.972 x 10^24 kg, the mass of the Moon is 7.347 x 10^22 kg, and the mass of the Sun is 1.989 x 10^30 kg. The average distance between the Earth and the Moon is 384,400 km, and the average distance between the Earth and the Sun is 149.6 million km.
The gravitational force between the Earth and the Moon is:
force = (G * (mass of Earth) * (mass of Moon)) / (distance between Earth and Moon)^2 force
= (6.67 x 10^-11 N*(m/kg)^2) * (5.972 x 10^24 kg) * (7.347 x 10^22 kg) / (384400 x 10^3 m)^2 force
= 2.9 x 10^20 N
The gravitational force between the Earth and the Sun is:
force = (G * (mass of Earth) * (mass of Sun)) / (distance between Earth and Sun)^2 force
= (6.67 x 10^-11 N*(m/kg)^2) * (5.972 x 10^24 kg) * (1.989 x 10^30 kg) / (149.6 x 10^9 m)^2 force
= 3.5 x 10^22 N
To find the net gravitational force on the Earth from the Sun and Moon combined, we add the two forces we found above.
Net force = 2.9 x 10^20 N + 3.5 x 10^22 N
= 3.5 x 10^22 N
When it is a Full Moon the distance is the same 384,400 km
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NO LINKS
According to "Patterns of Change," select the ways that rocks are changed naturally over time. Choose three answers. O A. water O B. location O C. animals D. wind O E. people O F temperature
Answer: A , D & F
Explanation:
A submarine has a 'crush depth" (that is, the depth at which water pressure will crush the submarine) of 100 m. What is the approximate pressure (water plus atmospheric) at this depth? (Recall that the density of seawater is 1025 kg/m³, g = 9.81 m/s², and 1 kg/(m•s²) = 1 Pa = 9.8692 x 10-⁶ atm.)
A) 10.9 atm
B) 9.9atm
C)37.9atm
D)25.9atm
Answer:
25.9atm
Explanation:
Answer: my grandfather was a marine so he kept me in check
25.8 atm
Explanation:
Total pressure is:
P = Patm + ρgh
where Patm is the atmosphere pressure,
ρ is the fluid density,
g is acceleration due to gravity,
and h is the depth of the fluid.
P = (1 atm) + (1025 kg/m³) (9.81 m/s²) (250 m) (9.8692×10⁻⁶ atm/Pa)
P = 1 atm + 24.8 atm
P = 25.8 atm
Which of the following are most likely to form a stable ionic bond
a
b
U
d
Carbon (Period IVA) and Oxygen (Period VIA)
Lithium (Period IA) and Fluorine (Period VIIA)
Magnesium (Period IIA) and Iron (Period VIIIB)
Potassium (Period IA) and Tin (Period IVA)
Lithium (Period IA) and Fluorine (Period VIIA) will most likely form a stable ionic bond.
What is stable ionic bond?
This is an bond formed by a metal and non metal.
The major factors that causes the formation of a stable ionic bonds is the large differences in electronegativity of atoms, which attract other atoms for the transfer of their electrons.
In the given examples;
Lithium is a metal with ionization number of +1Fluorine is non metal with ionization number of -1Li⁺ + F⁻ ---------> LiF
Thus, Lithium (Period IA) and Fluorine (Period VIIA) will most likely form a stable ionic bond.
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An object has a horizontal velocity component of 6 m/s
and a vertical velocity component of 4 m/s.
1a. Find its velocity.
2a. Find the angle it makes with the horizontal.
Answer:
answer here is 5 hope I'm right
A boy slides a book across the floor, using a force of 5 N over a distance of 2
m. What is the kinetic energy of the book after he slides it? Assume there is
no friction.
A. 5 J
B. 10 J
C. 20 J
D. 2.5 J
SUBMIT
The kinetic energy of the book after it is slids a distance of 2 meters will be 10 Joules.
How to determine the kinetic energy of an object?The work-energy theorem states that "the work done on an object is the change in its kinetic energy".
Hence;
Kinetic energy = work done
Note that: work-done is expressed as:
Work done = f × d
Where f is force applied and d is distance traveled.
Given that:
Force applied f = 5 newton
Distance d = 2 meters
Work done = ?
Plug these values into the above formula and solve for the workdone.
Work done = f × d
Work done = 5N × 2m
Work done = 10Nm
Work done = 10 Joules
Therefore, the kinetic energy is 10 Joules.
Option B) 10 J is the correct answer.
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The key insight that Bohr introduced to his model of the atom was that the angular momentum of the electron orbiting the nucleus was quantized. He introduced the postulate that the angular momentum could only come in quantities of nh/(2π), where h is Planck's constant and n is a nonnegative integer (0,1,2,3,…). Given this postulate, what are the allowable values for the velocity v of the electron in the Bohr atom? Recall that, in circular motion, angular momentum is given by the formula L= mvr.
Answer:
v = \(n \frac{\hbar }{m r}\)
the sppedof the electron is also quantized
Explanation:
The angular momentum of a rotating body is
L = m v r
in Bohr's atomic model the quantization postulate is that the angular momentum is equal to
L = n \(\hbar\)
we substitute
n \(\hbar\) = m v r
v = \(n \frac{\hbar }{m r}\)
where n is an integer.
Therefore, the sppedof the electron is also quantized, that is, sol has some discrete values.
How much current is in a circuit with a 1.5 V battery and three
2-ohm resistances (bulbs) in series?
Answer: 0.25A
Explanation: To calculate the current in the circuit, we can use Ohm's Law, which states that the current (I) flowing through a circuit is equal to the voltage (V) divided by the resistance (R):
I = V / R
In this case, the total resistance of the circuit is the sum of the individual resistances of the three bulbs in series, which gives us:
R = 2 + 2 + 2 = 6 ohms
The voltage of the battery is given as 1.5V.
So, using Ohm's Law, we can calculate the current in the circuit as:
I = V / R = 1.5 / 6 = 0.25 amps
Therefore, the current in the circuit is 0.25 amps.
The current in the circuit is 0.25 A.
Voltage across the circuit, v = 1.5 V
Resistance in each resistors, R = 2Ω
Since, the resistors are connected in series combination, their effective resistance,
R' = 3R
R' = 3 x 2
R' = 6Ω
According to Ohm's law, if the temperature and all other physical factors remain constant, the voltage across a conductor is directly proportional to the current that is flowing through it.
So, according to Ohm's law,
V = IR
Therefore, current flowing through the given circuit,
I = V/R
I = 1.5/6
I = 0.25 A
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Part A The potential energy for a certain mass moving in one dimension is given by U(x) = (2.0 J/m3)x3 - (15 J/m2)x2 + (36 J/m)x - 23 J. Find the location(s) where the force on the mass is zero. The potential energy for a certain mass moving in one dimension is given by U(x) = (2.0 J/m3)x3 - (15 J/m2)x2 + (36 J/m)x - 23 J. Find the location(s) where the force on the mass is zero. 3.0 m, 5.0 m 4.0 m, 5.0 m 2.0 m, 3.0 m 1.0 m
Answer:
The location are \(x_1 = 2 \ and \ x_2 = 3\)
Explanation:
From the question we are told that
The potential energy is \(U(x) = (2.0 \ J/m^3) * x^3 - (15 \ J/m) * x^2 + (36 \ J/m) * x - 23 \ J\)
The force on the mass can be mathematically evaluated as
\(F = - \frac{d U(x)}{d x } = -( 6 x^2 - 30x +36)\)
The negative sign shows that the force is moving in the opposite direction of the potential energy
\(F = - 6 x^2 + 30x - 36\)
At critical point
\(\frac{d U(x)}{dx} = 0\)
So
\(- 6 x^2 + 30x - 36 = 0\)
\(- x^2 + 5x - 6 = 0\)
Using quadratic equation formula to solve this we have that
\(x_1 = 2 \ and \ x_2 = 3\)
A cell of inter resistance of 0.5 ohm is connected to coil of resistance 4 ohm and 8 ohm joined in parallel.If there is current of 2A in 8 ohm,find the emf of the cell.
A cell of inter resistance of 0.5 ohm is connected to coil of resistance 4 ohm and 8 ohm joined in parallel.If there is current of 2A in 8 ohm, the electromotive force (emf) of the cell is approximately 14.5 volts.
To find the emf of the cell, we can apply Ohm's Law and Kirchhoff's laws to analyze the circuit.
Given:
Resistance of the coil, R1 = 4 ohm
Resistance of the other resistor, R2 = 8 ohm
Current passing through the 8-ohm resistor, I = 2A
First, let's analyze the parallel combination of the 4-ohm and 8-ohm resistors.
The total resistance of two resistors in parallel can be calculated using the formula:
1/Rp = 1/R1 + 1/R2
Substituting the given values, we have:
1/Rp = 1/4 + 1/8
1/Rp = 2/8 + 1/8
1/Rp = 3/8
Rp = 8/3 ohm
Now, let's consider the total resistance in the circuit, which includes the internal resistance of the cell (0.5 ohm) and the parallel combination of the resistors (8/3 ohm).
R_total = R_internal + Rp
R_total = 0.5 + 8/3
R_total = 1.833 ohm
Now, we can find the emf of the cell using Ohm's Law:
emf = I * R_total
emf = 2 * 1.833
emf ≈ 3.667 volts
Therefore, the emf of the cell is approximately 3.667 volts.
However, it is worth noting that the given current of 2A passing through the 8-ohm resistor does not affect the emf calculation since the emf of the cell is independent of the current in the circuit.
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A pitcher throws a baseball from the pitcher's mound to home plate in 0.46 s. The
distance is 18.4 m. What was the average speed of the baseball?
a. 40 m/s
b. - 40 m/s
c. 0.03 m/s
d. 8.5 m/s
The average speed of the baseball is option a. 40 m/s .
To calculate the average speed of the baseball, we use the formula:
Average Speed = Distance / Time
Given:
Distance = 18.4 m
Time = 0.46 s
Plugging in the values, we have:
Average Speed = 18.4 m / 0.46 s = 40 m/s
Therefore, the average speed of the baseball is 40 m/s.
Option a, 40 m/s, is the correct answer. This means that the baseball traveled an average distance of 40 meters per second from the pitcher's mound to home plate.
Average speed is a scalar quantity that represents the total distance traveled divided by the total time taken. It gives us an idea of how fast an object is moving on average over a given distance.
In this case, the baseball covered a distance of 18.4 meters in a time of 0.46 seconds. Dividing the distance by the time gives us the average speed of 40 m/s.
It's important to note that average speed is a measure of the overall rate of motion and does not provide information about the direction of motion. Therefore, negative values such as option b (-40 m/s) or extremely small values such as option c (0.03 m/s) are not appropriate in this context.
Option d (8.5 m/s) is also incorrect as it does not match the calculated average speed of 40 m/s.
Therefore, the correct answer is option a, 40 m/s, as it accurately represents the average speed of the baseball.
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Which of the following is true at the point where you reach the top of your jump on a trampoline?
The mechanical energy is zero
he potential energy is at maximum
The kinetic energy and potential energy are equal.
The potential energy is zero.
The potential energy is at the maximum when you reach the top of your jump on a trampoline. The correct answer is option B.
What is Potential EnergyPotential Energy is the type of energy an object possesses by virtue of its position relative to others, stresses within itself, electric charge, and other factors. Potential energy exists in various forms, including gravitational potential energy, elastic potential energy, chemical potential energy, and electrical potential energy.
This type of energy can be converted into another type of energies. Examples, a charged battery has potential energy and it can be used as electrical potential energy. Petrol, diesel and and gas have chemical potential energy and be used as kinetic energy.
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A force of 14N acts at an angle of 235° to the positive x-axis. Resolve this force into components parallel to the x- and y- axis.
The x component of the force is -8.03 N.
The y component of the force is -11.47 N.
What are the parallel components?The parallel components of the force is resolved into x and y components as follows;
The x component of the force is calculated as follows;
Fx = F cosθ
where;
θ is the angle of inclination of the forceF is the magnitude of the forceFx = 14 N x cos (235)
Fx = -8.03 N
The y component of the force is calculated as follows;
Fy = F sinθ
where;
θ is the angle of inclination of the forceF is the magnitude of the forceFy = 14 N x sin (235)
Fy = -11.47 N
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Light travels through air faster than it travels through water. How would
the light refract differently if the keys were in air, and the boy was looking
at them from underwater?
Answer:
The fastest thing in the whole universe is the speed of light in a vacuum (like outer space!), clocking in at a great 2.99 x 108 m/s. Light travels in waves, and we call this traveling propagation. Propagation of waves has both a speed and a direction, called the velocity. The velocity of light changes depends on the material it travels through.
I hope it is helpful. Please mark as brilliant
1. A ball rolls off the edge of a table that is 1.83m high and lands 1.2m from the base of A
the table.
a.
How much time passed between the moment the car left the table and the
moment it hit the floor? (3 steps)
b. What was the horizontal velocity of the car when it hit the ground?
(1 step with info from part a)
Time passed between the moment the car left the table and the moment it hit the floor is 0.95 second.
Speed, amount that designates how rapid and in what route a point is moving. A point always actions in a path that is tangent to its path; for a round direction, as an instance, its route at any immediately is perpendicular to a line from the factor to the centre of the circle (a radius).
Speed is the time charge at which an object is moving along a path, at the same time as velocity is the fee and route of an item's movement.
Calculation:-
S = ut + 1/2 at²
1.83 = 0.5t²
t² = 1.83/0.5
= 0.915
= 0.95 Second
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(a) If two sound waves, one in a gas medium and one in a liquid medium, are equal in intensity, what is the ratio of the pressure amplitude of the wave in the liquid to that of the wave in the gas? Assume that the density of the gas is 2.27 kg/m3 and the density of the liquid is 972 kg/m3. The speed of sound is 376 m/s in the gas medium and 1640 m/s in the liquid. (b) If the pressure amplitudes are equal instead, what is the ratio of the intensities of the waves (of the one in the liquid to that in the gas)?
Answer:
(a) The ratio of the pressure amplitude of the waves is 43.21
(b) The ratio of the intensities of the waves is 0.000535
Explanation:
Given;
density of gas, \(\rho _g\) = 2.27 kg/m³
density of liquid, \(\rho _l\) = 972 kg/m³
speed of sound in gas, \(C_g\) = 376 m/s
speed of sound in liquid, \(C_l\) = 1640 m/s
The of the sound wave is given by;
\(I = \frac{P_o^2}{2 \rho C} \\\\P_o^2 = 2 \rho C I\\\\p_o = \sqrt{2 \rho CI}\)
Where;
\(P_o\) is the pressure amplitude
\(P_o_g= \sqrt{2 \rho _g C_gI} -------(1)\\\\P_o_l= \sqrt{2 \rho _l C_lI}---------(2)\\\\\frac{P_o_l}{P_o_g} = \frac{\sqrt{2 \rho _l C_lI}}{\sqrt{2 \rho _g C_gI}} \\\\\frac{P_o_l}{P_o_g} = \sqrt{\frac{2 \rho _l C_lI}{2 \rho _g C_gI} }\\\\ \frac{P_o_l}{P_o_g} = \sqrt{\frac{ \rho _l C_l}{ \rho _g C_g} }\\\\ \frac{P_o_l}{P_o_g} = \sqrt{\frac{ (972)( 1640)}{ (2.27)( 376)} }\\\\\frac{P_o_l}{P_o_g} = 43.21\)
(b) when the pressure amplitudes are equal, the ratio of the intensities is given as;
\(I = \frac{P_o^2}{2 \rho C}\\\\I_g = \frac{P_o^2}{2 \rho _g C_g}-------(1)\\\\I_l = \frac{P_o^2}{2 \rho _l C_l}-------(2)\\\\\frac{I_l}{I_g} = (\frac{P_o^2}{2 \rho _l C_l})*(\frac{2\rho_gC_g}{P_o^2} )\\\\\frac{I_l}{I_g} = \frac{\rho _gC_g}{\rho_lC_l} \\\\\frac{I_l}{I_g} = \frac{(2.27)(376)}{(972)(1640)}\\\\ \frac{I_l}{I_g} = 0.000535\)
As observed from Earth, the Sun has an angular size of about 0.53o. From the observation, estimate the diameter of the Sun. How large in volume is the Sun when compared to Earth?
prepare a report on why a vehicle needs to be maintained/serviced after a certain period of time. How is servicing different in a petrol/diesel and electric vehicle?
Vehicles need to be serviced for several reasons such as preventing costly repairs and improving fuel economy.
Why should cars be maintained and / or serviced ?First, regular maintenance can help to prevent costly repairs down the road. Second, maintenance can help to improve fuel economy and emissions. Third, maintenance can help to keep your vehicle safe and reliable.
The servicing requirements for petrol/diesel and electric vehicles differ in a number of ways. Petrol/diesel vehicles require oil changes more frequently than electric vehicles. This is because petrol/diesel engines use oil to lubricate the moving parts, while electric motors do not. Petrol/diesel vehicles also require tune-ups more frequently than electric vehicles.
This is because petrol/diesel engines have more moving parts that need to be synchronized, while electric motors have fewer moving parts.
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light of wavelength 587.5 nm illuminates a slit of width 0.75 mm. at what distance from the slit should a screen be placed if the first minimum in the diffraction pattern is to be 0.85 mm from the central maximum?
1.085m
Explanation:
Using
a= lambda/sinစ
Sinစ= (587.5*10^-9) x 0.75*10^-3
= 0.000783
Sinစ=0.875*10^-3/d
0.000783= 0.875/d
d= 1.085m
I will give away all my points for whoever get's this right
I am taken from a mine, and shut up in a wooden case, from which I am never released, and yet I am used by almost everybody. What am I?
Answer:
Pencil lead.
Explanation:
no need for an explemation you can put two and two together XD
Answer:
Hello!!! Princess Sakura here ^^
Explanation:
It's pencil lead because the it's taken from a mine and then it goes inside a wooden pencil and everybody uses them if you're not using a pen.
7 The distance-time graph for a motorcyclist riding off from rest is shown in Figure 1.2.18.
a Describe the motion.
b Calculate how far the motorbike moves in 30 seconds.
c Calculate the speed.
The distance travelled by the motorbike is 600 m and the speed of the motorbike is 20 m/s.
What is the motion of the motorbike?The motion of the motorbike can be described as linear type of motion since the distance travelled by the motorbike increases with increase in the time of motion.
There is directly linear relationship between the distance travelled by the motorbike and the time of motion of the motorbike.
The distance travelled by the motorbike is calculated as follows;
from the given graph, at time 30 seconds, the corresponding the distance of the motorbike on the vertical axis is 600 m.
distance = 600 m
The speed of the motorbike is calculated as follows;
v = d/t
v = 600 m / 30 s
v = 20 m/s
Thus, the motion of the motorbike is a linear type of motion, the distance travelled by the motorbike increases with increase in the time of motion and the speed of the motorbike depends on the distance and time of motion.
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The area around a magnet containing all of magnetic Lines of force is called
Answer:
Magnetic Field
Explanation:
The area around a magnet containing all of magnetic Lines of force is called the magnetic field.
How does the tension in your arms compare when you let yourself dangle motionless by both arms and by one arm
When you support yourself with two arms, the tension in each arm is half of the tension you experience when you support your weight with only one arm.
The tension in your arm is directly proportional to the weight of your body.
T = W = mg
When you support your weight with your two arms;
the upward force balancing the downward force due to the weight of your body will be distributed equally in both arms.\(Tension \ in \ each \ arm = \frac{Total \ weight \ of \ your \ body}{2}\)
When you support the weight of your body with one arm,
the upward force balancing the downward force due to your weight will be on only one arm\(Tension \ in \ the \ one \ arm = Total \ weight \ of \ your \ body\)
Thus, when you support yourself with two arms, the tension in each arm is half of the tension you experience when you support your weight with only one arm.
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When you support yourself with two arms, the tension in each arm is half of the tension you experience when you support your weight with only one arm.
What is the current if the electricpotential is 120 V and the resistance is
60 ohms?
Answer:
2 amperes
Explanation:
V = IR
V/R = I
120 v / 60 ohms = 2 amps
"She finished the sprint with the speed of a cheetah." This statement represents which of the
following functions of language? (2 points)
correct answer is poetic.
Answer:
Poetic
Explanation:
I took the test
Answer:
Poetic
Explanation:
I got it right on the test
A gas expands from I to F in the figure. The energy added to the gas by heat is 465 J when the gas goes from I to F along the diagonal path. What is the change in internal energy of the gas?
The gas's internal energy that expands from I to F changes by 1015 J.
How to determine internal energy?Since the gas is expanding and energy is added to it by heat, the change in internal energy of the gas can be calculated using the first law of thermodynamics, which states that:
ΔU = Q - W
where ΔU = change in internal energy,
Q = heat added to the system, 465 J and
W = work done by the system.
Assuming that the process is quasi-static use approximation known as the "staircase approximation."
By adding up the work done in each step, find that the total work done by the gas is approximately -550 J. The negative sign indicates that work is done on the gas.
Therefore, using the first law of thermodynamics, we can calculate the change in internal energy of the gas as:
ΔU = Q - W
ΔU = 465 J - (-550 J)
ΔU = 1015 J
Therefore, the change in internal energy of the gas is 1015 J.
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how do the valves do in the heart
Answer:
The valves prevent the backward flow of blood. These valves are actual flaps that are located on each end of the two ventricles (lower chambers of the heart). They act as one-way inlets of blood on one side of a ventricle and one-way outlets of blood on the other side of a ventricle.
Explanation:
unit 2 Lesson 9: Temperature & Heat Unit Test does anyone have the answers
Explanation:
where is the question
I did not understood this question
Answers:
Here are the answers for the U2L9: Temperature & Heat Unit Test
1. Which describes how radiation moves?
B) Radiation moves from a warmer object to a cooler object
2. Which material most likely gets warmer when places in the Sun?
C) brown mulch
3. A thermogram of a house shows high amounts of thermal energy around the windows but not around the roof. Which conclusion is best supported by the thermogram?
C) The windows are not energy efficient, but the roof is.
4. Which best describes convection?
D) It is driven by temperature differences within a fluid.
5. A student heats a liquid on a burner. What happens to the portion of liquid that first begins to warm?
Any answer you choose is correct on Connexus (look at the screenshot)
6. Convection only occurs in ____.
B) fluids
7. Conduction involves the transfer of electric charge or ____.
A) thermal energy
8. A scientist designed a foam container to help keep frozen foods from melting. Which best explains how the foam works?
D) It reduces the amount of thermal energy that is transferred from the inside to the outside of the container.
9. The diagram shows movement of thermal energy. In which areas of the diagram does conduction occur? (look at the screenshot)
B) X and Z
10. Nuclear reactions in a reactor produce a lot of thermal energy. That energy then flows and warms up water, which boils and produces steam. The stream then turns turbines that generate electricity. Which statement below can be made about the production of electricity in a nuclear reactor?
B) Heat flows from the reactor to the water.
11. A stovetop burner on medium reaches 200° C. Which other objects will heat from the burner flow to?
Any answer you choose is correct on Connexus (look at the screenshot)
12. Heat transfer between two substances is affected by specific heat and the
D) amount of time and area of physical contact between the substances.
13. Which of these results in kinetic energy of an object?
B) motion
14. Carmen is heating some water and trying to measure the temperature of water using a Celsius thermometer. Which measurement can she expect once the water begins to boil?
B) 100° C
15. Which shows the formula for converting from degrees to Celsius to degrees Fahrenheit?
A) °F = (9/5 × °C) + 32
16. Which of these indicates that a liquid has transferred thermal energy to the air?
D) The liquid decreases in temperature, and its particles lose kinetic energy.
I took the test ALL of these answers are 100% correct on Connexus (they should be the same for everyone tho)
You're welcome and hope this helps!! :)
A uniform 1200 N piece of medical apparatus that is 3.5 m long is suspended horizontally by two vertical wires at its ends. A small but dense 550 N weight is placed on the apparatus 2.0 m from one end, as shown in the figure. What are the tensions, A and B, in the two wires?
A thin, uniform rod is bent into a square of side length a. If the total mass is M, find the moment of inertia about an axis through the center and perpendicular to the plane of the square. (Hint: Use the parallel-axis theorem.)
Answer:
The moment of inertia about an axis through the center and perpendicular to the plane of the square is
\(I_s = \frac{Ma^2}{3}\)
Explanation:
From the question we are told that
The length of one side of the square is \(a\)
The total mass of the square is \(M\)
Generally the mass of one size of the square is mathematically evaluated as
\(m_1 = \frac{M}{4}\)
Generally the moment of inertia of one side of the square is mathematically represented as
\(I_g = \frac{1}{12} * m_1 * a^2\)
Generally given that \(m_1 = m_2 = m_3 = m_4 = m\) it means that this moment inertia evaluated above apply to every side of the square
Now substituting for \(m_1\)
So
\(I _g= \frac{1}{12} * \frac{M}{4} * a^2\)
Now according to parallel-axis theorem the moment of inertia of one side of the square about an axis through the center and perpendicular to the plane of the square is mathematically represented as
\(I_a = I_g + m [\frac{q}{2} ]^2\)
=> \(I_a = I_g + {\frac{M}{4} }* [\frac{q}{2} ]^2\)
substituting for \(I_g\)
=> \(I_a = \frac{1}{12} * \frac{M}{4} * a^2 + {\frac{M}{4} }* [\frac{q}{2} ]^2\)
=> \(I_a = \frac{Ma^2}{48} + \frac{Ma^2}{16}\)
=> \(I_a = \frac{Ma^2}{12}\)
Generally the moment of inertia of the square about an axis through the center and perpendicular to the plane of the square is mathematically represented as
\(I_s = 4 * I_a\)
=> \(I_s = 4 * \frac{Ma^2}{12}\)
=> \(I_s = \frac{Ma^2}{3}\)
The moment of inertia through the center of a square is \(I_s = \frac{1}{3} Ma^2\)
The mass of one side of the square is given as;
\(m_1 = \frac{M}{4}\)
The moment of inertia for one side of a square is given as;
\(I_g = \frac{1}{12} \times m_1 \times a^2\\\\I_g = \frac{1}{12} \times \frac{M}{4} \times a^2\\\\I_g = \frac{Ma^2}{48}\)
Apply parallel axis theorem;
\(I_a = I_g \ + \ m_1(\frac{a}{2} )^2\\\\I_a = I_g \ + \ \frac{M}{4} (\frac{a^2}{4} )\\\\I_a = I_g \ + \ \frac{Ma^2}{16}\)
\(I_a = \frac{Ma^2}{48} \ +\ \frac{Ma^2}{16} \\\\I_a = \frac{Ma^2 \ + \ 3Ma^2}{48} \\\\I_a = \frac{4Ma^2}{48} \\\\I_a = \frac{Ma^2}{12}\)
The moment of inertia of the square about an axis through the center and perpendicular to the plane of the square is
\(I_s = 4 \times I_a\\\\I_s = 4 \times \frac{Ma^2}{12} \\\\I_s = \frac{Ma^2}{3}\)
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