The range of magnetic field strengths on the Earth's surface varies depending on the location and geological features of the area.
The magnetic field of the Earth is not uniform and varies in strength, direction, and intensity over time and location.
At the equator, the magnetic field strength is about 30,000 to 60,000 nanotesla (nT), while at the poles, the strength can be as high as 60,000 to 80,000 nT. In general, the magnetic field strength at the Earth's surface is typically between 25,000 to 65,000 nT.
However, the magnetic field of the Earth is subject to fluctuations and changes due to various factors, such as solar activity, geological changes, and other natural phenomena. These fluctuations can cause variations in the strength and direction of the magnetic field, which can have significant implications for a variety of fields, including navigation, geology, and space weather forecasting.
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While riding her bike, Ms. Parker average a velocity of 20m/s. If she maintains that velocity for a time of 20 seconds, how far does she rides?
Answer:
400 m
Explanation:
20m/s x 20s = 400m
A thin flat plate of length L, thickness t, and width W > L is thermally joined to two large heat sinks that are maintained at a temperature To. The bottom of the plate is well insulated, while the net heat flux to the top surface of the plate is known to have a uniform value of q0
a) Derive the differential equation that determines the steady-state temperature distribution T(x) in the plate.
b) Solve the foregoing equation for the temperature distribution, and obtain an expression for the rate of heat transfer from the plate to the heat sinks.
The rate of heat transfer from the plate to the heat sinks is given by the expression \($\frac{dQ}{dt} = kA\frac{q_0}{hL} = \frac{kAq_0}{hL}$\).
The differential equation that determines the steady-state temperature distribution T(x) in the plate is given by:\($$\frac{d^2T(x)}{dx^2}$ + \frac{hP}{kA}T(x) $= 0$$\) Where h is the convection heat transfer coefficient on the top surface of the plate, P is the perimeter of the plate, k is the thermal conductivity of the plate material, and A is the cross-sectional area of the plate.
Let the plate be divided into small elements of length dx. The net rate of heat transfer to this element is equal to the heat that enters the element from the left minus the heat that leaves the element from the right.
Hence we have,\($$dQ = -kA\frac{dT}{dx}$dx = (q_0 + hL(T(x)-T_0))dxdy$$$$\implies \frac{d^2T(x)}{dx^2} + \frac{hP}{kA}T(x) = 0$$\)
The solution to the above equation is given by \($$T(x) = \frac{q_0}{hL} $+ (T_0 - \frac{q_0}{hL})e^{-\frac{hP}{kA}x}$$\)
Therefore, the rate of heat transfer from the plate to the heat sinks is given by
\($$\frac{dQ}{dt}$ = kA\frac{dT}{dx}$\Bigg|_{x=0} = kA\frac{q_0}{hL} = \frac{kAq_0}{hL}$$\)
Therefore, the differential equation that determines the steady-state temperature distribution T(x) in the plate is given by the equation \($\frac{d^2T(x)}{dx^2} + \frac{hP}{kA}T(x) = 0$\). The solution to this equation is given by the expression \($T(x) = \frac{q_0}{hL} + (T_0 - \frac{q_0}{hL})e^{-\frac{hP}{kA}x}$\). The rate of heat transfer from the plate to the heat sinks is given by the expression \($\frac{dQ}{dt} = kA\frac{q_0}{hL} = \frac{kAq_0}{hL}$\).
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Phosphoric acid is triprotic and will undergo through successive ionization reactions to varying extents of water. which balanced equilibrium reaction will have the largest ka value?
Among the successive ionization reactions of phosphoric acid (H₃PO₄), the equilibrium reaction that will have the largest Ka value is the first ionization reaction.
The first ionization of phosphoric acid can be represented by the equation:
H₃PO₄ + H₂O ⇌ H₃O⁺ + H₂PO₄⁻
In this reaction, one hydrogen ion (H⁺) is released, forming the hydronium ion (H₃O⁺) and the hydrogen phosphate ion (H₂PO₄⁻). The Ka value represents the acid dissociation constant, which indicates the extent of ionization of an acid in water. A higher Ka value indicates a greater degree of acid strength.
In the case of phosphoric acid, the first ionization reaction has the largest Ka value because it is the initial and most significant ionization step.
As the subsequent ionization reactions proceed, the remaining hydrogen atoms become increasingly difficult to remove due to the decreasing strength of the acid.
Therefore, the first ionization reaction of phosphoric acid has the highest Ka value among its successive ionization reactions.
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How is the capacitance of a capacitor related to the charge stored on the capacitor and the potential difference across the capacitor?.
Answer:
Capacitance is the ratio of the charge to the potential difference. How is the charge stored on a capacitor related to the capacitance of the capacitor and the potential difference across the capacitor? The charge equals the product of the capacitance and the potential difference.
Explanation:
Hope this helps
Which wave form will Rayleigh waves most likely create?
A. an ocean wave
B. a skier moving down a mountain hill
C. a car traveling through the sand dunes
D. a whale gliding along the ocean's surface
5 A swimming pool is 50m long. A
swimmer covers it in 50s. Calculate
the average speed of the swimmer.
the answer is 150 000 s2
The average speed of the swimmer is equal to 1 m/s.
What is the average speed?The average speed can be defined as the total distance traveled by the object in a specific time interval. The average speed can be defined as a scalar quantity as it possesses only the magnitude and does not have any direction.
The average speed can be determined from the ratio of the total distance the object covers to the time taken to travel that distance.
The equation for average speed can be written as follows:
Average speed = Total distance/Total time taken
Given, the distance covered by the swimmer = 50 m
The total time taken by the swimmer = 50 sec
The average speed of the train = 50/50 = 1 m/s
Therefore, the average speed of the swimmer is equal to 1 m/s.
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find the absolute pressure of a motorcycle tire with a gauge pressure of 255 kpa
The absolute pressure of a motorcycle tire can be found by adding the gauge pressure to the atmospheric pressure.
Given that the gauge pressure is 255 kPa, we need to determine the atmospheric pressure to calculate the absolute pressure. The standard atmospheric pressure at sea level is approximately 101.3 kPa.Therefore, the absolute pressure of the motorcycle tire can be calculated as follows:
Absolute Pressure = Gauge Pressure + Atmospheric Pressure
Absolute Pressure = 255 kPa + 101.3 kPa
Absolute Pressure = 356.3 kPa
Hence, the absolute pressure of the motorcycle tire is 356.3 kPa.
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at what part of a path does a projectile have the least speed
Answer:
top
Explanation:
In the open ocean, 1 wave in ________ will be three times as high as the height of the wave average.
In the open ocean, the relationship between wave height and occurrence of larger waves can be described probabilistically. While the exact value may vary depending on several factors, it is often estimated that approximately 1 wave in every 100 will be three times as high as the average wave height.
Wave heights in the open ocean are influenced by various factors, including wind speed, duration, and fetch (the distance over which the wind blows). These factors determine the energy transferred to the water surface, resulting in the formation of waves. As waves propagate across the ocean, they undergo complex interactions, resulting in a distribution of wave heights.
The average wave height refers to the statistical mean of the wave heights observed over a given period. However, due to the randomness and variability of wave generation and propagation, it is expected that occasionally larger waves will occur. These larger waves can be significantly higher than the average, reaching up to three times its height.
It's important to note that this estimation may not hold true in all circumstances and locations. Wave conditions can be highly variable and depend on regional and seasonal factors. Therefore, wave forecasting models and empirical data collected specifically for a particular region can provide more accurate estimates of the occurrence of waves of a certain height relative to the average.
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derive an expression from the energy stored E, in a stretched wire of original length L cross sectional area A, e, tension e,and young modulus Y of the material of the wire
The expression for the energy stored (E) in a stretched wire of original length (L), cross-sectional area (A), tension (T), and Young's modulus (Y) is given by E = Y * e * ln(L) * A
How to explain the expressionThe work done to stretch the wire can be calculated by integrating the force applied over the displacement. In this case, the force applied is the tension (T) in the wire, and the displacement is the change in length (ΔL) from the original length (L) to the stretched length (L + ΔL).
The tension in the wire is given by Hooke's law, which states that the tension is proportional to the extension of the wire:
T = Y * (ΔL / L)
where Y is the Young's modulus of the material of the wire.
Now, let's calculate the work done to stretch the wire:
dW = T * dL
Integrating this expression from L to L + ΔL:
W = ∫ T * dL = ∫ Y * (ΔL / L) * dL
W = Y * ΔL * ∫ (dL / L)
W = Y * ΔL * ln(L) + C
Here, C is the constant of integration. Since the energy stored in the wire is zero when it is unstretched (ΔL = 0), we can set C = 0.
Finally, the expression for the energy stored in the wire (E) is:
E = W = Y * ΔL * ln(L)
or, if we substitute the cross-sectional area (A) and strain (e) of the wire, where e = ΔL / L:
E = Y * e * ln(L) * A
Thus, the expression for the energy stored (E) in a stretched wire of original length (L), cross-sectional area (A), tension (T), and Young's modulus (Y) is given by:
E = Y * e * ln(L) * A
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fusion reactions could not occur in a star without the pressure created by _____
Fusion reactions are reactions that occur when two or more atomic nuclei come close enough to form one or more different atomic nuclei and subatomic particles like protons and neutrons.
These reactions are important for a variety of reasons, including the energy they provide in the form of sunlight, the helium that forms during these reactions which is used in balloons, and the potential for fusion to provide a sustainable source of energy.
In stars, fusion reactions could not occur without the pressure created by the inward force of gravity. Fusion requires high temperatures and pressures to overcome the electromagnetic repulsion between positively charged atomic nuclei. In the core of a star, the high temperature and pressure created by gravity causes hydrogen nuclei (protons) to come together and form helium through a series of nuclear reactions known as the proton-proton chain.
This process releases a tremendous amount of energy in the form of light and heat, which provides the energy that stars need to shine and support life on planets like Earth.
Fusion reactions are incredibly important to our understanding of the universe and our ability to harness energy from sources that do not contribute to climate change.
While scientists have made great strides in developing fusion reactors that can produce energy on Earth, there is still much work to be done before we can fully realize the potential of this technology.
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The mean weight of loaves of bread produced at the bakery where you work is supposed to be 1 pound. You are the supervisor of quality control at the bakery, and you are concerned that new employees are Producing loaves that are too light? Suppose you weigh an SRS of bread loaves and find that the mean weight al is 0.975 pound. What conclusion would you make at the �=0.01α=0.01 significance level?
The significance level or α in statistics defines the probability of rejecting the null hypothesis when it is accurate. If the significance level is lower, then the risk of rejecting the null hypothesis when it is true is smaller.
We'll use a hypothesis test to address this. It will give us a proper conclusion about the concern.
Suppose the null hypothesis is \(H_0: \mu = 1\) pound
Suppose the alternative hypothesis is \(H_1: \mu < 1\) pound
Test Statistic \(T = (al - \mu) / [ s/ \sqrt {n} ]\)
where, al is the mean weight, µ is the population mean1 pound is the hypothesized value of \(\mu_s\) is the sample standard deviation n is the sample size
Here, al = 0.975 pound, n = 1 Since this is a one-tailed test, we need to use a one-tailed t-distribution with 1 degree of freedom to find the critical value. Critical value (CV) at α = 0.01 is given by CV = t0.01(1) where t0.01(1) is the 1st percentile of a t-distribution with 1 degree of freedom.
Using the t-distribution table, \(t0.01(1) = - 6.31\). The critical value is -6.31. We're looking for whether or not the hypothesis should be accepted or rejected. If the value of t is higher than the critical value (CV), we reject the null hypothesis. Otherwise, we accept the null hypothesis.
\(T = (al - \mu) / [ s/ \sqrt {n} ]= (0.975 - 1) / [ s/ \sqrt{1}]= -0.025 / s\)
The mean weight of bread loaves produced at the bakery is 1 pound, but the mean weight of an SRS of bread loaves produced at the bakery is 0.975 pound. Thus, the hypothesis will be rejected if the weight of the loaves in the sample is lower than the mean weight of loaves in the bakery. The test statistic is negative. This indicates that the observed value (0.975) is lower than the hypothesized value (1.0). Since it is only a one-tailed test, the P-value for a t-distribution with 1 degree of freedom can be calculated using the following formula:
P-value = P (T ≤ t)where T is the t-distribution with n - 1 degrees of freedom. The P-value at T = - 0.79 (from the t-table) is 0.4289. Since this value is higher than the significance level of 0.01, we can't reject the null hypothesis. Hence, there is no proof of insufficient bread weight.
Therefore, we accept the null hypothesis that the average weight of loaves of bread produced at the bakery is 1 pound.
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a firefighter is helping the woman shown in the figure below. the woman's weight is 120 lb. what's the tension (in lb) in the rope connecting the woman to the firefighter?
The tension in the rope is equal to the weight of the woman, which is 120 lb. Since the woman is not accelerating, the forces acting on her must be balanced, meaning the tension in the rope must equal her weight. Therefore, the tension in the rope is 120 lb.
What is tension?
Tension is a state of mental or emotional strain, resulting from opposing forces or influences. It is a feeling of inner strain caused by a clash of emotions, ideas, or beliefs. It can also result from physical causes such as a lack of sleep, worry, physical exertion, and even hunger.
Tension can manifest itself in physical symptoms such as headaches, neck pain, muscle tightness, and fatigue. It can also lead to emotional problems such as anxiety, irritability, and depression. It is important to recognize and address tension in order to maintain good mental and physical health.
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2. A metal cube with an edge length x is expanding uniformly as a consequence
of being heated. Find the:
(a) Change in volume of the cube as x increases from 2.00 to 2.01 centimeters.
(b) Average rate of change of volume of the cube with respect to an edge length as x
increases from 2.00 to 2.01 centimeters.
(c) Instantaneous rate of change of volume of the cube with respect to an edge length
at the instant when x = 2 centimeters.
3. Use the definition of the derivative to find the equation of the line that passes through
the point (1, 5) and is parallel to the tangent line to f (x) = 1
x at x = 3.
A. the change in volume of the cube is approximately 0.120601 cm^3. B. the average rate of change of volume of the cube with respect to an edge length is approximately 12.0601 cm^3/cm. C. the equation of the line that passes through the point (1, 5) and is parallel to the tangent line to f(x) = 1/x at x = 3 is y = (-1/9)x + 14/9.
(a) To find the change in volume of the cube as x increases from 2.00 to 2.01 centimeters, we need to calculate the difference in volume between these two values.
The volume of a cube is given by V = x^3, where x is the edge length.
For x = 2.00 cm, the volume V1 = (2.00 cm)^3 = 8.00 cm^3.
For x = 2.01 cm, the volume V2 = (2.01 cm)^3 = 8.120601 cm^3.
The change in volume is ΔV = V2 - V1 = 8.120601 cm^3 - 8.00 cm^3 ≈ 0.120601 cm^3.
Therefore, the change in volume of the cube is approximately 0.120601 cm^3.
(b) The average rate of change of volume of the cube with respect to an edge length as x increases from 2.00 to 2.01 centimeters can be calculated by dividing the change in volume by the change in edge length.
ΔV = 0.120601 cm^3 (from part a)
Δx = 2.01 cm - 2.00 cm = 0.01 cm
The average rate of change of volume is ΔV/Δx = 0.120601 cm^3 / 0.01 cm ≈ 12.0601 cm^3/cm.
Therefore, the average rate of change of volume of the cube with respect to an edge length is approximately 12.0601 cm^3/cm.
(c) The instantaneous rate of change of volume of the cube with respect to an edge length at the instant when x = 2 centimeters can be found by taking the derivative of the volume function V = x^3 with respect to x and evaluating it at x = 2.
dV/dx = 3x^2
At x = 2 cm, the instantaneous rate of change of volume is dV/dx evaluated at x = 2:
dV/dx = 3(2 cm)^2 = 12 cm^2.
Therefore, the instantaneous rate of change of volume of the cube with respect to an edge length at x = 2 centimeters is 12 cm^2.
To find the equation of the line that passes through the point (1, 5) and is parallel to the tangent line to f(x) = 1/x at x = 3, we need to determine the slope of the tangent line.
The derivative of f(x) = 1/x is given by f'(x) = -1/x^2.
At x = 3, the slope of the tangent line is f'(3) = -1/(3^2) = -1/9.
Since the line we want to find is parallel to the tangent line, it will have the same slope. So the slope of the line is -1/9.
Using the point-slope form of a linear equation, we can write the equation of the line as:
y - y1 = m(x - x1),
where (x1, y1) is the given point (1, 5) and m is the slope.
Substituting the values, we have:
y - 5 = (-1/9)(x - 1).
Expanding and rearranging the equation, we get:
y = (-1/9)x + 14/9.
Therefore, the equation of the line that passes through the point (1, 5) and is parallel to the tangent line to f(x) = 1/x at x = 3 is y = (-1/9)x + 14/9.
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One mole of titanium contains how many atoms?
O A. 60.2 x 1024
O B. 6.02 x 10-23
O C. 1.0
O D. 6.02 x 1023
SUBMIT
Answer:
\(\boxed {\boxed {\sf D. \ 6.02*10^{23} \ atoms}}\)
Explanation:
One mole of a substance contains the same amount of representative particles. These particles can be atoms, molecules, ions, or formula units. In this case, the particles are atoms of titanium.
Regardless of the particles, there will always be 6.02*10²³ (also known as Avogadro's Number) particles in one mole of a substance.
Therefore, the best answer for 1 mole of titanium is D. 6.02*10²³ atoms.
Answer:
D) 6.02 x 1023
Explanation:
A.P.E.X
(A)derive the equation for circular motion,a=rw^2, where a is the centripetal acceleration w is the angular velocity and r the radius of the circle
(B) (i) the moon orbits the earth in a circle of radius 400000km. considering only these two objects, state what force act on the moon and explain how newton third law of motion applies to the system.
(ii) find the time for one complete revolution of the moon about the earth.
The equation for centripetal acceleration can be written as follows : a = v² / r = (rw)² / r = r × w² , the relationship between angular velocity and linear velocity : v = r × w
Evaluation :A.The following equation can be used to calculate the centripetal acceleration during a circular motion:
Consider a particle of mass m traveling at an angular velocity w in a circle of radius r. The particle's velocity is calculated as v = rw, where v is its linear velocity.
The net force exerted on the particle can be calculated using Newton's second law as follows:
F = m × a,
where a is the particle's acceleration.
The centripetal force is the net force exerted on the particle, which must be directed toward the circle's center.
As a result, the equation for centripetal acceleration can be written as follows:
a = v² / r = (rw)² / r
= r × w²
This equation is usually written as:
a = r × w².
What is the Third Law of Motion of Newton?According to Newton's third law of motion, there is an equal and opposite reaction to every action. The gravitational force exerted by the moon in this system is the same as that exerted by the Earth in this system. Newton's third law of motion, also known as the action-reaction pair of forces, describes this phenomenon.
B) (i) The equation below describes the gravitational force that is exerted on the moon:
F =G × (m_earth × m_moon) / r²
G is the gravitational constant, m_earth is the Earth's mass, m_moon is the moon's mass, and r is the distance between the Earth's and moon's centers.
(ii) We need to divide the circumference of the moon's circular path by its linear velocity in order to determine the time it takes for the moon to complete one complete revolution around the Earth:
C = 2 × pi × r
v = C / T
where C is the circumference of the moon's circular path, r is the circular path radius, T is the time it takes to complete one revolution, and v is the moon's linear velocity.
We obtain: by substituting the values:
C = 2 × pi × 400000 km = 800000 × pi km
v = C / T = (800000 × pi km) / T
We need to know the moon's angular velocity in order to calculate the time. These numbers indicate the relationship between angular velocity and linear velocity :
v = r × w
Substituting the values, we get:
T = C / (r × w)
= (800000 × pi km) / (400000 km × w)
= 2 × pi / w
Since the angular velocity w is not specified, it is not possible to determine how long it would take for the moon to complete one complete revolution around the Earth.
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a student tries to produce notes of higher frequency by blowing a trumpet harder. he will succeed?
Answer:
Please mark as Brainliest!!
Explanation:
He will not succeed as it blows the trumpet harder that only increase the amplitude of the sound wave that means the intensity of the sound will increase but the frequency remains the same.
Answer:
he wont
Explanation:
The musical tone a piano has a frequency of 346HZ and a wavelength of 1.3 M what is the speed of the sound
Answer:
v= 449.8 m/s
Explanation:
Given data
Frequency= 346Hz
Wave length= 1.4m
The expression below is used to find the speed
\(v= f \lambda\\\\\)
substitute
\(v= 346*1.3\\\\v= 449.8 m/s\)
Hence the speed is v= 449.8 m/s
A dish is given to you, which contains a blackish-yellow powder. When you move a magnet over it, you are amazed to see black particles, (which you find out are iron) fly upwards and get stuck to the magnet, and all that's left in the dish is a yellow powder, which you discover to be sulfur. Was your original powder an element, compound or mixture?
Answer:
In the case of the blackish-yellow powder, the black color is due to the presence of a iron and yellow color is due to sulfur. As the iron has retained its original properties it has got attached to the magnet. Thus the blackish-yellow powder is considered a mixture.
Explanation:
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A 50 kg student holding a 7 kg backpack rides a 4 kg skateboard down the sidewalk at 3 m/s. What is the total momentum of the student, backpack, and skateboard?
Answer:
183 MLT^-1Explanation:
Mass = 50kg +7kg +4kg =61 kg
Velocity = 3m/s
Momentum = mass × velocity
\(p =61\times 3\\\\p =183MLT^-^1\)
Answer:
Mass= 61 kg. Success to The homework.
4. ____________ occurs when one object slides over another.
a. Sliding friction
b. Static friction
c. Rolling friction
d. Net force
Answer:
A. Sliding friction
Explanation:
Sliding friction is weaker than static friction
Answer:
Rolling Friction
Explanation:
I know this because the definition of rolling friction is : type of friction that happens when one body rolls over another
How much work do you do when you push a couch 3 m across the floor using a force of 60 N?
what is magnetization?
Answer:
In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Movement within this field is described by direction and is either Axial or Diametric
5. the location and gimbal limits of the flir sensor prevent the p* from seeing the terrain directly beneath the aircraft. what must the p* do prior to conducting a landing from a hover?
Your ability to land safely is the primary prerequisite in order to protect your passengers and people on the ground.
Explain about the gimbal?
In the same way as a tripod would if you were shooting a picture or remained in one place while taking it, a gimbal employs sensors and motors to stabilize and support your camera.
The majority of contemporary rockets, including the Space Shuttle and the Saturn V moon rocket, employ a technique known as gimbaled thrust. The rocket's exhaust nozzle can be moved in either direction when using a gimbaled thrust system. In relation to the rocket's centre of gravity, the thrust direction changes when the nozzle is moved.
When using Euler angles in applied mathematics, the gimbal lock problem arises; creators of 3D computer programmes, such as 3D modelling, embedded navigation systems, and video games, must take care to avoid it.
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PLEASE HELP
The most distant objects in the Universe known to
astronomers are 14 billion ly away. Convert this value
to metres.
Answer:
I'm in ninth grade, but-
Explanation:
According to my calculator
14 billion light years = 1.32450227 x 1026 meters?
Sorry if this doesn't help:(
have a good night
When light hits a surface it usually bounces off at a larger angle. True or false? Justify
Answer:That only applies to highly polished surfaces, eg mirrors.
If you take a high quality laser (ie with low divergence) and aim it at a wall, you can see the spot where the laser beam reaches the wall from anywhere with a direct line-of-sight to the spot where the laser beam reaches the wall. This due to micro imperfections on the surface of the wall. At a microscopic level, the wall surface is very rough and pointing in all directions.
As to why, a beam of light bounces of a highly polished surface, I can only surmise that it is essentially due to kinematics, ie the only force opposing the light beam is normal to the surface, hence there no forces along the reflective surface. Since there are no forces along the reflective surface, the speed component of light along the reflective surface remains unchanged. However, on the plane perpendicular to the reflective surface the, the light photons bounce off at the same speed at which the hit the reflective surface because the mass of the reflective surface is much much much larger than the mass of the photons, which means that the reflective surface won’t move at all. Since conservation of momentum requires that momentum after the collision be the same as the momentum before the collision then the only way for that to happen is if the velocity of the photon perpendicular to the reflective surface is of exactly the same magnitude but in the opposite direction. Vector resolution of the speed component of the reflected beam means that the angle of reflection must be the same as the angle of incidence.
Explanation:
output work is less than input work why?
Answer:
In general, the concept of output work being less than input work does not align with the laws of physics, specifically the principle of conservation of energy. According to this principle, energy cannot be created or destroyed, but it can be transformed from one form to another. Therefore, the total amount of energy in a closed system remains constant.
When considering work, which is the transfer of energy through the application of force over a distance, the input work and output work should theoretically be equal if no energy is lost to other forms, such as heat or friction. However, in real-world scenarios, various factors can result in a decrease in output work compared to input work. Some possible reasons for this disparity include:
Inefficiencies: Real systems are not perfectly efficient, and energy losses can occur due to factors like friction, heat dissipation, electrical resistance, or mechanical limitations. These losses reduce the amount of useful work obtained from the input energy.
Energy conversion: If the input work is in one form of energy (such as electrical or chemical), and the output work is in a different form (such as mechanical), energy losses can occur during the conversion process. The efficiency of the conversion process determines the amount of output work obtained.
External forces: External factors, such as resistance or opposing forces, can require additional work to overcome, resulting in a decrease in net output work compared to the input work.
It's important to note that while output work can be less than input work in certain situations due to these factors, the total amount of energy remains conserved. Energy that is not converted into useful work is typically dissipated as waste heat or other forms of energy loss.
Answer:
The output work is always less than the input work because of friction.
Explanation:
Friction is a force that opposes the relative motion of two surfaces in contact. When a machine is used, frictional forces are created between the moving parts of the machine and the surfaces they rub against.
These frictional forces require some of the input work to be used to overcome them, which reduces the amount of work that is available to do the desired task.
a horizontal pipe of diameter 0.888m has a smooth constriction to a section of diameter 0.5328m. The density of oil floating in the pipe is 821kg/m^3. I the pressure of the pipe is 7980N/m^2 and in the constricted section is 5985N/m^2,what is the rate at which oil is flowing?
The m dot = 1A1v1 = (821 kg/m3)(0.618 m2)(2.117 m/s) 1077 kg/s is the flow rate of the oil.
What is the horizontal pipe formula?fluid moving through a horizontal pipe P1 + ½ρv12 = P2 + ½ρv22. The pressure will depend on the fluid's speed if it is flowing frictionlessly through a horizontal pipe with a variable cross-sectional area as a liquid (or a gas that is not being compressed).
The fluid's velocity and cross-sectional area before and after the pipe's constriction can be compared using the continuity concept.
ρ1A1v1 = ρ2A2v
Moreover, we may link the fluid's pressure and velocity before and after the constriction using Bernoulli's equation:
P1 + 1/2ρ1v1² = P2 + 1/2ρ2v2²
v2 = (ρ1/ρ2) × (A1/A2) × v1
P1 + 1/2ρ1v1² = P2 + 1/2ρ1(A1/A2)²(v1)²
Solving for v1, we get:
v1 = sqrt(2(P1 - P2)/ρ1(1 - (A1/A2)²))
v1 = sqrt(2(7980 - 5985)/(821)(1 - (0.618/0.223)^2)) = 2.117 m/s.
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On a dry winter day, if you scuff your feet across a carpet, you build up a charge and get a shock when you touch a metal doorknob. In a dark room you can actually see a spark about 2 cm long. Air breaks down at a field strength of 3 × 10^6 N/C. How much charge have you built up? As- sume that just before the spark occurs, all the charge is in your finger, drawn there by in- duction due to the proximity of the doorknob. Approximate your fingertip as a sphere of di- ameter 1.42 cm, and assume that there is an equal amount of charge on the doorknob 2 cm away. Answer in units of C How many electrons does this correspond to? The elemental charge is 1.60218 × 10-19 C.
The number of electrons that corresponds to the number of charges is 2.71 × 10¹⁰ electrons.
How much charge have you built up?
The breakdown field strength of air is 3 × 10⁶ N/C, and the distance between the fingertip and the doorknob is 2 cm, so the electric field between the two is given by:
E = 3 × 10⁶ N/C
The electric field causes the charge on the fingertip to be drawn towards the doorknob, so we can calculate the charge on the fingertip using the formula:
q = 4π ε_0 x Er²
where;
r is the radius of the fingertip (0.71 cm) and
ε_0 is the permittivity of free space (8.854 × 10^-12 C^2/Nm²).
q = 4 x π x 8.854 × 10⁻¹² x 3 × 10⁶ x 0.71²
q = 2.17 × 10⁻⁸ C
The charge on the doorknob is equal and opposite to the charge on the fingertip, so the total charge on both is calculated as;
Q_total = 2 x 2.17 × 10⁻⁸ C
= 4.34 × 10⁻⁸ C.
The number of electrons is calculated as follows;
number of electrons = q / e
where;
e is the elementary charge (1.60218 × 10⁻¹⁹ C).number of electrons = ( 4.34 × 10⁻⁸ C / 1.60218 × ⁻¹⁹ C )
number of electrons = 2.71 × 10¹⁰ electrons
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(b) A ball is thrown vertically upwards with
velocity of 20 m/s from the top of a tower of
height 25 m from ground. How long does it
remain in air? (g = 10 m/s²)
Answer:
5 seconds
Explanation:
The vertical position of the ball will be given by the equation
df = do + vo t + 1/2 a t^2 df = final position = 0 ( on the ground
do = original position ( 25 m )
vo = original velocity (+ 20 m/s)
a = - 10 m/s^2
So this becomes
0 = 25 + 20 t - 1/2 (10)t^2
= - 5 t^2 +20 t + 25 Use Quadratic Formula a = -5 b=20 c = 25
to find the positive value of t = 5 seconds