The mass near the equator is thrown outward by their quick rotation. In comparison to any terrestrial planet, the jovian planets rotate significantly more quickly.
A planet would be spherical due to gravity alone, but due to their rapid rotation, material around the equator is thrown outward, flattening out their spherical outlines. At some point, a part of this matter falls toward the center and forms a star, and the rotating cloud starts to flatten into a disk. Planets are created from this moving protoplanetary disk of gas and dust, leading to a comparatively flat solar system. Synchronous rotation is the name given to this kind of rotation. To find out more about synchronous rotation, click here. The small moons outnumber the big moons by a wide margin.
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a gps global positioning system satellite orbits earth twice a day. find the: a) orbit radius from earth center. (compare with earth radius) g
Using the Time period formula for a Satellite,
the radius of orbit from earth center is 6.7590.
Time period : The satellite period is the time it takes for a satellite to make one orbit around the Earth, denoted by T. Therefore, T = distance traveled in 1 revolution/orbital velocity = 2πr/V.
We have the following information,
the Satellite revolves the earth twice in a day .
As we know,
mass of the earth(M) is 5.97 × 1024 kg
Gravitational constant (G)= 6.67 × 10-11 Nm²/kg²
The time taken to complete two rounds is a day. Time taken by the satellite in one alone will be cost to one by the day i.e., T = 24 hours
The time period of the satellite must be equal to
2T = 2×24×60×60 sec = 172800 sec.
According to Kepler's 3Rd law ,
T² = ( 4π²/GM )r³---(1)
where, T ---> time period
M --> mass of earth
G--> gravtional constant
r --> radius of orbit
putting all the values in above formula
(172800)² = ( 4×(3.14)²/(6.67 × 10-11 Nm²/kg²× 5.97 × 1024 kg))r³
=> r³ = (172800)²/96,720,640.93= 308.722
=> r = 6.75890 ~ 7
Hence, the radius of orbit is 6.75890
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A ball hits a bat with a velocity of 30 m/s and leaves the bat travelling with a velocity of 20 m/s in the opposite direction m. The ball is in contact with the bat for 0.10 s. What is the magnitude of the acceleration of the ball whilst it is in contact with the bat?
Answer:
100 m/s^{2}
Explanation:
the given information we have is:
vi = 30m/s
vf = 20m/s
t = 0.10s
we need to find a so we will use the following kinematics equation
[tex]vf=vi+at[/tex]
we can rearrange the equation so it will give us our desired answer like so:
[tex]a = \frac{vf-vi}{t}[/tex]
now we can plug in our given numbers
[tex]a = \frac{20 m/s - 30 m/s}{0.10s}[/tex]
which will equal
[tex]100 m/s^{2}[/tex]
Uppoe Galileo dropped a lead ball (100 kilogram) and a gla ball (1 kilogram) from the Leaning Tower of Pia. Which one hit the ground firt? (Aume that there i no air reitance)
The glass & lead ball will both fall to the ground simultaneously. Galileo lowered two walls from the roof of Pisa. Whichever one lands on the ground first must be determined.
Describe a lead ball.To shape metal, fill forming bags or use them as counterbalance. A minimum of 97% of the material is pure lead. All of these balls have precisely made for a flawless finish. They are additionally called lead shot.
Lead balls are used where?Lead balls are frequently used in radiation protection for fill and melt into cracks and holes in lead shields in which other lead products, such as lead sheet or lead bricks, are inaccessible. The substance has a low point of melting and thus is simple to work with and quick to form a uniform barrier layer.
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Find the magnitude of the sum
of these two vectors:
BI
16.3 m
7.70 m
A
27.8°
20.0°
The magnitude of the sum of these two vectors is 23.95 m.
What is the sum of the vectors?The sum of the vectors is the resultant vector obtained by resolving the vectors into x and y component.
the horizontal component of the vector (x) = v cosθ
the vertical component of the vector (y) = v sinθ
where;
v is the vectorθ is the directionFor the first vector;
x = 16.3 m x cos(27.8) = 14.42 m
y = 16.3 m x sin(27.8) = 7.6 m
For the second vector;
x = 7.7 m x cos(20) = 7.24 m
y = 7.7 m x sin(20) = 2.63 m
Net horizontal and vertical vector;
∑x = 14.42 m + 7.24 m = 21.66 m
∑y = 7.6 m + 2.63 m = 10.23 m
The magnitude of the sum of these two vectors is calculated as;
v = √(∑x² + ∑y²)
v = √(21.66² + 10.23²)
v = 23.95 m
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A ball thrown vertically into the air with an initial velocity U; what is the greatest height reached?
The highest height attained is 2gu.
At the highest point, what is the beginning velocity?The vertical velocity is 0 at its highest point. Once more increasing in magnitude as the item descends back toward Earth, the vertical velocity now faces away from the initial vertical velocity.
When a ball is tossed vertically up and allowed to fall in free fall, what is the vertical velocity at the top of the path?0 m/s. Any projectile at its highest point has an instantaneous speed of zero. The time to reach maximum height is equal to the time to arrive at the destination since gravity accelerates the ball by the same amount whether it is moving up or down.
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In order to lift a bucket of concrete, you must pull up harder on the bucket than it pulls down on you.
True or False?
In order to lift a bucket of concrete, you must pull up harder on the bucket than it pulls down on you is referred to as a false statement.
What is Force?This is referred to as an external agent which is capable of influencing the motion of an object or body. It is also capable of changing the state of rest of a body and the unit in Newton.
When lifting the bucket, the total opposite forces and not only the weight which is what pulls it down must be overcome in other to lift the object or body successfully which is why false was chosen.
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Particles q1 = -20.5 MC, 92 = -9.30 MC, and
93 = -31.6.0 MC are in a line. Particles q1 and q2 are
separated by 0.980 m and particles 92 and 93 are separated by 0.750 m. What is the net force on particle 92?
The magnitude of the net force on particle Q₂ is 6.487 x 10⁶ N.
What is the net force on particle Q₂?
The net force on particle Q₂ is obtained by applying Coulomb's law of electrostatic force.
Force between Q₁ and Q₂;
F₁₂ = kq₁q₂/r²
where;
k is Coulomb's constantr is the distance between q₁ and q₂q represent chargesF₁₂ = (9 x 10⁹ x 20.5 x 10⁻³ x 9.3 x 10⁻³)/(0.98)²
F₁₂ = 1.787 x 10⁶ N
Force between Q₂ and Q₃;
F₂₃ = kq₂q₃/r²
F₂₃ = (9 x 10⁹ x 9.3 x 10⁻³ x 31.6 x 10⁻³)/(0.75)²
F₂₃ = 4.7 x 10⁶ N
The net force on particle Q₂;
F(net) = F₁₂ + F₂₃
F(net) = 1.787 x 10⁶ N + 4.7 x 10⁶ N
F(net) = 6.487 x 10⁶ N
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which of the following springs (described by its spring constant) has the shortest period when attached to a 100 g mass?
-400 N/m spring constant has the shortest period when attached to a 100 g mass
F=800 N
x=2 m
F=kx
k=F/x
k=800 N/2 m
k=-400 N/m
The spring constant is the amount of force required to restore a spring to its initial shape after each unit of extension. This indicates that if we know the spring constant, we can easily calculate the amount of force needed to bend the spring. The reason is because if we exert more force on the spring than it can withstand, SHM will no longer be possible. N/m is its unit (Newton per meter). As a spring's length grows, less power is required to bring it to equilibrium, and vice versa.
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eeping the mass at 1.0 kg and the velocity at 10.0 m/s, record the magnitude of centripetal acceleration for each given radius value. include units.
The centripetal acceleration for radius 2.0 m = 50 m/s²
The centripetal acceleration for radius 4.0 m = 25 m/s²
The centripetal acceleration for radius 6.0 m = 16.67 m/s²
The centripetal acceleration for radius 8.0 m = 12.5 m/s²
The centripetal acceleration for radius 10.0 m = 10 m/s²
What is Centripetal acceleration?An object that moving in a circle and has an acceleration vector pointing towards the center of the circle is called centripetal acceleration.
a₀ = v²/r
Where, a₀ = Centripetal acceleration
v = velocity of the object
r = radius of circular path
Given,
m = 1 kg
v = 10 m/s
r = 2.0 m, 4.0 m, 6.0 m, 8.0 m, 10.0 m
Now,
a₀₁ = 10²/2
a₀₁ = 50 m/s²
a₀₂ = 10²/4
a₀₂ = 25 m/s²
a₀₃ = 10²/6
a₀₃ = 16.67 m/s²
a₀₄ = 10²/8
a₀₄ = 12.5 m/s²
a₀₅ = 10²/10
a₀₅ = 10 m/s²
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The complete question is as follows:
"Keeping the mass at 1.0 kg and the velocity at 10.0 m/s, record the magnitude of centripetal acceleration for each given radius value. Include units. Radius: 2.0 m 4.0 m 6.0 m 8.0 m 10.0 m Acceleration: Radius factor: Acceleration factor:"
Imagine a girl climbing a rope ladder to ride a zip line. It takes effort for her to get to the top of the ladder, but the she zips to the ground with ease. She travels down easily because she has stored energy. What's your guess about where this energy came from?
Answer:
See below
Explanation:
The energy is her Potential Energy acquired by her doing work against gravity to climb up the rope ladder to the height of the zip line start.
Kelley is playing pool and hits the cue into the nine ball, which is directly in the center of the pool table. The nine ball travels a total of 7 meters before stopping, 1 meter to the left of the initial starting point of the nine ball. Which sentence reflects the correct statement regarding distance and displacement when considering the motion of the nine ball?.
The distance is 7m while the displacement is 1m. Option A
What is the displacement?We know that the displacement is defined as the distance that is covered in a specified direction. We must note that there are two kinds of quantities that we have in physics and these are the vectors and the scalars. The vectors are the quantities that have both magnitude and direction while the scalars are the quantities that have magnitude but do not have direction.
Now we know that when we are dealing with the vectors that we must be able to consider the direction of the vector in question. This is not important when we are dealing with a scalar.
Now, distance is a vector and displacement is a scalar hence we must be able to consider the direction as we deal with the displacement of the ball.
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A student moves a box of books by pulling on a rope attached to a box. The student pulls with a force of 185n horizontally. The box has a mass of 35. 0kg, and the coefficient of kinetic friction between the box and the floor is 0. 27. Find the acceleration of the box.
The box's acceleration is 2.75m/s².
What is equilibrium force and an illustration?It is said that an equilibrium is stable when small, externally induced displacements from it result in forces that have a tendency to oppose the displacement and bring the body or particle back to the equilibrium state. A brick placed flat on the ground or a weight suspended by a spring are two examples.
Given,
F = 185 N is the amount of force that the student applied
Horizontal is at an angle of θ = 25°
Mass of box = 35kg
Between the box and the floor, there is a kinetic friction coefficient of
µ = 0.27
The equilibrium of forces is the foundation for the presented issue. We also need to find the equation of motion for the force's horizontal and vertical components in order to solve the problem. So,
Across the horizontal axis,
Tcosθ - µN = ma (1)
The forces acting in the vertical direction are,
N + Tsinθ = mg
N = mg - Tsinθ (2)
Replace (1) with the value of equation (2) as,
Tcosθ - µ( mg - Tsinθ) = ma
a = Tcosθ - µ( mg - Tsinθ)/m
The applied force, T = F = 185 N, causes the tension force on the rope.
fixing as,
a = 185×cos25× -(0.25)×35×9.8+((185)sin25)/35
a = 2.75m/s².
Consequently, we can say that the box's acceleration is a = 2.75m/s².
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ow much energy is needed to change the temperature of 50.0 g of water by 15.0oc? (specific heat of water
50.0 g of water will require 3135 Joules energy is needed to change temperature by 15.0 C .
mass is 50 g
temperature is 15
Q=mC8ΔT
where,
m is mass of substance
C8=4.18 jouls /g
Q=50*4.18*15
Q=3135 J
The temperature is a numerical indicator of how cold or hot something is. One can measure temperature by using a thermometer. The calibration of thermometers involves using various temperature scales, which historically defined them using various reference points and thermometric materials. Several scales, including Fahrenheit and Celsius, can be used to express temperature, which is a unit of measurement. A hotter body (one with a higher temperature) will spontaneously move heat energy in the opposite direction to a cold body, as shown by temperature. the level of heat or cold in a body or environment the sensation of coldness or heat.
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trevor starts his motorcycle to go for a ride. if he accelerates at 10 m/s2 over a distance of 80m, how fast is he going if he started at rest?
He is going at the velocity of 40m/s even though he started at rest.
What is acceleration?
Acceleration is the rate at which velocity changes with respect to both speed as well as distance. If an object speeds up or down and is moving in a straight line, then the object is said to be accelerated. In a circular motion, the speed remains constant but the body is accelerated as the direction keeps on changing. The SI Unit is meter per second m/s2
Acceleration= 10m/s2
Initial velocity= 0m/s as the body started at rest.
Distance = 80 m
v2= u2+ 2aS
= 02+ 2 10 80
= 1600
v= 40m/s
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Pls help I’ll give BRAINLIEST!
Answer:
Yes. Producers are the basis of all food webs, for if there weren't any producers, there wouldn't be any food web whatsoever. The role of producers is the building block of food webs. They start out as not needing any other organism to be dependent of, then get consumed to form such a food web, whether it's in the ocean, in a jungle, or in the Arctic.
Explanation:
Answer: The producers play the main role in the food web .
Explanation:
Only producers have the ability to make food by trapping sunlight. Consumers require this energy because they cannot make it on their own. This energy is passed own throughout the individual food chains which make up the food webs. All these organisms provide energy for all other trophic levels ( organisms called consumers that consume (eat) other organisms for energy). that come above them. So there producers are considered as the basis of all food webs
If a steady magnetic field exerts a force on a moving charge, that force is directed.
Answer:
F = q V X B = I L X B are descriptions of the force on a moving charge
Suppose that a battery terminal is + on the left connected by a wire to a - charge on the right, the X indicates a cross product so the force on the moving charge is perpendicular to both the magnetic field and the moving charge.
If one wraps the hand around the wire with the thumb pointing in the direction of the "conventional" current, the induced field will be in the direction of the fingers - V X B is the cross product of the moving charge and the magnetic field;
Note q V = q L / t = (q / t) * L = I L
suppose the sun's gravity were switched off. the planets would leave their orbits and fly away in straight lines as described by newton's first law. (assume the mass of the sun is 1.99 1030 kg, the orbital radius of jupiter is 7.78 1011 m, and the orbital radius of saturn is 1.43 1012 m.)
Jupiter can never be farther from the sun than Saturn if the mass of the sun is 1991030 kg, the orbital radius of Jupiter is 7781011 m, and the orbital radius of Saturn is 1431012 m.
Fc = m v² / r
Fg = G M m / r²
Fc = Centripetal force
Fg = Gravitational force
m = Mass of planet
v = Linear Velocity of planet
r = Orbit radius
G = Gravitational constant
M = Mass of sun
Fc = Fg
G M m / r² = m v² / r
v² = G M / r
M = 1991030 kg
G = 6.67 * [tex]10^{-11}[/tex] N m² / kg²
v² = G M / r
For Jupiter,
r = 7781011 m
vj² = 6.67 * [tex]10^{-11}[/tex] * 1991030 / 7781011
vj² = 1.17 * [tex]10^{-11}[/tex]
vj = 3.42 * [tex]10^{-6}[/tex] m / s
For Saturn,
r = 1431012 m
vs² = 6.67 * [tex]10^{-11}[/tex] * 1991030 / 1431012
vs² = 9.28 * [tex]10^{-11}[/tex]
vs = 9.63 * [tex]10^{-6}[/tex] m / s
vs > vj
Therefore, Jupiter can never be farther from the sun than Saturn
The given question is incomplete. The complete question is :
Suppose the sun's gravity were switched off. the planets would leave their orbits and fly away in straight lines as described by newton's first law. (assume the mass of the sun is 1991030 kg, the orbital radius of Jupiter is 7781011 m, and the orbital radius of Saturn is 1431012 m. Would Jupiter ever be farther from the Sun than Saturn?
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Thomas went to his favorite resturant, Mac Burger Box. He ordered his food and ate it. Then went about his day, alive and well.What is the main energy conversion during digestion? a Electrical Energy to Radiant Energy b Chemical Energy to Chemical Energy c Thermal ( Heat ) Energy to Positive Energy d Chemical Energy to Thermal Energy
a force of 80 newtons is applied to two different objects. it causes object A to accelatate at 20m/s2 , and object B to accelarate at 40 m/s2
A force of 80 newtons is applied to the combined masses.acceleration of the system is =40/3 or 13.33 metre/sec².
what is acceleration?acceleration, rate at which velocity changes with time, in terms of both speed and direction. A point or an object moving in a straight line is accelerated if it speeds up or slows down. Motion on a circle is accelerated even if the speed is constant, because the direction is continually changing.
acceleration of object A= FORCE APPLIED ÷ MASS OF A
=80÷ mass of A
mass of A = 80÷ acc of object A
mass of A= 80÷20=4kg
mass of A = 4kg
acc of object B = force applied ÷ mass of B
mass of object B =force applied ÷ acc of object B
mass of object B=80÷40=2kg
mass of object B =2Kg
when same force is applied to the combined system of 4kg and 2kg then acceleration of the combined mass is = force applied ÷ total mass
=80÷[4+2]
=80÷6
=40÷3
=13.333 metre/sec²
acc of the combined system is 13.333 metre/sec²
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A 10.0 g rifle bullet is fired with a speed of 380 m/s into a ballistic pendulum with mass 10.0 kg, suspended from a cord 70.0 cm long. Part A Compute the initial kinetic energy of the bullet. Express your answer in joules. Part B Compute the kinetic energy of the bullet and pendulum immediately after the bullet becomes embedded in the pendulum. Express your answer in joules. Part C Compute the vertical height through which the pendulum rises. Express your answer in centimeters.
A) The initial kinetic energy of the bullet is 722J
B) Kinetic energy of the bullet and pendulum immediately after the bullet becomes embedded in the pendulum 0.68J
C) The vertical height through which the pendulum rises 0.69cm
The following data-
Mass of the bullet - 10.0g
speed - 380m/s
mass of the pendulum - 10.0kg
length of cord - 70.0cm
To find the initial kinetic energy of the bullet -
KE=1/2mv^2
KE = 1/2 x 0.010 x 380^2
KE= 722J
initial kinetic energy = 722 J
To find the Kinetic energy of the bullet and pendulum immediately after the bullet becomes embedded in the pendulum, we need to first find the final velocity and vertical height through which pendulum rises-
we will find final velocity by applying the law of conservation of momentum
We know, Momentum of bullet is equal to the sum of the momentum of bullet and pendulum.
MbVb= (Mb+Mp)V
where,
Mb= mass of bullet
Mp = mass of pendulum
Vb = velocity of bullet
V = Final velocity
0.010 x 380 = ( 0.010 + 10)V
3.8 = 10.01V
V = 3.8/10.01
v = 0.37m/s
The final velocity = 0.37m/s
now, to find the vertical height
height = V^2/2g
= 0.37^2/2 x 9.8
= 0.136/19.6
= 0.00693m
converting to cm
0.00693 x 100 = 0.69 cm
To find the kinetic energy of the bullet and pendulum immediately after the bullet becomes embedded in the pendulum -
KE = 1/2 (Mb + Mp)V^2
KE = 1/2 ( 0.010 + 10) x 0.37 ^2
KE = 1/2 ( 10.01) x 0.1369
KE = 0.68J
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4. Use your research to explain whether the observations of your windmill
relate to current, real-world advances in windmill technology. Describe the
problems with windmill technology and how engineers have solved them.
Provide specific real-world examples of where new windmill technology is
being used.
Answer:
windmill, device for tapping the energy of the wind by means of sails mounted on a rotating shaft. The sails are mounted at an angle or are given a slight twist so that the force of wind against them is divided into two components, one of which, in the plane of the sails, imparts rotation.
Explanation:
The use of windmills was increasingly widespread in Europe from the 12th century until the early 19th century. Their slow decline, because of the development of steam power, lasted for a further 100 years. Their rapid demise began following World War I with the development of the internal-combustion engine and the spread of electric power; from that time on, however, electrical generation by wind power has served as the subject of more and more experiments
To work efficiently, the sails of a windmill must face squarely into the wind, and in the early mills the turning of the post-mill body, or the tower-mill cap, was done by hand by means of a long tailpole stretching down to the ground. In 1745 Edmund Lee in England invented the automatic fantail. This consists of a set of five to eight smaller vanes mounted on the tailpole or the ladder of a post mill at right angles to the sails and connected by gearing to wheels running on a track around the mill
The most important use of the windmill was for grinding grain. In certain areas its uses in land drainage and water pumping were equally important. The windmill has been used as a source of electrical power since P. La Cour’s mill, built in Denmark in 1890 with patent sails and twin fantails on a steel tower. Interest in the use of windmills for the generation of electric power, on both single-user and commercial scales, revived in the 1970s.
a) state the null and the alternate hypothesis in complete statements for the current context. b) is there a significant linear relationship between the variables? explain your reasoning.
The independent variables of measuring physical properties are given below -
What is physical properties?
A physical properties in any property that is measurable, whose value describe a state of physical system.
The changes in the physical properties of a system can be used to describe its changes between the momentary that state of
Physical properties are often referred to as observables.
They are not modal properties.
Any variable that can be attributed a value without attributes a value to any to any other variables is called independent variables.
It is a variable that stands alone and isn't changed by other variables you are trying to measure.
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Infrared light waves are the closest or farthest in wavelength to visible light?.
imagine you are a photon of light. how long would it take you to travel from one edge of our galaxy to the opposite side?
The time taken to travel from one edge of our galaxy to the opposite side for a photon of light is 36.5 * [tex]10^{6}[/tex] days
v = d / t
v = Velocity
d = Distance
t = Time
Distance from one edge of our galaxy to the opposite side = 100,000 light years
1 light year = 9.46 * [tex]10^{12}[/tex] km
100,000 light years = 9.46 * [tex]10^{17}[/tex] km
Speed of light = 300,000 km / s
t = d / v
t = 9.46 * [tex]10^{17}[/tex] / 300,000
t = 3.15 * [tex]10^{12}[/tex] s
t = 8.76 * [tex]10^{8}[/tex] hr
t = 36.5 * [tex]10^{6}[/tex] days
Therefore, the time taken to travel from one edge of our galaxy to the opposite side is 36.5 * [tex]10^{6}[/tex] days
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A roller coasters accelerates from an initial velocity of of 6.0 m/s to a final velocity of 70 m/s over 4 seconds. What's the acceleration?
16 m/s² is the acceleration when a roller coasters accelerates from an initial velocity of of 6.0 m/s to a final velocity of 70 m/s over 4 seconds.
a=(v-u)/t
a=acceleration=?
v= final velocity = 70m/s
u=initial velocity = 6m/s
t=time= 4 second
a=(v-u)/t
a=(70-6)/4
a=16 m/s²
The rate at which an item changes its velocity is known as acceleration, a vector variable. If an object's velocity is changing, it is accelerating. A moving object can occasionally alter its velocity by the same amount every second. a moving object that changes its speed by 10 m/s per second. Since the velocity is changing by a fixed amount every second, this is known as a constant acceleration. It is important to distinguish between an item with a constant acceleration and one with a constant velocity. Be not deceived! An object is accelerating if its velocity is changing, whether by a fixed amount or a variable quantity. Additionally, a moving item with a constant speed is not accelerating.
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an inductor is connected in series to a fully charged capacitor. which of the following statements are true? check all that apply. an inductor is connected in series to a fully charged capacitor. which of the following statements are true?check all that apply. as the capacitor is charging, the current is increasing. the stored electric field energy can be greater than the stored magnetic field energy. the stored electric field energy can be equal to the stored magnetic field energy. the stored electric field energy can be less than the stored magnetic field energy. as the capacitor is discharging, the current is increasing.
Option B. the stored electric field energy can be greater than the stored magnetic field energy. An inductor is connected in series to a fully charged capacitor.
An inductor, additionally known as a coil, choke, or reactor, is a passive-terminal electric issue that stores electricity in a magnetic field whilst electric modern flows through it. An inductor normally includes an insulated twine wound into a coil.
An inductor is a passive digital element that's able to store electrical power in the form of magnetic electricity. basically, it uses a conductor this is wound into a coil, and while power flows into the coil from the left to the proper, this will generate a magnetic subject in the clockwise direction.
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a disk is to be rotated around an axis perpendicular to its face. we can place the axis through the center or through a point on the rim of the disk. how will the rotational inertia of the first choice compare with the rotational inertia of the second choice?
In such a motion, the rigid body rotates along a fixed axis that is parallel to a fixed plane.
In other words, with respect to an inertial frame of reference, the axis is stationary and does not move or change direction. I=jmjr2j, where mj is the mass of the point particle and rj is its distance from the rotation axis, is the moment of inertia for a system of point particles revolving about a fixed axis. The angle of rotation is the angle at which an object revolves (turns) around a given point. Constant angular speed rotation is the most basic type of rotation around a fixed axis. The total torque then becomes zero.
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Determine the force P on the cable if the spring is compressed 0.5 in. when the mechanism is in the position shown. The spring has a stiffness of k = 800 lb/ft. Determine the magnitude of the gripping forces produced when two 50-lb forces are applied as shown.
The force P on the cable if the spring is compressed 0.5 in with a stiffness of k = 800 lb/ft is 46.91 lb
k = Fe / δ
k = Stiffness of spring
Fe = Force on spring
k = 800 lb / ft = 6.67 lb / in
δ = 0.5 in
Fe = k δ
Fe = 6.67 * 0.5
Fe = 33.33 lb
At joint A,
∑ MA = 0
( - Bx * 6 ) + ( - By * 6 ) + ( 33.33 * 30 ) = 0
Bx + By = 166.67 → ( 1 )
At joint D,
∑ MD = 0
( - By * 6 ) + ( P * 4 ) = 0
By = 0.067 P → ( 2 )
∑ Fx = 0
- Bx + FCD cos 30° = 0 → ( 3 )
At joint B,
∑ MB = 0
( - FCD sin 30° * 6 ) + ( P * 10 ) = 0
FCD = 3.33 P
Sub FCD in ( 3 ),
- Bx + 3.33 P cos 30° = 0
Bx = 2.8867 P
Sub Bx and By in ( 1 ),
2.8867 P + 0.667 P = 166.67
P = 46.91 lb
Therefore, the force P on the cable if the spring is 46.91 lb
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1. A man walks on a straight road from his home to market 2.5 km away with a speed of 5km/h. Finding the market closed, he instantly turns and walks back home with a speed of 7.5 km/h. The average speed of the man over the interval of time 0 to 40 min is equal to :
A) 5 km/h
B) 25/4 km/h
C) 30/4 km/h
D) 45/8 km/h
How does the angle at which a ray of light strikes a pane of window glass compare with the angle at which it passes out the other side?.
The angle at which a ray of light strikes a pane of window glass is smaller than the angle at which it passes out the other side.
When light go through window glass it will experience refraction due to change of light speed. The relation between angle of incidence and angle of refraction is given by the Snell's law:
n₁ sin∅₁ = n₂ sin∅₂
Where:
n₁ = incident index (refractive index of medium 1)
n₂ = refraction index ((refractive index of medium 2)
∅₁ = incident angle
∅₂ = refraction angle
Typical refractive index for glass is around 1.5 while refractive index for air is 1.000273.
In the given case, the ray of light is from the window glass and pass out the other side. Hence,
n₂ = air
n₁ = glass
Since n₁ > n₂ , the velocity in the air is greater than the velocity in the window glass. Hence, ∅₁ < ∅₂ or the incident angle is smaller than the refracted angle.
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