Answer:
The location of the center of gravity of the fourth mass is \(\vec r_{4} = (-0.961\,m,-0.779\,m)\).
Explanation:
Vectorially speaking, the center of gravity with respect to origin (\(\vec r_{cg}\)), measured in meters, is defined by the following formula:
\(\vec r_{cg} = \frac{m_{1}\cdot \vec r_{1}+m_{2}\cdot \vec r_{2}+m_{3}\cdot \vec r_{3}+m_{4}\cdot \vec r_{4}}{m_{1}+m_{2}+m_{3}+m_{4}}\) (1)
Where:
\(m_{1}\), \(m_{2}\), \(m_{3}\), \(m_{4}\) - Masses of the objects, measured in kilograms.
\(\vec r_{1}\), \(\vec r_{2}\), \(\vec r_{3}\), \(\vec r_{4}\) - Location of the center of mass of each object with respect to origin, measured in meters.
If we know that \(\vec r_{cg} = (0,0)\,[m]\), \(\vec r_{1} = (0,0)\,[m]\), \(\vec r_{2} = (0, 4.1)\,[m]\), \(\vec r_{3} = (1.9,0.0)\,[m]\), \(m_{1} = 6\,kg\), \(m_{2} = 1.5\,kg\), \(m_{3} = 4\,kg\) and \(m_{4} = 7.9\,kg\), then the equation is reduced into this:
\((0,0) = \frac{(6\,kg)\cdot (0,0)\,[m]+(1.5\,kg)\cdot (0,4.1)\,[m]+(4.0\,kg)\cdot (1.9,0)\,[m]+(7.9\,kg)\cdot \vec r_{4}}{6\,kg+1.5\,kg+4\,kg+7.9\,kg}\)
\((6\,kg)\cdot (0,0)\,[m]+(1.5\,kg)\cdot (0,4.1)\,[m]+(4\,kg)\cdot (1.9,0)\,[m]+(7.9\,kg)\cdot \vec r_{4} = (0,0)\,[kg\cdot m]\)
\((7.9\,kg)\cdot \vec r_{4} = -(6\,kg)\cdot (0,0)\,[m]-(1.5\,kg)\cdot (0,4.1)\,[m]-(4\,kg)\cdot (1.9,0)\,[m]\)
\(\vec r_{4} = -0.759\cdot (0,0)\,[m]-0.190\cdot (0,4.1)\,[m]-0.506\cdot (1.9,0)\,[m]\)
\(\vec r_{4} = (0, 0)\,[m] -(0, 0.779)\,[m]-(0.961,0)\,[m]\)
\(\vec r_{4} = (-0.961\,m,-0.779\,m)\)
The location of the center of gravity of the fourth mass is \(\vec r_{4} = (-0.961\,m,-0.779\,m)\).
Urgent!!!!! A student heated 235 g of water in a beaker until the water reached 100°C. The student removed the beaker from the heat and placed the beaker on a counter in a 23°C room. The student recorded the temperature of the water every 4 minutes for 20 minutes. The data are shown in the table. Estimate the average temperature of the air in the room at 20 min. explain your answer.
The average temperature of the air in the room at 20 min is 23°C.
What is temperature?Temperature is the degree of hotness or coldness of the object.
A student heated 235 g of water in a beaker until the water reached 100°C. The student removed the beaker from the heat and placed the beaker on a counter in a 23°C room. The student recorded the temperature of the water every 4 minutes for 20 minutes.
The surrounding is vast, its temperature does not get affected by small amount of water. So, the temperature of air remains constant.
Thus, the average temperature of the air in the room at 20 min is 23°C.
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A computer monitor accelerates electrons between two plates and sends them at high speed to form an image on the screen. If the elec- trons gain 4.1 * 10-15 J of kinetic energy as they go from one accelerat- ing plate to the other, what is the voltage between the plates?
The voltage between the plates is 3.9 × \(10^-^3\) V.
The work-energy theorem states that the delta in the equation equals the change in kinetic energy plus the change in potential energy. Here, a charge's potential energy is expressed as qV, where V is the position's electric potential. The greater the change in voltage per unit distance, the greater the electric field.
The kinetic energy of the electrons = 4.1 × \(10^-^1^5\) J
Charge of the electron = 1.602 × \(10^-^1^9\) coulomb
Using,
ΔU = q × ΔV
4.1 × \(10^-^1^5\) = 1.602 × \(10^-^1^9\) × ΔV
ΔV = 3.9 × \(10^-^3\) V
Therefore, the voltage between the plates is 3.9 × \(10^-^3\) V.
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Consider an object sitting motionless on a flat surface. No on is pushing on it or touching the object in a way, and no tools are used to push or touch the object. How many forces are acting on the object
Consider an object sitting motionless on a flat surface.
No one is pushing or touching the object in any way, and no tools are used to push or touch the object.
Zero forces are acting on the object.
What is force?
In mechanics, a force is any action that seeks to preserve, modify, or deform a body's motion. Newton's first law states that until a force is applied to a body, it will remain in either its resting or uniformly moving state in a straight path. According to the second law, when an external force acts on a body, the body accelerates (changes velocity) in the force's direction.To know more about force, click the link given below:
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Which bond(s) shown are double bonds?
Answer:
I'm pretty sure its the 2nd one.
A person standing on a scale feels a normal force of 655 N pushing up on him. What is his mass?
Answer: 66.8 kilograms
7th grade science i mark as brainliest
Given the functions f(x)=(1/x-3)+1 and g(x) = (1/1+4)+3
Which statement describes the transformation of the graph of function f onto the graph of function g?
O The graph shifts 2 units right and 7 units down.
O The graph shifts 7 units left and 2 units up.
O
e graph shifts 7 units right and 2 units down.
O The graph shifts 2 units left and 7 units up.
The statement that describes the transformation of the graph of function f onto the graph of function g is: The graph shifts 2 units right and 7 units down.
To determine the transformation of the graph of function f onto the graph of function g, we compare the two functions f(x) and g(x) and observe the changes in the equations.
The function f(x) = (1/x - 3) + 1 represents a reciprocal function that is shifted vertically 1 unit up and horizontally 3 units to the right. The reciprocal function is reflected about the line y = x.
The function g(x) = (1/(1 + 4)) + 3 simplifies to g(x) = 4 + 3 = 7, which is a constant function representing a horizontal line at y = 7.
By comparing the equations, we can see that the transformation from f(x) to g(x) involves the following changes:
The term 1/x in f(x) is replaced by the constant 1/(1 + 4) in g(x), resulting in a vertical shift of 7 units up.
The term -3 in f(x) is replaced by 3 in g(x), resulting in a vertical shift of 3 units up.
The +1 in f(x) is replaced by +3 in g(x), resulting in an additional vertical shift of 2 units up.
Therefore, the overall transformation is a shift of 2 units to the right and 7 units down.
Hence, the correct statement is: The graph shifts 2 units right and 7 units down.
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Is a ball standing still potential or kinetic?
How much net- work is required to accelerate a 1200-kg car from 25 m/s to 45 m/s?
The net-work required to accelerate the car of mass 1200 kg is 840000 J.
What is work done?Work can be deifned as the product of force and distance.
To calculate the amount of net-work required to accelerate 1200 kg car from 25 m/s to 45 m/s, we use the formula
Formula:
W' = m(v²-u²)/2............ Equation 1Where:
W' = Net-work required to accelerate the carm = Mass of the carv = Final velocityu = Initial velocityFrom the question,
Given:
m = 1200 kgv = 45 m/su = 25 m/sSubstitute these values into equation 1
W' = 1200(45²-25²)/2W' = 1200×1400/2W' = 840000 JHence, the net-work required is 840000 J.
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A liquid x at 25 degree Celsius is poured to a height of 40cm in a capillary tube of length 70cm and the diameter is 1cm .Assume that volume does not change with temperature. A find the initial volume of the liquid in cm^3. B. The temperature is reduced by 10°C causing the liquid to reduce in height to 37cm.Find the volume coefficient of the thermal expansion of the liquid. C. At the initial height of 40cm and temperature of 25°C , what change in temperature is needed for liquid to rise to a height of 49cm.
The initial volume of the liquid is 31.4 cm³. The volume coefficient of thermal expansion of the liquid is 0.002 per degree Celsius. A temperature increase of 109.5°C is needed for the liquid to rise to a height of 49cm.
The initial volume of the liquid can be found using the formula for the volume of a cylinder:
V = πr²h
where r is the radius (half the diameter), h is the height, and π is approximately 3.14. Plugging in the given values, we get:
V = π(0.5 cm)²(40 cm)
V = 31.4 cm³
The volume coefficient of thermal expansion (β) is defined as the fractional change in volume per degree Celsius change in temperature. It can be calculated using the formula:
β = ΔV/(VΔT)
where ΔV is the change in volume, V is the initial volume, and ΔT is the change in temperature. We can rearrange this formula to solve for ΔV:
ΔV = βVΔT
We know that ΔT = -10°C (a decrease of 10°C) and that the height decreased from 40cm to 37cm, or by 3cm. The change in volume can be found using the formula for the volume of a cylinder again, with the new height of 37cm:
ΔV = π(0.5 cm)²(40 cm - 37 cm)
ΔV = 0.59 cm³
Plugging in all the values, we get:
0.59 cm³ = β(31.4 cm³)(-10°C)
β = 0.002
To find the change in temperature needed for the liquid to rise to a height of 49cm, we can use the same formula as before, but solve for ΔT:
ΔT = ΔV/(βV)
We know that ΔV is the difference between the initial volume and the volume at the new height, which is:
ΔV = π(0.5 cm)²(49 cm - 40 cm)
ΔV = 6.86 cm³
Plugging in all the values, we get:
ΔT = 6.86 cm³/(0.002)(31.4 cm³)
ΔT = 109.5°C
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(ii) A second drill is used with the extension lead. The power of this drill is
1200 W.
The instructions for using the extension lead include the following information.
When in use the lead may get hot:
DO NOT go over the maximum power
lead wound inside the case: 820 watts
lead fully unwound outside the case: 3100 watts
It would not be safe to use this drill with the extension lead if the lead was left wound
inside the plastic case.
Explain why
customer complains of an aluminum foil mixed with his salad? what will you do?
Answer:
offer them a refund or a remake/ replacement of food item whilst apologizing sincerely
A dolphin has a mass of 125 kg and is moving along with 775 J of kinetic energy. How fast is it moving? (Hint: use the formula to solve for KE)
Question 43 options:
12.4 m/s
3.52 m/s
0 m/s
6.2 m/s
Answer: 3.52m/s
Explanation:
Kinetic energy is calculated as:
= 1/2mv²
where,
m = mass
v = velocity
Therefore,
775 = 1/2 × 125 × v²
775 = 62.5v²
v² = 775/62.5
v² = 12.4
v = ✓12.4
v = 3.52m/s
19. What energy transformation occurs in a battery?
A. chemical energy to thermal energy
C. electric energy to chemical energy
B. chemical energy to electric energy
D. thermal energy to chemical energy
i think correct answer is b
Answer:
B.chemical energy changes to electric energy.Explanation:
I hope l helped you. ❤❤
An object
moves through space with balanced forces acting on it. Which statement
best describes the speed and direction of the object as long as the forces acting on it
remain balanced?
Pls answer number 4 and an explanation
Answer: G the speed and direction of the object will remain constant.
A 15 kg box is pushed with a force of 35 N in the +x direction, and the box accelerates to the right. It does not accelerate up or down
The box accelerates to the right due to the applied force of 35 N in the +x direction.
Newton's second law states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. In this case, the net force acting on the box is 35 N in the +x direction, and its mass is 15 kg. Therefore, we can calculate the acceleration using the formula:
acceleration = net force / mass
acceleration = 35 N / 15 kg = 2.33 m/s² (rounded to two decimal places)
Since the box is not accelerating up or down, we can conclude that the force applied is only causing the box to accelerate in the horizontal direction.
Other forces such as gravity and friction are not considered in this scenario. Thus, the 15 kg box will experience an acceleration of approximately 2.33 m/s² in the +x direction due to the applied force of 35 N.
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Suppose that the electric field in the Earth's atmosphere is E = 131 N/C, pointing downward. Determine the electric charge (in C) in the Earth. (Assume the electric field is measured at the surface of the Earth. Include the sign of the value in your answer.) Hint
Answer:
the electric charge in the Earth is -5.91 × 10⁵ C
Explanation:
Given the data in the question;
Electric field E = 131 N/C
we know that; radius of the earth r = 6,371 km = 6371000 m
and Coulomb's constant k = 8.99 × 10⁹ Nm²/c²
Now, using the following formula to calculate the charge;
E = k × Q/r²
we make Q the subject of the formula
Q = Er² / k
so we substitute
Q = [ 131 N/C × ( 6371000 m )² ] / 8.99 × 10⁹ Nm²/c²
Q = [ 5.317242971 × 10¹⁵ ] / [ 8.99 × 10⁹ ]
Q = 5.91 × 10⁵ C
Since the electric field pointing downward
Q = -5.91 × 10⁵ C
Therefore, the electric charge in the Earth is -5.91 × 10⁵ C
During which phase is the moon not visible?
A) Full Moon
B) First quarter
C) New moon
D) Waxing crescent
Answer:
they are right it is a new moon
Explanation:
took the test
24. A body A rests on a smooth horizontal table. Two bodies of mass 2 kg and 10 kg hanging freely, are attached to A by strings which pass over smooth pulleys at the edges of the table. The two strings are taut. When the system is released from rest, it accelerates at 2 m/s2 . Find the mass of A.
The two strings are taut. When the system is released from rest, it accelerates at 2 m/s2 then, Mass of A = 8m/5 kg.
Let the mass of the body A be ‘m’.
The two strings are taut so they exert a tension ‘T’ on body A.
Let ‘a’ be the acceleration produced in the system.
The free body diagram of body A is given below: mA + 2T = mA + ma = mA + m(2)mA + 10T = mA + ma = mA + m(2)
As the two strings are taut, we can say that tension in both strings is equal.
Therefore 2T = 10T or T = 5T As the body A is resting on a smooth horizontal table, there is no friction force acting on the body A.
The net force acting on body A is the force due to tension in the strings. ma = 2T – mg …(1)
As per the given problem, the system is released from rest.
Hence the initial velocity is zero.
Also, we are given that the system accelerates at 2 m/s2.
Therefore a = 2 m/s2 …(2)
From the equations (1) and (2), we get, m(2) = 2T – mg …(3)⇒ m(2) = 2×5m – mg⇒ 2m = 10m – g⇒ g = 8m/5
Thus, the mass of A is 8m/5 kg.
Answer: Mass of A = 8m/5 kg.
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A charge +Q and a charge -2Q are a distance 3x apart. Point P is on the line joining the charges, at a distance x from +Q.
The magnitude of the electric field produced at P by the charge +Q alone is E.
What is the total electric field at P?
The total electric field at point P, taking into account both charges, +Q and -2Q, is given by:
E_total = k * |Q| * [(1 / x²) - (4 / (9x²)]).
To determine the total electric field at point P, we must consider the contributions of both charges, +Q and -2Q.
The electric field (E) at P due to a single charge can be calculated using Coulomb's law. An electric field is defined as the force per unit positive charge at a given point. Mathematically, it is expressed as follows:
E = k * (|q| / r²),
where k is the electrostatic constant, q is the charge, and r is the distance from the charge to the point where the electric field is measured.
In this case we have a charge +Q at a distance x from point P. The electric field at point P due to +Q alone can be calculated as:
E1 = k* (|Q|/x2).
Similarly, the electric field at P due to -2Q can be calculated as:
E₂ = k * (|-2Q| / (3x)²) = 4k * (|Q| / (9x²)).
The total electric field (E_total) at point P is the vector sum of the electric fields produced by +Q and -2Q. Because they have opposite charges, the electric fields will have opposite directions.
E_total = E1 - E₂.
By substituting the expressions for E₁ and E₂:
E_total = k * (|Q| / x²) - 4k * (|Q| / (9x²)).
Further simplification:
E_total = k * |Q| * [(1 / x²) - (4 / (9x²)]).
Please note that the direction of the electric field will depend on the signs of the charges (+Q and -2Q) and their relative positions with respect to point P.
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Which statement is true about the theory of plate tectonics and the theory of continental drift?
A) The theory of plate tectonics proves the theory of continental drift completely wrong.
B) The theory of plate tectonics tells exactly where the continents were before Pangaea divided.
C) The theory of plate tectonics gives the method by which continents can move as part of plates.
D) The theory of plate tectonics does not explain how continental movements could occur.
The statement that is true about the theory of plate tectonics and the theory of continental drift C. The theory of plate tectonics gives the method by which continents can move as part of plates .
What is theory of plate tectonics and the theory of continental drift ?According to the scientific hypothesis of plate tectonics, the underground movements of the Earth create the primary landforms. By explaining a wide range of phenomena, including as mountain-building events, volcanoes, and earthquakes, the theory, which became firmly established in the 1960s, revolutionized the earth sciences.
The scientist Alfred Wegener is most closely connected with the concept of continental drift. Wegener wrote a paper outlining his notion that the continents were "drifting" across the Earth, occasionally crashing through oceans and into one another, in the early 20th century.
According to tectonic theory, the Earth's surface is dynamic and can move up to 1-2 inches every year. The numerous tectonic plates constantly move and interact. The outer layer of the Earth is altered by this motion. The result is earthquakes, volcanoes, and mountains.
Therefore, option C is correct.
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3. A car with a mass of 1600 kg has a kinetic energy of 125 000 J. How fast is it moving?
The car is moving at approximately 12.5 meters per second.
The kinetic energy (KE) of an object can be calculated using the formula:
KE = 1/2 * m * \(v^2\)
where
KE = kinetic energy,
m =Mass of the object, and
v = velocity.
In this case, we are given the mass (m) of the car as 1600 kg and the kinetic energy (KE) as 125,000 J. To find the velocity .
Substituting the values , we have:
125,000 J = 1/2 * 1600 kg *\(v^2\)
Now, we can solve for v by rearranging the equation:
\(v^2\) = (2 * 125,000 J) / 1600 kg
\(v^2\) = 156.25 \(m^2/s^2\)
Taking the square root, we find:
v = √156.25\(m^2/s^2\)
v ≈ 12.5 m/s
Therefore, the car is moving at approximately 12.5 meters per second.
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Thomas the Train chugs along at 2 m/s. Thomas needs to go faster so more coal is shoveled into his engine and he accelerates for 10 seconds until he is going 4.33 m/s. What is Thomas' acceleration?
The acceleration of Thomas is 0.233 m/s^2.
Acceleration is the rate of change of velocity. Thomas the Train chugs along at a velocity of 2 m/s.
Thomas needs to go faster so more coal is shoveled into his engine and he accelerates for 10 seconds until he is going 4.33 m/s.
We are to find the acceleration of Thomas.
The formula for acceleration is given as :
acceleration = (final velocity - initial velocity) / time
In the given problem, the initial velocity of Thomas, u = 2 m/s.
The final velocity of Thomas, v = 4.33 m/s The time for which Thomas accelerates, t = 10 s.
Therefore, the acceleration of Thomas will be given as:
a = (v - u) / ta = (4.33 - 2) / 10s => 2.33 / 10s => 0.233 m/s^2
Thus, the acceleration of Thomas is 0.233 m/s^2.
To summarize, the acceleration of Thomas is 0.233 m/s^2.
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4.2 Determine the reactions of the loads L and R. ↓ 5m
↓ 7 kN 6m 3 kN 4m R (8)
The reaction of load L is 0 (no horizontal force), and the reaction of load R is 10 kN (vertical upward force).
How to find reaction?To determine the reactions of the loads L and R, consider the equilibrium of the forces acting on the structure.
First, analyze the vertical equilibrium. The sum of the vertical forces must be zero:
ΣFy = R − 7 kN − 3 kN
ΣFy = 0
This gives:
R = 10kN
Next, analyze the horizontal equilibrium. The sum of the horizontal forces must be zero:
ΣFx = L
ΣFx = 0
This indicates that there is no horizontal force acting on the structure.
Therefore, the reaction of load L is zero (no horizontal force), and the reaction of load R is 10 kN (vertical upward force).
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A wave with a frequency of 17 Hz has a wavelength of 5 meters. At what speed will this wave travel?
Answer:
85
Explanation:
soln
given that;
frequency=17Hz
wavelength=5m
speed?
formula for wavelength is;
wavelength= speed/frequency
then ; making v the subject formula
we have that v=wavelength*frequency
v=17*5=>85ms
The graph below shows the position of an ant as it crawls over a flat picnic blanket. The total time for the ant to go from the start to the end position takes 1 minute and 45 seconds.
What is the average speed and average velocity of the ant?
A.) Average speed is 0.200 cm/s and average velocity is 0.0988 cm/s to the upper right.
B.) Average speed is 0.152 cm/s and average velocity is 0.910 cm/s to the upper right.
C.) Average speed is 0.975 cm/s and average velocity is 1.95 cm/s to the upper right.
D.) Average speed is 0.276 cm/s and average velocity is 0.136 cm/s to the upper right.
The average speed of the ant is 0.276 cm/s and the average velocity is 0.136 cm/s.
The correct answer is option D.
In the given graph, we can deduce the following;
the total time of the motion, = 1 mins + 45 s = 60 s + 45 s = 105 sThe average speed of the ant is calculated as;
\(average \ speed = \frac{total \ distance }{total \ time }\)
The total distance from the graph is calculated as follows;
first horizontal distance from 2 cm to 8 cm = 8 - 2 = 6 cmfirst upward distance from 3 cm to 5 cm = 5 - 3 = 2 cmsecond horizontal distance from 8 cm to 6 cm = 8 - 6 = 2 cmsecond upward distance from 5 cm to 12 cm = 12 - 5 = 7 cmthird horizontal distance from 6 cm to 13 cm = 13 - 6 = 7 cmfourth downward distance from 12 cm to 9 cm = 3 cmfinal horizontal distance from 13 cm to 15 cm = 2cmThe total distance = (6 + 2 + 2 + 7 + 7 + 3 + 2) cm = 29 cm
\(average \ speed = \frac{total \ distance }{total \ time } = \frac{29 \ cm}{105 \ s} = 0.276 \ cm/s\)
The average velocity is calculated as the change in displacement per change in time.
The displacement is the shortest distance between the start and end positions.
This shortest distance is the straight line connecting the start and end position. Call this line PFrom the end position at x = 15 cm, draw a vertical line from y = 9 cm, to y = 3 cm. The displacement = 9 cm - 3 cm = 6 cmAlso, draw a horizontal line from start at x = 2 cm to x = 15 cm. The displacement = 15 cm - 2 cm = 13 cmNotice, you have a right triangle, now calculate the length of line P.
↓end
↓
↓ 6cm
↓
start -------------13 cm------------
Use Pythagoras theorem to solve for P.
\(P^2 = 6^2 + 13^2\\\\P^2 = 36 + 169\\\\P^2 = 205\\\\P= \sqrt{205} \\\\P = 14.318 \ cm\)
The average velocity of the ant is calculated as;
\(average \ velocity= \frac{\Delta displacemnt }{total\ time }= \frac{14.318 \ cm}{105 \ s} = 0.136 \ cm/s \\\\\)
Thus, the average speed of the ant is 0.276 cm/s and the average velocity is 0.136 cm/s.
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Can someone make a list of 10 simple things people can do to maintain fitness ? Please I literally need help.
Answer:
1. drink lots of water
2. eat healthy breakfast
3. plan your meals
4. set a deadline
5. exercise at least 30 minutes a day even 10 minutes 3 times a day is good
6. eat fruits and vegetables
7. eat whole grains instead of white
8. get a good night's sleep
9. stay motivated
10. take time for mental health
Sun, Earth, Moon Models Lab Quiz
What was the purpose of the experiment?
HELP PLS
The aim of this study is to develop a Sun-Earth-Moon model that will serve to describe "the real and apparent movements of the Sun-Earth-Moon system and the results of these movements".
A fundamental topic in astronomy, that is difficult To properly understand the why requires three-dimensional thinking and imagination. In this context;
• Students have difficulty understanding basic concepts of astronomy; H.
such as creating seasons, phases of the moon, lunar and solar eclipses that require three-dimensional thinking must be properly understood. So to teach difficult abstract concepts,
• To solve the problem of the lack of materials and tools related to matter.
• To enhance learning retention by engaging students' multiple senses,
• Capturing concepts visually and verbally increases skills. Remember the image of this concept when you meet its verbal equivalent, or reversed. Therefore, to help students remember what they are learning,
• Have students see tools, objects, and events that they cannot see perceive with their five senses,
• Show students tools, objects, and events that they cannot reach
or bring to class,
• Attract attention and arouse interest in a topic, needed a model to grow.
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Water flows at a speed of 13 m/s through a pipe that has a diameter of 1.2 m. What is the
diameter of the smaller end of the pipe that the water comes out with a speed of 30 m/s?
The diameter of the smaller end of the pipe is approximately 0.78 meters.
To determine the diameter of the smaller end of the pipe, we can use the principle of conservation of mass. According to this principle, the mass flow rate of water should remain constant throughout the pipe.
The mass flow rate is given by the equation:
Mass flow rate = density of water * cross-sectional area * velocity
Since the density of the water remains constant, we can write:
Cross-sectional area1 * velocity1 = Cross-sectional area2 * velocity2
Given that the velocity1 is 13 m/s, the diameter1 is 1.2 m, and the velocity2 is 30 m/s, we can solve for the diameter2 using the equation:
(pi * (diameter1/2)^2) * velocity1 = (pi * (diameter2/2)^2) * velocity2
Simplifying the equation:
(1.2/2)^2 * 13 = (diameter2/2)^2 * 30
Calculating the equation:
(0.6)^2 * 13 = (diameter2/2)^2 * 30
0.36 * 13 = (diameter2/2)^2 * 30
4.68 = (diameter2/2)^2 * 30
Dividing both sides by 30:
0.156 = (diameter2/2)^2
Taking the square root of both sides:
0.39 = diameter2/2
Multiplying both sides by 2:
0.78 = diameter2
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12. Which of the following phrases describes the motion of the bus from O to A?
Answer:
Fast, constant, and positive direction
Explanation:
From O to A, there is a straight line in the graph. It means that the distance is increasing when time is increasing. So, the bus is moving in the positive direction and it is fast. Finally, it is constant because the graph is a straight line.
Therefore, the answer is:
Fast, constant, and positive direction.