They would have an 11-times higher equivalent resistance if they were joined in series.
What is an example of resistance?Consider the scenario of a person navigating a busy market and encountering difficulty moving from one business to another to better understand resistance. Undoubtedly, this circumstance is comparable to a particle trying to pass through a wire.
What factors affect resistance?An electrical conductor's resistance is determined by its length, resistivity, and cross-sectional area. The relationship between conductance and resistivity must be understood; the more conductive that anything is, the less resisting it is.
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The complete question is-
three resistors, 1 ohm, 2 ohm, 3 ohm are connected in a parallel. if they were connected in series instead their equivalent resistance would be
a. 13 times as great
b. 11 times as great
c. 9 times as great
d. 7 times as great
e. none of the above
an object moves with constant speed of 18.8 m/s on a circular track of radius 100 m. what is the magnitude of the object's centripetal acceleration?
The calculated answer is 5.31. For an object travelling at a constant speed, v, around a circle with radius, r, the value is given by a = v2/r.
The displacement that an object or particle experiences with respect to time is expressed vectorially as velocity. The meter per second (m/s) is the accepted unit of velocity magnitude (also known as speed). Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path. In other words, velocity is a vector, whereas speed is a scalar value. Additionally, we will confirm that the acceleration vector points in the direction of the circle's center. It is acceptable to assume that an object travelling in a circle at a constant speed is accelerating as a result of this. Because the velocity vector's direction is shifting, it is accelerating. A = v2/R.
speed= distance/ time
= 100/18.8
=5.31
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When nitrogen and hydrogen gas combine to make ammonia, the chemical equation looks like this:
2N2 + 3H2 => 2NH3
If the hydration energy of 2N2 + 3H2 is equal to + 2251.3 kJ/mol and the lattice energy of 2NH3 is equal to -2343.52 kJ/mol, what is the total energy change of this reaction and is the reaction endothermic or exothermic?
(a) The total energy change of this reaction is -4,594.82 kJ/mol.
(b) The reaction is exothermic.
What is the change total energy change of this reaction?
The total energy change of the given reaction is determined by taking the difference between the energy of the product and the reactant.
ΔH = Hp - Hr
where;
Hp is the energy of the productHr is the energy of the reactantThe given parameters;
energy of the product = -2343.52 kJ/molenergy of the reactant = 2251.3 kJ/molΔH = -2343.52 kJ/mol - 2251.3 kJ
ΔH = -4,594.82 kJ/mol
Based on the negative change in the total energy, the reaction is exothermic.
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how do the escape speeds for two rockets, the first weighing 20 n and the second weighing 20,000 n compare?
Escape velocity doesn't depends on the weight of a rocket.So, The escape velocity for the lighter rocket is the same as that for the heavier rocket.
Velocity:
Velocity is the primary measure of object position and velocity. It can be defined as the distance traveled by an object in unit time. Velocity can be defined as the displacement of an object in unit time.
Speed:
The rate of change of the object's position in any direction. Velocity is measured as the ratio of distance traveled and time traveled. Velocity is a scalar quantity because it has only direction and not magnitude.
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why does an artesian well flow without pumping? group of answer choices the water table is at the surface in an artesian aquifer. the water in an unconfined aquifer is pressurized. the water in a confined aquifer is pressurized. the hydraulic head is very high in the aquifer.
An artesian well flows without pumping because the water in a confined aquifer is pressurized.
The correct option is C.
What are artesian wells?Artesian wells are aquifers in which the pressure in the aquifer forces the water confined within the ground above the ground surface so that the well will flow without pumping.
Aquifers are underground layers of permeable rock, rock fractures, or sediments that contain water stored or trapped within them.
Types of aquifers include:
Confined aquifers - these are aquifers that have a layer of impenetrable rock or clay above themUnconfined aquifers - these are aquifers that lie below a permeable layer of soil.Artesian wells are examples of aquifers and do not require pumping.
Some aquifers on the other hand require pumping of the water stored within.
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During laboratory investigation, students determined a large block of iron to have a density of 7.75 g/mL. If the block were to be cut in half, what would be the density of the smaller block?
a. 7.75 g/mL
b. 15.5 g/mL
c. 3.88 g/mL
d. 5.58 g/mL
Answer: (a) 7.75 g/mL
Explanation: Density is calculated as mass/volume. When you cut the block in half, you cut the mass in half and the volume in half, meaning that the density is the same.
EX: 2/2 = 1; also 1/1 = 1
shows the light intensity on a screen behind a double slit. the slit spacing is 0.20 mm and the screen is 1.7 m behind the slits. what is the wavelength (in nm ) of the light?
The wavelength of light is 619.04 nm.
Solution:
From the figure, the distance between four maxima Y = 2.0 cm
Distance between successive bright fringes Ay Y/4=0.5 cm = 0.005m
We know Ay - 2D d (1)
d = 0.20mm = 1.7 x 10m
D= 17m
From equation (1)
∧ =Δyd/D
∧ = 0.005×0.20×10⁻³/17 = 619.04 nm
Wavelength is the distance between identical points in adjacent cycles of a waveform signal propagating in space or along a wire. In wireless systems, this length is usually expressed in meters, centimeters, or millimeters. Wavelength is the distance between two wave crests and the same for wave troughs.
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how might the motion of the cart change when two people push the cart rather than when the boy pushes the cart by himself?
When two people push the cart, then it will move with a faster speed.
According to Newton's third law of motion, for every action there is an equal and opposite reaction.
When we push the cart, our action of pushing causes the reaction of the cart moving with the same force as that of our push in the opposite direction.
If only the boy pushes the cart, then there will be a smaller force of push and hence the cart will move slowly. When two people will push the cart, the force will be larger and as a result the cart will move at a faster speed.
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a ball is thrown vertically upward with a velocity of 20m/s from the top of a multistory building. the height of the point where the ball is thrown is 25 m from the ground. then find a. how height will the ball rise?
B how long will it be before the ball hip the ground?
A ball is thrown vertically upward with a velocity of 20m/s from the top of a multistory building. The height of the point where the ball is thrown is 25 m from the ground. The height will the ball rise is 20m. 5s long will it be before the ball hip the ground.
What is velocity ?The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar quantity. In essence, velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate.
A. for solving how high will ball go , velocity at the top point will be 0 this gives ,
s = v² - u² / 2a
= 0 - 20² / -2 × 10
= 20m
B. Time to reach maximum height can be obtained from v = u + at
0 = 20 + ( − 10 ) t
t = 2s
s = ut + 0.5at²
= 20 ( 2 ) + 0.5 ( −10 ) ( 2 )²
= 20m
Therefore, the total distance for maximum height is 45 m
s = ut + 0.5at²
45 = 0 + 0.5 ( 10 ) ( t )²
t = 3s
Then,
Total time = 3+2
= 5s
Thus, A ball is thrown vertically upward with a velocity of 20m/s from the top of a multistory building.The height will the ball rise is 20m. 5s long will it be before the ball hip the ground.
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suppose that the uncertainty in the measurement of an electron's position is zero. part a if measured simultaneously, what is the uncertainty in the electron's momentum?
The uncertainty in the electron's momentum is infinity.
What is Heisenberg Uncertainty Principle?
According to Heisenberg's uncertainty principle, it is impossible to precisely measure or quantify an object's location or momentum. The wave-particle duality of matter serves as the foundation for this idea. The uncertainty in the location and velocity of objects with relatively high masses is insignificant in the macroscopic world, therefore Heisenberg's uncertainty principle may be disregarded; nevertheless, in the quantum world, it has important implications. Due to the extremely tiny masses of atoms and subatomic particles, any improvement in positional precision will be followed by a corresponding rise in velocity uncertainty.
Heisenberg's uncertainty principle is a fundamental idea in quantum mechanics that explains why it is impossible to measure more than one quantum variable at once.
From Heisenberg uncertainity principle
Dx. Dp >h/2pi
Dx =0,
Dp = infinite
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looking for planets orbiting even the nearest stars is like looking from san francisco for pinheads and marbles orbiting a ? in washington dc
Proxima Centauri's third planet can be seen by observing variations in brightness over a period of more than two years. The third planet that orbits Proxima Centauri, the star nearest to the Sun, has been found by astronomers.
What, looking for planets orbiting even the nearest stars?The transit method has so far been used to discover the great majority of planets orbiting other stars.
Therefore, 3 New Planets Found By Kepler Telescope In The “Goldilocks Zone” The planets that circle distant stars are around the size of Earth and are orbiting. At a distance from their suns that keeps the temperatures on their surfaces in the middle.
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A proton follows the path shown in (Figure 1). Its initial speed is v0 = 2.2×106 m/s.What is the proton's speed as it passes through point P?Express your answer to two significant figures and include the appropriate units.
The proton's speed as it passes through point P is 1.6×10⁶ m/s.
The proton's speed at point P can be determined by the equation:
KE = PE + ( mv²/2 )
where,
KE= kinetic energy
PE = potential energy
m = mass of the proton
v = speed of the proton.
Given
Proton's initial speed is v₀ = 2.2×10⁶ m/s
By putting the values in the question the solution is as follows so as the Proton's speed at point P can be calculated as:
v = √(2KE/m)
= √(2 ×2.2 × 10⁶ m/s² / 1.67 × 10⁻²⁷ kg)
= 1.6 × 10⁶ m/s
Therefore, the proton's speed as it passes through point P is 1.6×10⁶ m/s.
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An adult inhales about 6.0×10^−4 m^3 of fresh air during a breath. only 20% of fresh air is oxygen. assume the pressure in the lungs is 1.0×10^5 pa and the air is at a temperature of 300 k. How many oxygen molecules are in each breath?
Number of oxygen molecules in each breath is 2.9X10^21
Given that the volume of air inside a breath (V) = 6.0×10^−4 m^3
oxygen in fresh air = 20%
volume of oxygen in fresh air = 20/100 x 6.0×10^−4 = 1.2x10-4m^3
pressure in the lungs (P)= 1.0×10^5 pa
Temperature of air (T) =300K
Using ideal gas equation find the number of moles of oxygen
PV = nRT
Then n = 1.0×10^5 x 1.2x10-4 / 8.314 x 300 = 4.8x10-3mol
We know the number of molecules in 1 mol is 6.023x10^23
Then the number of molecules in 4.8x10-3mol of oxygen is =
4.8x10-3molx 6.023x10^23 = 2.9x10^21
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where in the universe do we see young galaxies? in the local group in the local supercluster in all regions of space billions of light-years away
The Milky Way is a member of the Laniakea Supercluster, which is a member of the Virgo Supercluster, which is a member of the Local Group galaxy group (which includes more than 54 galaxies).
Are the Local Group galaxies relocating away from us?Does the Local Group grow together with the universe as a whole? (Intermediate) The Local Group of Galaxies (Andromeda, Milky Way, etc.) is moving in the direction of the Local Supercluster.
Where can one find young stars in our galaxy?While the cooler red star predominates the bulge, hot young stars are mostly found in the spiral arms of the disk. The galaxy as a whole undergoes a dramatic change in appearance as we go through the various star populations.
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for each of the following cases, indicate whether the work done on the second object in each example will have a positive or a negative value. a. the road exerts a friction force on a speeding car skidding to a stop. b. a rope exerts a force on a bucket as the bucket is raised up a well. c. air exerts a force on a parachute as the parachutist falls to earth.
a) The work done by frictional force on the skidding car is negative.
b) Positive work is accomplished by the rope's force on the bucket.
c) The work done by the force exerted by the air on the parachutist is negative.
W = F * d = F d cos gives the amount of work done.
where, force is F and displacement is d
a) The road exerts a frictional force on a speeding car skidding to a stop.
In this instance, the frictional force F works in opposition to the direction of motion and opposes the motion itself. The angle between displacement and frictional force, which is in the opposite direction and equals 180°.
So, the work done by the frictional force on the skidding car is negative.
b) A bucket is being raised up a well while being pulled by a rope.
The bucket is raised upward by the rope's upward force F. The force and displacement are in the same direction, and their angle is equal to zero.
So, the work done by the force exerted by the rope on the bucket is positive.
c) As a parachutist falls to the ground, air pulls on a parachute.
The air opposes the parachutist's descent with a force F as they both plummet to the ground under the influence of gravity. The force exerted by the air is in a direction opposite to the motion of the parachutist. The force of air and displacement have an angle of 180 degrees.
So, the work done by the force F exerted by the air on the parachutist is negative.
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a 575 kg satellite is in a circular orbit at an altitude of 525 km above the earth's surface. because of air friction, the satellite eventually falls to the earth's surface, where it hits the ground with a speed of 2.20 km/s. how much energy was transformed into internal energy due to air friction?
Energy transformed into internal energy due to air friction is found to be 1.799 ×10¹⁰ J.
This question can be solved by the use of work energy theorem.
According to work energy theorem the work done by all the forces is equal to the change in kinetic energy of the system.
Given, mass of satellite m= 575 kg
distance of satellite from earth's surface (h)= 525 km
final velocity of the satellite [tex]v_{f}[/tex]= 2.20 km/s= 2.20×10³ m/s
We know that mass of sun M =6ˣ10²⁴ kg
Radius of earth R= 64ˣ10⁵ m
The total energy of satellite when in orbit is given by [tex]E= -G\frac{Mm}{2r}[/tex]
Here G is the gravitational constant= 6.67430×10⁻¹¹ m³kg⁻¹s⁻²
r= R+h= 6925000m
On putting all the values and solving we get
E= -1.661ˣ10¹⁰ J (This is the initial energy when the satellite was orbiting sun)
According to question the satellite hits the earth surface with [tex]v_{f}[/tex]= 2.20 km/s= 2.20×10³ m/s.
So, the gravitational potential energy is given by [tex]U= -G\frac{Mm}{R}[/tex]
On putting the values and solving we get U= -3.59×10¹⁰ J
The satellite will also have kinetic energy when it hits the surface given by K.E= [tex]\frac{1}{2}mv^{2}[/tex]
On putting the values and solving we get K.E= 0.13×10¹⁰ J
Total energy (T.E) of the satellite when it hits the ground is the sum of kinetic energy and potential energy
T.E= K.E+U= -3.46×10¹⁰ J
The energy which was transferred into internal energy due to the air friction is the difference of the total initial energy (E) and total final energy (T.E)
Internal energy= E- T.E
= (-1.661+3.46)×10¹⁰ J
=1.799 ×10¹⁰ J
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The velocity of a particles moving along a straight path increase from 10m/s to 15m/s in 4 second.what is the displacement covered by the particle in the given time?
The displacement covered by the particle in the given time is 50 meter.
What is velocity?The rate at which a body's displacement changes in relation to time is known as its velocity. Velocity is a vector quantity with both magnitude and direction. SI unit of velocity is meter/second.
Initial velocity of the particle: u = 10 m/s.
Final velocity of the particle: v = 15 m/s.
Time interval: t = 4 second.
Hence, the average velocity of the particle = (10+15)2 m/s = 12.5 m/s.
The displacement covered by the particle in the given time:
s = average velocity × time interval
= 12.5 m/s × 4 second.
= 50 meter.
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true or false: for a star moving away from you, you would observe the light to be shifted toward the blue end of the spectrum.
The given statement that a star moving away from us, we observe the light to be shiftest towards the blue end of spectrum is a false statement.
This phenomenon is called doppler effect. Doppler effect of light can be described as the apparent change in the frequency of the light observed by the observer due to relative motion between the source of light and the observer
In the given situation, the source of the waves is the star, which emits light (the waves). The observer is on Earth, and the star (the source of the waves) is moving away from the observer, so, wavelength of the light observed by us is shifted with respect to the original wavelength of the light emitted by the star.
when the star moves away, the wavelength increases, so it shift towards the red end of spectrum. This effect is called red-shifted.
In the given case, the star is moving away from us, so light will shift towards red end of spectrum.hence, The given statement is false.
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the nucleus of a uranium atom has a diameter of 1.5×10−14m and a mass of 4.0×10−25kg.
A uranium atom's nucleus measures 1.5 x 10^-14 mm in diameter and weighs of 2.2635 x 10^17 kg.
The Earth's crust contains 2.8 parts per million of uranium, an element that is found naturally. It is virtually always present in little amounts. It is almost the same in abundance as tin, somewhat less abundant than cobalt, lead, or molybdenum, and more abundant than gold, silver, or mercury.
Nucleus density is determined by the ratio of mass to volume.
Proton mass equals nucleus mass.
Nucleus volume is equal to (4/3)*pi*r3. and r is the radius
A uranium atom's nucleus has a mass of 4.0*10^-25 kg and a diameter of 1.5*10^-14 m.
first, locate volume.
Radius is calculated as follows: 1.5*10^-14 m/2 = 7.5*10^-15 m radius
vol is equal to (4/3)*pi*(7.5*10^-15)3 = 1.76715*10^-42 of volume.
Locate density using the formula d=m/vol (kg/m³)
d = 4.0*10^-25 kg / 1.76715*10^-42 m^3
d = 2.2635*10^17 (kg/m³)
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Correct Question:
The Nucleus Of A Uranium Atom Has A Diameter Of 1.5*10^-14 M And A Mass Of 4.0*10^-25 Kg.
a child (32 kg) jumps up and down on a trampoline. the trampoline exerts a spring restoring force on the child with a constant of 5000 n/m. at the highest point of the bounce, the child is 1.0 m above the level surface of the trampoline. what is the compression distance of the trampoline? neglect the bending of the legs or any transfer of energy of the child into the trampoline while jumping.
x =−0.422 m is the compression distance of the trampoline.
What does the term "energy conservation" mean?Energy efficiency a basic rule of physics and chemistry states that despite internal changes, the overall energy in an isolated system remains constant. It is the underlying principle of the first rule of thermodynamics, which is most frequently stated as "energy cannot be generated or destroyed."
How to calculate the compression distance in the trampoline?Given, Mass m = 32 kg
restoring force, k = 5000 n/n
height, h = 1 m
According to the concept of Conservation of energy,
initial total Energy = final total Energy
Ui + Uepe +Ki = Uf + Uepe + Kf
here,
Ui,Uf = initial,final potential energy
Uepe = elastic potential energy
Ki,Kf = initial,final Kinetic energy
mgh+1/2kx²+0 = mgh+1/2kx²+0
32×9.8×1+0+0 = mgx+1/2kx²
313.6 = 313.6x +1/2×5000×x²
0 = 313.6 + 313.6x + 2500x²
x = [313.6± (√313.6² - 4× -2500×313.6)]/2×313.6
x = -0.422 0r x = 0.29
The compressing of the spring should be considered to be represented by the negative figure of x.
x =−0.422 m is the compression distance of the trampoline.
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to keep the voltage drop of a 277v circuit to a maximum of 3%, what would be the maximum allowable voltage drop?
The voltage across the circuit is 277 V. To keep the voltage drop to a maximum of 3%, the allowable voltage drop will be 8.31 V.
What is voltage?Voltage is the potential difference applied between the two opposite terminal of the circuit. The unit of voltage is represented as V. According to Ohm's law voltage in a circuit is the product of current and resistance through the circuit.
The applied voltage cannot be utilised by 100%. There occurs a voltage drop across the circuit. Given that the total voltage applied is 277 V. The maximum allowed voltage drop is 3%.
Thus, maximum allowable voltage drop for 277 v = 277 × 3/100 = 8.31 V.
Therefore, the maximum allowable voltage drop is 8.31 V.
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_____ refers to how reactive a substance is with oxygen
A Reduction
B Combustibility
Answer:
B is the correct one
Explanation:
Answer: Combustibility refers to how reactive a substance is with oxygen.
Explanation:
Combustibility is a measure of a substance's ability to burn or ignite when exposed to oxygen. Substances that are highly combustible are more reactive with oxygen and are more prone to catching fire or burning. Some common examples of combustible substances include wood, paper, and gasoline.
Reduction, on the other hand, refers to a chemical reaction in which a substance gains electrons or hydrogen atoms, or loses oxygen atoms. Reduction reactions are the opposite of oxidation reactions, in which a substance loses electrons or hydrogen atoms, or gains oxygen atoms. Reduction and combustibility are not directly related to each other.
Degeneracy pressure stops the crush of gravity in all the following except:_____.A) a brown dwarf.
B) a white dwarf.
C) a neutron star.
D) a very massive main-sequence star.
E) the central core of the Sun after hydrogen fusion ceases but before helium fusion begins.
Degeneracy pressure stops the crush of gravity in all the following except a brown dwarf. The correct option is a.
What is Degeneracy pressure?Electron degeneracy pressure is a subset of the broader phenomenon of quantum degeneracy pressure.
The Pauli exclusion principle prevents two identical half-integer spin particles from occupying the same quantum state at the same time.
Electron degeneracy pressure, in particular, is what protects white dwarfs from gravitational collapse, as well as the Chandrasekhar limit (the maximum mass a white dwarf can attain) arises naturally as a result of electron degeneracy physics.
Thus, the correct option is a.
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a spaceship moving toward earth with a speed of 0.85c launches a probe in the forward direction with a speed of 0.15c relative to the ship. find the speed of the probe relative to earth.
The speed of the probe relative to the earth is 0.80c.
Given that,
Speed of the spaceship towards the earth v₁₂ = 0.85c
Speed of the probe relative to the ship v₃₁ = - 0.15c
Speed of the probe relative to the earth v₃₂ = ?
The expression to find out the speed of the probe relative to the earth is given as
v₃₂ = (v₁₂ + v₃₁)/[1 + (v₁₂* v₃₁)/c²] = (0.85c - 0.15c)/[ 1 - (0.85c* 0.15c)/c²]
⇒ 0.7c / [ 1 - 0.1275] = 0.7/0.8725 = 0.80c
Thus, the speed of the probe relative to the earth is 0.80c.
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calculate the force of gravity in newtons, between the earth and a 70 kg huma standing on the surfac
The force of gravity, between the earth and a 70 kg human standing on the surface is 688N.
What is the plain meaning of gravity?The force that pulls items toward the center of a planet or even other body is known as gravity. Each of the planet are kept in orbit about the sun by gravity. But in a wider sense, gravity is a force because it represents the interaction that happens when two masses are in close proximity to one another. Fundamentally, the stretching of space and the movement of items through the stretched spacetime are what produce gravitational effects. However, the outcome appears to be the result of applying force.
Briefing:the force of gravity ⇒ Fg = G Mm/ R²
Fg=gravitational force
G=gravitational constant
M=mass of Earth
m=mass of object
R=distance from earth's centre to object's centre
Fg = (6.67 × [tex]10^{-11}[/tex]× 5.98[tex]10^{24}[/tex]×70)/ (6.37×[tex]10^{6}[/tex])×(6.37×[tex]10^{6}[/tex])
⇒ Fg ≅ 688N.
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If stormy weather were approaching, the pressure tendency would probably be ______. answer choices. falling. rising. steady. none of these.
Option A - Falling is the pressure tendency ,If stormy weather were approaching .
Stormy weather, namely when it includes components like dark clouds, strong winds, thunder, lighting, and rain, is defined as weather that has generated storms or that indicates storms are imminent. It's frequently used in sentences that refer to stormy weather. Low pressure causes active weather. As a result of air rising because it is lighter than the air masses around it, the atmosphere becomes unstable. When the air pressure increases, vapour in the condenses, creating clouds and rain, among other things. Both violent storms and active weather, such as wind and rain, are produced by low pressure systems.
Low-pressure areas have relatively thin atmospheres. Inward winds are a factor in these locations. Low-pressure storms are frequently well-organized.
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A soccer player takes a free kick from a spot that is 26m from the goal. The ball leaves his foot at an angle of 26˚, and it eventually hits the crossbar of the goal, which is 2.4m from the ground
At what speed did the ball leave his foot?
The speed of the ball when it left his foot is 11.13 m/s.
What is the motion of the projectile?A projectile is an object that is launched or projected into the air and is only subject to the acceleration of gravity. Projectile and trajectory both refer to the same thing: an object.
The given parameters;
distance of the goal, d = 26 m
angle of projection of the ball, = 26°
height of the cross bar, H = 2.4 m
The speed of the projectile will be calculated by applying the formula for maximum height reached by a projectile;
[tex]H=U^{2} sin^{2}/2g[/tex]
[tex]u^{2} =2gh/x=sin^{2}[/tex]
[tex]u^{2} =2*9.8*2.4/sin^{2} 26[/tex]
[tex]u^{2} =81.10[/tex] m/s
u=9 m/s
Thus, the speed of the ball when it left his foot is 9 m/s.
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if the disk is replaced by a hollow, thin-walled cylinder of the same mass and diameter, what will be the angular acceleration of the disk about its center of mass?
Fnet=mTacom, where Fnet is the net external force acting on the system and mT is the system's total mass, can be used to quickly compute the acceleration of the center of mass.
As a result, the system's center of mass accelerates by 2/3 ms2. The fixed point of rotation for things is their center of mass. There is no angular acceleration when a force is applied to the center of mass because the torque produced is zero. 12.5 radians per second squared is the size of the disk's angular acceleration. The position of the point in relation to the axis of rotation affects the rigid body's linear speed and acceleration at any given moment. Think about the disk's point B once more.
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Santa Claus entered the North Pole Annual Elf Throwing Competition. He fired his elf with a
horizontal speed of 25 m/s from the top of an iceberg of height 110 m. What was the elf's range and
time of flight?
Answer:
To find the range and time of flight of the elf, we need to use the equations of motion under the influence of gravity. The range is the horizontal distance covered by the elf and the time of flight is the total time that the elf is in the air.
The initial velocity of the elf in the x-direction (horizontal direction) is 25 m/s and the initial velocity in the y-direction (vertical direction) is 0 m/s, since the elf is thrown horizontally from the top of the iceberg. The acceleration due to gravity is -9.8 m/s^2 in the downward direction.
Using these values, we can find the range and time of flight of the elf using the following equations:
Range:
x = x0 + v0x*t
Where x is the range, x0 is the initial position (in this case, x0 is 0 since the elf is thrown from the top of the iceberg), v0x is the initial velocity in the x-direction (25 m/s), and t is the time of flight.
Time of flight:
y = y0 + v0y*t + (1/2)at^2
Where y is the vertical position of the elf, y0 is the initial position (in this case, y0 is 110 m since the elf is thrown from the top of the iceberg), v0y is the initial velocity in the y-direction (0 m/s), a is the acceleration due to gravity (-9.8 m/s^2), and t is the time of flight.
We can solve for t in the second equation and then substitute it into the first equation to find the range.
Solving for t in the second equation:
t = (-v0y +/- sqrt(v0y^2 - 4a(y0 - y))) / (2*a)
Where y is the vertical position of the elf (0 m since the elf lands on the ground), y0 is the initial position (110 m), v0y is the initial velocity in the y-direction (0 m/s), and a is the acceleration due to gravity (-9.8 m/s^2).
Substituting this expression for t into the first equation:
x = x0 + v0x*((-v0y +/- sqrt(v0y^2 - 4a(y0 - y))) / (2*a))
Plugging in the values:
x = 0 + 25*((-0 + sqrt(0^2 - 4*(-9.8)(110))) / (2(-9.8)))
Simplifying:
x = 25*(sqrt(5832) / -19.6)
x = 25*(sqrt(5832) / -19.6)
x = (25*74.6) / -19.6
x = 1865.4 / -19.6
x = -95.1 m
So, the range of the elf is approximately -95.1 m. This means that the elf lands 95.1 m to the left of the starting point (the top of the iceberg).
The time of flight can be found by solving for t in the second equation:
t = (-v0y +/- sqrt(v0y^2 - 4a(y0 - y))) / (2*a)
Plugging in the values:
t =
Explanation:
Please Help me! Please show all work!
Jeremiah the Bullfrog rode a roller coaster around a loop. Being a good friend, he took some measurements for you during his journey. The 1.5kg amphibian noted that at the bottom of the loop, the speed of the roller coaster was 33m/s. You know from the informational poster next to the entrance that the loop has a radius of 22m. How much force did the seat exert on Jeremiah at the bottom of the loop?
74.25 N much force did the seat exert on Jeremiah at the bottom of the loop.
What is centripetal force?This is an acceleration technique. When an item is moving in a circle, it is moving ahead while being turned by a consistent force that is directed inward. The Centripetal Force is the name given to this internal resultant force.
Given that,
Mass (m) = 1.5 kg
speed (v) = 33 m/sec
radius (r) = 22m
As we know,
centripetal force (F) = mv²/r
or, F = [1.5 × (33)²] / 22
or, F = 74.25 N
So, 74.25 N much force the seat exert on Jeremiah at the bottom of the loop.
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if a is a matrix with columns that span rn, then ax = b has a solution for all b in rn.
The statement "If a is a matrix with columns that span rn, then ax = b has a solution for all b in rn" is true.
If a matrix has columns that span rn, it means that the columns of the matrix are linearly independent and can be used to form a basis for rn. This means that any vector b in rn can be written as a linear combination of the columns of the matrix.
Since ax = b has a solution for all b in rn, this means that for any given b, there exists a unique solution x such that ax = b. This is because the columns of the matrix are linearly independent and can be used to form a basis for rn, so any vector in rn can be written as a linear combination of the columns of the matrix.
Therefore, the statement is true.
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