:Quantities that are conserved when balancing a nuclear reaction are mass number and atomic number
Nuclear reactions involve the emission, absorption, or transformation of atomic nuclei.
These reactions include changes in the composition of an atomic nucleus, which necessitates balancing the number of protons and neutrons in the initial and final products.
When balancing a nuclear reaction, it is important to ensure that the mass number and atomic number are conserved. The mass number of the elements before and after the reaction should be the same, as should the atomic number, which represents the number of protons in the nucleus.
Summary:Quantities that are conserved when balancing a nuclear reaction are mass number and atomic number. A nuclear reaction can be balanced by adjusting the coefficients that are placed in front of the atomic symbols. The coefficients should be chosen in such a way that the mass number and atomic number of the elements are the same before and after the reaction. In addition, the total number of atoms should be conserved on both sides of the reaction.
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edge 2020 waves and diffraction lab report d a t a
Answer:
Explanation:
Waves and Diffraction: Lab ReportTitle:Lab: Waves and DiffractionPurpose:When a wave encounters a small obstacle or the edge of a barrier, the phenomenon known asdiffraction will occur. The wave theory of light can help explain diffraction, although observingdiffraction of light directly is difficult due to the very short wavelengths of light. In this lab, you willuse a “ripple tank” simulation, which provides a convenient way to study wave diffraction on alarger scale, since the principles of wave diffraction apply to physical waves (such as soundwaves and waves in liquid) as well as electromagnetic waveswaves
A carrot hangs from the ceiling by a rope,
What is the correct free body diagram for the carrot?
Answer: Diagram B
Explanation:
A free body diagram shows the forces acting on an object in a certain scenario.
In this scenario there are two forces acting on the carrot: the Tension force (Ft) from the rope that the carrot is hanging from and Gravitational force(Fg) which is pulling the carrot to the Earth.
The diagram depicting this is diagram B.
Answer:
ft and fg
Explanation:
which substance can be separated by physical means and it is not the same throughout.
A.a compound
B.a heterogeneous mixture
C.an element
D.a homogeneous solution
Answer:
B. heterogenous mixture
Explanation:
The substance that can be separated by physical means include heterogenous mixtures, where the components forms separate faces. They can be easily separated using methods based on their physical properties.
What is heterogenous mixtures?Mixtures are combination of two or more individual components mixed physically or through chemical bonds. There are both homogenous and heterogenous mixtures.
In homogenous mixtures all the components are forms a single phase and appear to be one system. For example, salt solution, sugar solution etc. are homogenous mixtures.
In heterogenous mixtures, the components forms different phases which appears to be separated components. They are just physically mixture components and can be easily separated using physical methods.
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dentify the following terms associated with the water cycle.
Water changes from a gas to a liquid phase.
Water falls to the Earth in the form of a liquid or solid.
Liquid water changes into a gas.
Water evaporates from the leaves of plants.
Answer:
condensation, precipitation, evaporation, transpiration
Explanation:
condensation is when gas condenses into liquid, precipitation is when water comes from the sky like in rain, evaporation is when water is converted from liquid to gas, transpiration is when water is evaporated from leaves.
what is the correct tight asymptotic bound for T(n) in 1,2,3 where T(1)=c ?
T(n) = 10T(n/10)+100n
T(n) =T(n/10)+100n
T(n) = T(n/10)+100
The correct tight asymptotic bound for T(n) in 1, 2, 3 where T(1)=c is Θ(n log n).
To find the tight asymptotic bound of T(n), we will use the Master Theorem. So, let's take a look at each recurrence relation:
1. T(n) = 10T(n/10)+100nApplying the Master Theorem: a = 10, b = 10, f(n) = 100nlogb a = log10 10 = 1 Since f(n) = Θ(n) = Θ(n1), Case 2 of the Master Theorem applies. The solution, therefore, is Θ(n log n).
2. T(n) = T(n/10)+100n Here, a = 1, b = 10, f(n) = 100nlogb a = log10 1 = 0 Since f(n) = Θ(n0) = Θ(1), Case 1 of the Master Theorem applies. The solution, therefore, is Θ(n).
3. T(n) = T(n/10)+100 Here, a = 1, b = 10, f(n) = 100logb a = log10 1 = 0 Since f(n) = Θ(1) = Θ(n0), Case 2 of the Master Theorem applies. The solution, therefore, is Θ(log n).Therefore, the correct tight asymptotic bound for T(n) in 1, 2, 3 where T(1)=c is Θ(n log n).
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Let's use the Master Theorem to find the asymptotic tight bound for each of the three recurrence relations given in the problem statement.
1. T(n) = 10T(n/10) + 100n Here, a = 10, b = 10, and f(n) = 100n. We can calculate the value of logb a as follows: log10 10 = 1 Since f(n) = Θ(n1), we can apply Case 2 of the Master Theorem and get: T(n) = Θ(n log n)Therefore, the correct tight asymptotic bound for T(n) in the first case is Θ(n log n).
2. T(n) = T(n/10) + 100n Here, a = 1, b = 10, and f(n) = 100n. We can calculate the value of logb a as follows: log10 1 = 0 Since f(n) = Θ(n1), we can apply Case 1 of the Master Theorem and get: T(n) = Θ(n)Therefore, the correct tight asymptotic bound for T(n) in the second case is Θ(n).
3. T(n) = T(n/10) + 100 Here, a = 1, b = 10, and f(n) = 100. We can calculate the value of logb a as follows: log10 1 = 0 Since f(n) = Θ(1), we can apply Case 2 of the Master Theorem and get: T(n) = Θ(log n) Therefore, the correct tight asymptotic bound for T(n) in the third case is Θ(log n). Hence, the three asymptotic tight bounds for T(n) are Θ(n log n), Θ(n), and Θ(log n), respectively.
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Which of the following represents an upside-down image?O A. +doO B. -doO c. +mO D.-m
"-m" represents a negative image distance which implies an inverted or upside-down image formation. Therefore the correct answer is (D) -m.
In optics, the notation "do" refers to object distance and "di" refers to image distance.
The sign convention for object and image distances is as follows:
- If the object distance (do) is positive, it indicates that the object is located on the same side as the incident light.
- If the object distance (do) is negative, it indicates that the object is located on the opposite side of the incident light.
- If the image distance (di) is positive, it indicates that the image is formed on the opposite side of the light.
- If the image distance (di) is negative, it indicates that the image is formed on the same side as the light.
In the given options, "-m" represents a negative image distance, indicating that the image is formed on the same side as the light.
This implies an inverted or upside-down image formation.
Therefore, option (D) -m represents an upside-down image.
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Please Help!
In all organisms, cells are the most basic units of structure and function. The structure of an organism is affected by the way its cells are shaped and organized. Many of the functions that an organism needs to carry out to stay alive happen inside its cells. A cell is the smallest unit that can get and use energy, remove waste, and carry out other processes necessary for life.
The micrographs below show cells from two different organisms: an onion plant, which is multicellular, and a diatom, which is unicellular.
Answer:
Essential processes happen in a cell: Onion plant and Diatom
A cell is its basic unit of structure: Onion plant and Diatom
Made up of one cell: Diatom
Made up of many cells: Onion plant
Generators convert mechanical energy to electrical energy by using _________.
Answer:
Magnetic Induction.
Explanation:
That be your answer.
because sound is energy created by vibrations, through which medium will it move the fastest?
Answer:
solids
Explanation:
Sound travels fastest through solids. This is because molecules in a solid medium are much closer together than those in a liquid or gas, allowing sound waves to travel more quickly through it. In fact, sound waves travel over 17 times faster through steel than through air
The table shows the specific heat capacities of various substances. How much energy is required to raise the temperature of 5g of air by 10°C? Use the table below to help you.
Answer:
50.25 j
Explanation:
Alex HEYYYYYYYYY
Answer:
The table shows the specific heat capacities of various substances. How much energy is required to raise the temperature of 5g of air by 10°C? Use the table below to help you.
"10 J" is WRONG
The right answer is "50.25 J"
Explanation:
hope this helps
How to find accelration compentts from magnitue and ange
To find the acceleration components from magnitude and angle, you can use the following equations ax = a * cos(θ) and ay = a * sin(θ)
The acceleration components from magnitude and angle:
ax = a * cos(θ)ay = a * sin(θ)Where ax and ay are the x and y components of the acceleration, a is the magnitude of the acceleration, and θ is the angle.
By plugging in the values for magnitude and angle into these equations, you can find the acceleration components in the x and y directions.
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Halley's comet orbits the Sun with a period of 76.2 years.
a) Find the semi-major axis of the orbit of Halley's comet in astronomical units.
b) If Halley's comet is 0.56 AU from the Sun at perihelion, what is the maximum distance from the Sun, and what is the eccentricity of its orbit?
According to Kepler's law of planetary motion, the square of the period of an orbit is proportional to the cube of the semi-major axis. By rearranging the equation, we can solve for the semi-major axis.
a) The semi-major axis (a) can be calculated using the formula:
\(a= (T^{2} * k)x^{(1/3)}\), where T is the period of the orbit and k is a constant. Plugging in the values, we have \(a= (76.2^{2} * k)^{(1/3)}\)
Since we want the answer in astronomical units (AU), we need to find the value of k. By using the known semi-major axis of Earth's orbit (1 AU) and its period (1 year), we can determine that k = 1. Therefore, the semi-major axis of Halley's comet's orbit is \((76.2^{2} * 1)^{(1/3)}\) AU.
b) If Halley's comet is 0.56 AU from the Sun at perihelion, we can determine the maximum distance from the Sun by adding the semi-major axis (a) to the perihelion distance. The maximum distance is given by a + perihelion distance = \((76.2^{2} * 1)^{(1/3)} + 0.56\)AU. To find the eccentricity (e) of the orbit, we can use the formula: e = (a - perihelion distance) / (a + perihelion distance). Plugging in the values, the eccentricity is \((76.2^{2} * 1)^{(1/3)} - 0.56\) AU divided by \((76.2^{2} * 1)^{(1/3)} + 0.56\)AU.
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you are driving along a country road when you suddenly notice a log in the road ahead of you and immediately apply your brakes. you travel a distance of s(t)
a. The car will not hit the tractor.
b. The car would travel a distance of 52.07 m before stopping
c. At the moment when the car stopped, the tractor is 11.5 m in front of the car.
Linear motion
From the question, we are to determine of you will hit the tractor before you stop
First, we will determine the time it will take the car to stop
From the given information,
Initial velocity, u = 27.0 m/s
a = -7 m/s² (Negative sign indicates deceleration)
v = 0 m/s (Since the car will come to stop)
From one of the equations of linear motion,
v = u + at
Where v is the final velocity
u is the initial velocity
a is the acceleration
and t is the time taken
Putting the parameters into the equation, we get
0 = 27 + (-7)t
7t = 27
t = 27/7
t = 3.857 secs
This is the time it will take the car to stop
Now, we will determine the distance the car would travel after applying the brakes
Using the formula
S = (u + v) / t
Where S is the distance traveled
S = [(27 + 0) / 2] * 3.857
S = 13.5 * 3.857
S = 52.0695 m
S ≅ 52.07 m
This means the car would travel 52.07 m after applying the brakes
Now, we will determine the distance the tractor would have traveled when the car came to a stop
Speed of the tractor = 10.0 m/s
Time taken for the car to stop = 3.857 secs
Using the formula,
Distance = Speed × Time
Distance = 10.0 × 3.857
Distance = 38.57 m
Now, we will determine the distance between the car and the tractor when the car finally stopped
Distance between the car and the tractor = Distance ahead + Distance traveled by the tractor after the car stopped - Distance traveled by car after applying the brakes
Distance between the car and the tractor = 25 m + 38.57 m - 52.07 m
Distance between the car and the tractor = 11.5 m
Therefore, the distance the tractor was ahead of the car + the distance the tractor traveled after the car stopped is more than the distance the car traveled after applying the brakes (25 m + 38.57 m > 52.07), the car will not hit the tractor.
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[NOTE: THIS IS AN INCOMPLETE QUESTION. THE COMPLETE QUESTION IS: You are driving your car along a country road at a speed of 27.0 m/s. as you come over the crest of a hill, you notice a farm tractor 25.0 m ahead of you on the road, moving in the same direction as you at a speed of 10.0 m/s. you immediately slam on your brakes and slow down with a constant acceleration of magnitude 7.00 m/s2 .
a.will you hit the tractor before you stop?
b.how far will you travel before you stop or collide with the tractor?
c.if you stop, how far is the tractor in front of you when you finally stop?]
a 2100 kg truck traveling north at 41 km/h turns east and accelerates to 51 km/h. (a) what is the change in the truck’s kinetic energy? what are the (b) magnitude and (c) direction of the change in its momentum?
The change in momentum would have both x and y components. The direction can be represented by an angle or a vector.To calculate the change in the truck's kinetic energy, we need to find the difference between the initial and final kinetic energy. The formula for kinetic energy is KE = 0.5 * mass * velocity^2.
First, let's convert the velocities from km/h to m/s. To convert km/h to m/s, divide the value by 3.6.
Initial velocity: 41 km/h = 41 / 3.6 m/s ≈ 11.39 m/s
Final velocity: 51 km/h = 51 / 3.6 m/s ≈ 14.17 m/s
Now, let's calculate the initial and final kinetic energy.
Initial kinetic energy: KE1 = 0.5 * mass * velocity1^2
Final kinetic energy: KE2 = 0.5 * mass * velocity2^2
Substituting the values:
KE1 = 0.5 * 2100 kg * (11.39 m/s)^2
KE2 = 0.5 * 2100 kg * (14.17 m/s)^2
Finally, to find the change in kinetic energy, we subtract the initial kinetic energy from the final kinetic energy:
Change in kinetic energy = KE2 - KE1
(b) To find the magnitude of the change in momentum, we can use the equation: change in momentum = mass * (final velocity - initial velocity)
Change in momentum = 2100 kg * (14.17 m/s - 11.39 m/s)
(c) To determine the direction of the change in momentum, we can consider the directions of the initial and final velocities. The truck initially traveled north (in the y-direction) and then turned east (in the x-direction). Therefore, the change in momentum would have both x and y components. The direction can be represented by an angle or a vector.
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Which statement correctly describes magnetic field lines?
Answer: I believe the correct answer would be they join north pole to south pole. The direction of these lines always goes from the direction of north to south pole. These lines forms loops in order to favor the way which requires or has less resistance. Hope this helps.
what fraction of ice is submerged when it floats in freshwater, given the density of water at is very close to 1000?
To explain what fraction of ice is submerged when it floats in freshwater, let's consider Archimedes' Principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. The density of freshwater is very close to 1000 kg/m³.
First, let's assume the volume of the ice is V and its density is ρ_ice. When the ice floats, it displaces an equal volume of water, V_submerged. The weight of the submerged volume of ice is equal to the weight of the displaced water.
Weight of submerged ice = Weight of displaced water
ρ_ice * V_submerged * g = ρ_water * V_submerged * g
Here, g is the acceleration due to gravity. As the problem involves the ratio of volumes, we can eliminate g from the equation.
ρ_ice * V_submerged = ρ_water * V_submerged
Now, divide both sides by the density of water (ρ_water).
V_submerged / V = ρ_ice / ρ_water
Since the density of ice is about 917 kg/m³ and the density of water is about 1000 kg/m³, the fraction of ice submerged can be calculated as:
V_submerged / V = 917 / 1000
V_submerged / V ≈ 0.917
Therefore, approximately 91.7% of the ice is submerged when it floats in freshwater.
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Which of the following is true about wedges?
A.)Wedges are a type of ramp.
B.)Wedges are a type of screw.
C.)Wedges are a type of inclined plane.
D.)Wedges are a type of lever.
Answer:
wedges are a type of inclined plane.
Explanation:
i just answered :) :) :)
Wedges are a type of inclined plane is true about the wedges.aThe type of wedges is categorized on the basis of the angles of the inclined plane.
What are wedges?
A piece of wood, metal, or other material with one thick end and a thin edge that is used to attach or separate two things or sections of an object."A wedge was used to fasten the door"
The wedge family consists of four designs: pitching wedge, gap wedge, sand wedge, and lob wedge. Each stick has a different loft, which makes it better for various shots.
The Pitching Wedge is the wedge with the lowest loft. It may be utilized for full swings toward the greens as well as lengthy chip shots.
Hence wedges are a type of inclined plane is true about the wedges.
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I need help asap!
please..
a )The error in the micrometer is -0.003 cm.
b) the correct diameter of the wire is 0.632 cm.
Along with other metrological instruments like dial, Vernier, and digital calipers, a micrometer—also referred to as a micrometer screw gauge—is a tool with a calibrated screw that is frequently used for precise measurement of components in mechanical engineering, machining, and most mechanical trades.
b) correct reading of the wire = main scale + LC* Vernier reading + error
= 0.6 + 0.001*35 -0.003
= 0.632 cm
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A cloth line of length 10 m is made of stainless steel wire of mass 6 x 1.0² kgm. A boy taps one end with a knife. How long does the signal take to get- to the other end.
The using the terms "steel wire" and focus on the relevant information. Here is the step-by-step explanation: We know that the cloth line is 10 meters long and made of stainless-steel wire.
The mass of the steel wire as 6 x 1.0² kg., which equals 6 kg. To find the time it takes for the signal to travel through the steel wire, we need to know the speed of sound in steel. The speed of sound in steel is approximately 5000 meters per second (m/s). Now that we know the speed of sound in steel, we can calculate the time it takes for the signal to travel the length of the wire (10 meters) using the formula: time = distance / speed. Plugging in the values, we get time = 10 meters / 5000 m/s. After calculating, we find that the time it takes for the signal to travel through the steel wire is 0.002 seconds, or 2 milliseconds. So, it takes 2 milliseconds for the signal to travel from one end of the steel wire to the other end after the boy taps it with a knife.
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Una pelota q rodaba a 93,6 dm/s, luego de 14,4 segundos se detiene.¿cual fue el valor de su aceleracion?
Answer:
-6,5 ms ^ 2
Explanation:
Dado que;
Velocidad inicial (u) = 93,6 m / s
Velocidad final (v) = 0 m / s
aceleración (a) =?
tiempo empleado (t) = 14,4 segundos
De;
v = u + en
0 = 93,6 + 14,4a
a = -93,6 / 14,4
a = -6,5 ms ^ 2
Describe the laws of liquid pressure and Explain the term fluid. (Please give the correct answer, it's really urgent)
Answer:
The laws of liquid pressure are
(i) Pressure inside the liquid increases with the depth from the free surface of the liquid.
(ii) Pressure is same at all points on a horizontal plane, in case of stationary liquid.
(iii) Pressure is same in all directions about a point inside the liquid.
(iv) Pressure at same depth is different in different liquids. It increases with the increase in the density of the liquid.
(v) A liquid will always seek its own level.
A Fluid is any liquid or gas or generally any material that cannot sustain a tangential, or shearing, force when at rest.
Explanation:
Increasing the distance between an electromagnet and the compass will cause the observed effect of the compass to _____.
Increasing the distance between an electromagnet and the compass will cause the observed effect of the compass to decrease in strength
What would the Increasing the distance between an electromagnet and the compass cause?
The strength of the magnetic field produced by an electromagnet decreases as the distance from the electromagnet increases. This means that if the distance between the electromagnet and the compass increases, the magnetic field that the compass is experiencing will weaken.
As a result, the observed effect of the compass will decrease in strength as the distance between the electromagnet and the compass increases.
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The egc for a flexible metal conduit connection to a motor supplied with a 20 a circuit is:_________
The EGC for a flexible metal conduit connection to a motor supplied with a 20A circuit is a 12 AWG copper conductor.
The EGC (Equipment Grounding Conductor) for a flexible metal conduit connection to a motor supplied with a 20A circuit is determined by the sizing requirements of the NEC (National Electrical Code). The NEC specifies the minimum size of the EGC based on the size of the circuit conductors and the type of conduit used.
To determine the minimum size of the EGC, we need to consult the NEC Table 250.122, which provides the minimum size of the EGC based on the size of the circuit conductors.
Since the circuit is supplied with a 20A current, we will assume that the circuit conductors are sized accordingly. According to the NEC Table 310.15(B)(16), a 20A circuit typically uses a 12 AWG copper conductor.
Next, we need to determine the type and size of the flexible metal conduit used for the connection. Different types of conduits have different requirements for the EGC sizing. For instance, for a flexible metal conduit, the NEC Table 250.122 specifies that a 12 AWG copper conductor should be used if the conduit is 3/4" or smaller.
Therefore, based on the information provided, the EGC for a flexible metal conduit connection to a motor supplied with a 20A circuit is a 12 AWG copper conductor.
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calculate the x component and the y component of the vector with magnitude 24.0 m and direction 56.0degree
The X component was 13.4m and the Y component was 19.9m.
define magnitude ?
A crucial question in science is undoubtedly what is magnitude in physics. Magnitude is a term used to describe size or distance. We can connect the amount of the movement to the size and movement speed of the item.
The magnitude of a thing or a quantity is its size. A automobile moves at a quicker pace than a motorcycle, just like in terms of speed. In this situation, the car's speed is greater than the motorbike's. Let's now talk about what magnitude means in physics.
y=m sin(∅)
x=m cos(∅)
y=2+sin(56)=19.89
=19.89 ≈ 19.9m
x=2+cos(56)=13.42
=13.42≈13.4m
The X component was 13.4m and the Y component was 19.9m.
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A theme park is planning out a new free-fall ride. The drop is almost perfectly frictionless, with a distance of 190 meters. Assuming that the initial velocity was zero, what would be the speed at the bottom of the drop?
a-53 m/s
b-61 m/s
c-67 m/s
d-72 m/s
Answer:
Approximately \((-61)\; {\rm m\cdot s^{-2}}\), assuming that \(g = 9.81\; {\rm m\cdot s^{-2}}\).
Explanation:
Under the assumptions, the vehicle would be in a free fall. Acceleration would be constant: \(a = (-g) = (-9.81)\; {\rm m\cdot s^{-2}}\).
Let \(u\) denote the initial velocity of the vehicle. Let \(v\) denote the velocity of the vehicle at the bottom of the drop. Let \(x\) denote the displacement of the vehicle during the drop.
It is given that the initial velocity is \(u = 0\; {\rm m\cdot s^{-1}}\). During the drop, displacement would be \(x = (-190)\; {\rm m}\) (negative since the vehicle is below where it started.) The value of final velocity \(v\) needs to be found.
It is known that the vehicle is moving downwards at the end of the fall. Therefore, the value of \(v\!\) would be negative. Apply the SUVAT equation \(v^{2} - u^{2} = 2\, a\, x\) to find \(v\) from \(u\), \(a\), and \(x\).
\(\begin{aligned}v^{2} &= u^{2} + 2\, a\, x\end{aligned}\).
\(\begin{aligned}v &= -\sqrt{u^{2} + 2\, a\, x} \\ &= -\sqrt{(0\; {\rm m\cdot s^{-1}})^{2} + 2\, (-9.81\; {\rm m\cdot s^{-2}})\, (-190\; {\rm m})} \\ &\approx (-61)\; {\rm m\cdot s^{-1}}\end{aligned}\).
(Note that \(v\) is negative.)
In other words, the velocity of the vehicle would be approximately \((-61)\; {\rm m\cdot s^{-1}}\) at the end of the drop.
PLZ HELP ME I HAVE A TIMER!!!
Plz find the initial value (u)
Thank you soo much!!!
answer:
u =11
Explanation:
brackets were inserted in the 1st step,to make it simpler as multiplication is done first, before addition.
hope this helps:))
why does the green colour of iron (ii) chloride change to yellow when chlorine gas is bubbled into it
Answer:
FeCl2 has a high melting point.
Explanation:
Iron is seen to get oxidized by addition of chlorine 3 as the product is rust colored and on dissolving in water has a yellow orange color. This is characterized by the aquatic iron and is due to the monohydroxyHere photosynthesis in a nutshell. Can you explain what is happening?
Answer:
Photosynthesis is the process of using water, carbon dioxide and sunlight to produce sugar. The process of photosynthesis requires specialized cellular structures called chloroplasts to capture energy from the Sun and converted into chemical energy.
Explanation:
can anyone tell me the answer of these whole question? thank you so much!
Answer:
a) the most dangerous combination of tires and roads surfaces are old tires on wet concrete because it shows the longest distance moved by a car when the brake is pushed
b) Old tires on wet concrete
c) wet tires require longer braking distance than dry tires because the wet surface on the tires slide rather
than stopping gradually.
A spring-loaded gun is cocked by compressing a short, strong spring by a distance d. It fires a signal flare of mass m directly upward. The flare has speed v 0
as it leaves the spring and is observed to rise to a maximum height h above the point where it leaves the spring. After it leaves the spring, effects of drag force by the air on the flare are significant. (Express answers in terms of m,v 0
,d,h, and g.) (a) How much work is done on the spring during the compression? (b) What is the value of the force constant k ? (c) Between the time of firing and the time at which maximum elevation is reached, how much mechanical energy is dissipated into thermal energy?
A spring-loaded gun is cocked by compressing a short, strong spring by a distance d. It fires a signal flare of mass m directly upward. The flare has speed v0 as it leaves the spring and is observed to rise to a maximum height h above the point where it leaves the spring.
After it leaves the spring, effects of drag force by the air on the flare are significant. The work done on a spring by compressing or stretching it is given by:W = (1/2)kx²where,W is the work donek is the force constantx is the distance by which the spring is compressed or stretchedTherefore, work done on the spring during compression,W = (1/2) k d² ...(1) From the work done on the spring,W = (1/2) k d²Using this formula, the force constant can be calculated,k = 2W/d² ...(2)
The total mechanical energy of the flare when it is fired from the spring,Em = (1/2)mv₀²where,m is the mass of the flarev₀ is the speed of the flare when it leaves the spring When the flare reaches its maximum height h, all of its kinetic energy is converted into potential energy. Thus,mgh = (1/2)mv₀²i.e.,gh = (1/2)v₀² ...(3)The amount of mechanical energy dissipated into thermal energy is equal to the initial mechanical energy minus the mechanical energy at maximum height. Thus, Ethermal = Em - mgh Ethermal = (1/2)mv₀² - mgh Substituting the value of v₀² from equation (3),Ethermal = (1/2)m(2gh) - mgh Ethermal = mgh .
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