Choosing the proper quantities that are related to place and time and result in a graph with a straight line earns you 1 point.
Examples of answers include: x and t^2, x and 1/2 t^2
2x and t^2, sqrt(x) and t.
What is the equation for acceleration?Acceleration is the rate of change of velocity with respect to time. Mathematically, acceleration is described by the equation a = Δv/Δt, where a is acceleration, Δv is the change in velocity, and Δt is the change in time. To calculate acceleration, we need to know the initial and final velocity and the amount of time that has elapsed between them. For instance, if a car's velocity changes from 10 m/s to 20 m/s in 5 s, the acceleration can be calculated as follows: a = (20 m/s − 10 m/s) / 5 s = 2 m/s2.The equation for acceleration can also be written as a = (vf − vi) / t, where vf is the final velocity, vi is the initial velocity, and t is the amount of time elapsed.Finally, acceleration can also be calculated by dividing the change in momentum by the mass of the object. In this case, the equation is a = Δp/m, where Δp is the change in momentum and m is the mass of the object.To learn more about acceleration refer to:
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TRUE/FALSE. waves are formed by the interrption of the crest of the wave as it slows down over the faster moving bottom of the wave.
False: Waves are generated when the wave's crest crashes into the bottom of the wave, which is travelling more quickly.
How do waves work?A wave is an energetic disturbance in such a medium that doesn't include any net particle motion. Elastic deformation, a change in pressure, a magnetic or electrical intensity, an electric potential, or a change in temperature are a few examples.
What do waves go by?Transverse and longitudinal waves are the two types of waves. While longitudinal waves are similar to those of sound, composed of alternating compressions & rarefactions in a medium, transverse waves were like those on water, having their surface moving up and down.
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The diagram shows part of a spring that is shaken from side to side to produce a wave.
0.60m
The distance between successive peaks is 0.60 m and the frequency is 2.5 Hz.
How long does it take for a wave to travel 3.0 m along the spring?
A 0.20 s
B 0.50s
C 2.0s
D 5.0 s
It takes 5.0 s for a wave to travel 3.0 m along the spring.
The time it takes for a wave to travel 3.0 m along the spring is 5.0 s. This can be calculated by dividing the distance (3.0 m) by the wave speed, which is equal to the frequency (2.5 Hz) multiplied by the distance between successive peaks (0.60 m).
3.0 m / (2.5 Hz x 0.60 m) = 5.0 s
What is frequency?
Frequency is a measure of the number of times a particular event or phenomenon occurs within a given period of time. It is usually expressed as an oscillations per second (Hertz). Frequency is an important measure in many fields, including physics, engineering, electronics, and music.
Therefore, It takes 5.0 s for a wave to travel 3.0 m along the spring.
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A feather and a rock dropped at the same time from the same height would land at the same time when dropped
In a vacuum, both the feather and the rock would fall at the same rate due to the absence of air resistance.
What is resistance?However, in the real world, air resistance can have a significant effect on the feather's descent.Air resistance acts as a drag force on the feather, slowing it down and causing it to fall at a slower rate than the rock.The rock, being denser and heavier, falls faster as it is less affected by air resistance.The difference in their descent is due to the size, shape, and weight of the feather and rock.The feather has a larger surface area relative to its weight, which makes it more susceptible to air resistance.The rock, on the other hand, has a smaller surface area relative to its weight and is less affected by air resistance.Therefore, if both the feather and the rock were dropped from the same height in an environment where air resistance is present, the rock would hit the ground first.However, if air resistance were not present, both would fall at the same rate and hit the ground at the same time.To conclude, the feather and the rock would fall at the same rate in a vacuum, but in the real world, air resistance affects the feather's descent, causing it to fall at a slower rate than the rock, making the rock hit the ground first.To learn more about resistance refer:
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a bead slides without friction around a loopthe-loop. the bead is released from a height of 23.8 m from the bottom of the loop-theloop which has a radius 8 m. the acceleration of gravity is 9.8 m/s 2 .
Now the force equation at point A is given as f (n)= 0.05N
What height must the bead be launched from in order for it to complete the loop, minimum height h?h < (1/2)R.This means that the ball must start at a height that is at least half a radius above the top of the loop, or 2.5 radii above the ground, in order to travel around the entire circle.
v = 12.45m/s
Part B)
F(n) = 0.05N
As we know that the point A lies on the top of the loop
so we will have by energy conservation
so the speed at point A is given as
mg (H-2R) = 1/2 mv ²
v = √2 g (H-2R)
V= 12.45 m/s
Now the force equation at point A is given as
F (n)= 0.05N
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using the definition of the scalar product, find the angle between the following vectors. (find the smallest nonnegative angle.
When calculating the scalar and vector products, the angle between the vectors is taken into account. The dot product and inner product are other names for the scalar product.
Describe a vector ?In physics, a vector is a quantity with both direction and magnitude. It is often represented by such an arrow whose length was proportional to the size of the number and whose orientation is identical to that of the quantity. In science, anything with also a path and a magnitude is referred to as a vector. They are typically represented by pointing lines, each length of which denotes the size of the vector.
Describe a scalar ?Scalar quantities can be described by their size or magnitude alone and do not require any other information. So, 10 cm, 50 seconds, and 7 litres.
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water as a resource unit review practice 1 of 91 of 9 itemspause question which of the following describes the relationship between population growth and the underground water supply?(1 point)
Increased population expansion directly increases the demand for resources like water. When the population's need for water exceeds the availability from sources on the surface, such as rivers and lakes underground water is tapped.
What connection is there between population and water?In example, population growth will reduce the amount of water per person accessible since increased per capita water usage brought on by development will raise water demand, placing stress on the local water supply.
What effects does population growth have on groundwater?Producing food Population growth results in increased water consumption as well as increased water requirements for food production. We will need to pump groundwater more quickly than it can be extracted in order to meet the demands for food production brought on by the rapid increase in population.
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The ' region shown below is the base of a solid. For this solid, each cross section perpendicular to the x-axis is an equilateral triangle Find the volume of this solid.
As per the problem statement the volume of the solid is (√3/4)*x^2.
What is volume?Volume is the measure of space occupied by an object or contained within a space. It is typically measured in cubic units, such as cubic centimeters, cubic meters, or cubic feet.
The region shown is the base of a solid with an equilateral triangle as each of its cross section perpendicular to the x-axis. Since the cross sections are equilateral triangles, the length of the sides of each triangle will be the same, which is the value of x.
Therefore, the volume of the solid can be calculated using the formula V = A*h, where A is the area of the base and h is the height of the solid.
The area of the base can be calculated using the formula A = (√3/4)*x^2, where x is the length of the sides of the equilateral triangle.
The height of the solid can be calculated using the formula h = y2-y1, where y1 and y2 are the y-coordinates of the two endpoints of the region.
Consequently, the solid's volume is determined by:
V = (√3/4)*x^2*(y2-y1)
For the given region, the volume of the solid is V = (√3/4)*x^2*(1 - 0) = (√3/4)*x^2
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A basketball player shoots from beyond the 3-point arc. The ball leaves the band with an initial velocity of 8m/s angled 52° from the horizontal. What are the horizontal and vertical velocities of the basketball?
The area of a telescope lens is 7903 mm2. If a technician takes 45 s to polish an area of 135 mm2, how long (in hours) does it take to polish the whole lens? Select all the statements that are correct and relevant to solving this problem. Check all that apply. The starting point for the calculation is 7903 mm2. The solution to the problem will have units of mm2/s. Thc probiem aumes thr the conversóon betven econds and hours s nwm The information contains the conversion factor 5 135 mm The solution to the problem is 0.016 h. Do you know the answer?
The statements that are correct and relevant to solving this problem are:
-The information contains the conversion factor 45s/135mm²
-The starting point for the calculation is 7903 mm².
-The problem assumes that the conversion between seconds and hours is known.
What does "simple computation" mean?Calculation is both a process and a movement. Calculation's ultimate result is also a consequence of calculated action.
The calculator is a machine which thus calculates the average numbers and displays the results on a screen. It has a numerical keypad.
starting point is 7903 mm²
whit will be
A sec, min or her. (Here hour)
hour.
Assumes that the conversion between second and
hour is known.
Conversion factor.4513545-X 7903 = 2634.33 sec135
or 2634.33
0.732 hour
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Complete question:
which of the following statements does not use the term angular size or angular distance correctly? view available hint(s)for part a which of the following statements does not use the term angular size or angular distance correctly? the angular distance between those two bright stars in the sky is about 2 meters. the angular size of the sun is about the same as that of the moon. the angular distance between those two houses in the distance is 30 degrees. you can use your outstretched hand against the sky to estimate angular sizes and angular distances.
There are two prominent stars in the sky that are spatially separated by about two meters.
Which constellation has two of the brightest stars in the universe?
Second brightest and the brightest star in the night sky is Sirius, which is in the constellation Canis Major. With an apparent magnitude of -1.46, Sirius, the second brightest star, can be seen from anywhere. The Canis Major constellation contains the bright star in question. It is the Alpha star of this constellation.
Which of the two shining stars is it in the sky?
The Sun is the brightest star that can be seen from Earth and has a magnitude of 26.74. Sirius comes in second with a magnitude of 1.46 mag.
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Repe
For a linearly decreasing force, the best way to find the area under the curve ques
is
rectangular approximation
take a wild guess
basic geometry
multiply the force times the distance
calculus
Increasing the separation distance between objects decreases the force of attraction or repulsion between the objects.
What is linearly decreasing force?
The electric lines of force start from a positive charge and ends on a negative charge.The electric lines of force always enter or leave the charged surface normally.Electric lines of force can never intersect each other.Every electric line of force starts with a positive charge and ends with a negative charge. The electric lines of force resist each other in the same direction but In opposite directions, electricity.On Earth all bodies have a weight, or downward force of gravity, proportional to their mass, which Earth's mass exerts on them. Gravity is measured by the acceleration that it gives to freely falling objects.To learn more about force refers to:
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A 3.0 kg object, initially moving to the right with a velocity of + 4.0 m/s experiences a positive net force that decreases linearly throughout the displacement as shown on the graph above. what is the kinetic energy of the object at the instant the net force is zero?
The kinetic energy of an object at a given instant is given by the formula KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.
In this scenario, the net force acting on the object decreases linearly throughout the displacement, as shown on the graph, and reaches zero at the end of the displacement. Therefore, the object's velocity at the instant the net force is zero is equal to its final velocity, which is the velocity of the object when it comes to rest.
Since the net force acting on the object is zero at this point, the work done by the net force is also zero. Therefore, the initial kinetic energy of the object is equal to its final kinetic energy, which is the kinetic energy of the object when it comes to rest.
Therefore, we can use the formula for kinetic energy to find the kinetic energy of the object at the instant the net force is zero:
KE = 1/2 * m * v^2
KE = 1/2 * (3.0 kg) * (0 m/s)^2
KE = 0 J
The kinetic energy of the object at the instant the net force is zero is 0 J. This means that the object has come to rest and all its kinetic energy has been transformed into other forms of energy like heat or sound.
A piece of aluminum with mass 1.00kg and density 2700kg/m 3
is suspended in air from a string and then completely immersed in a container of water. Calculate the tension in the string (a) before and (b) after the metal is immersed. Take, g=10m/s 2
, density of water =10 3
kgm −3
.
The tension in the string before the metal is immersed is 10 N. The tension in the string after the metal is immersed is 6.296 N.
What causes a string's tension?The forces tugging on the rope from either end cause a certain strand of string or rope to be under strain. Recall that force equals mass times acceleration. Any change in acceleration or mass of the objects the rope is supporting will result in a change in tension in the rope, assuming the rope is stretched firmly.
(a) The tension in the string before the metal is immersed,
Given,
Mass of place of aluminum (m) = 1.00 kg
density of aluminum (ρ_s) = 2700 kg/m^3
density of water (ρ_w) = 1000 kgm^-3
When the aluminum piece is suspended in air,
T = mg
T = 1 ×10
T = 10 N
(b) When the aluminum piece is completely immersed in water,
mg = T +F_B
Where, F_B = buoyant force acting on aluminum
T= tension in the string
T= mg − F_B
T = ρ_sV_s×g - ρ_LV_L×g
After simplifying we get,
T = mg (1 - ρ_L/ρ_s)
T = 1 × 10(1 - 1000/2700)
T = 10(1 - 10/27)
T = 6.296 N
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Which one of the following options gives the correct procedure to A. moles x molar mass B. molar mass /moles C. moles molar /mass
A is provided with the proper procedure by moles x molar mass. This same mass metric grams of one mole of an ingredient is its molar mass.
What is matter's mass?The proportion of substance in a thing is measured by its mass. That thing will be the same mass no matter where it is in the enormous universe. Contrarily, weight is a measurement that indicates how much gravitational potential energy is being applied to an object.
Is one mole of mass equal?A pure element's atomic mass in number of atoms (amu) or grams for every mole (g/mol) is proportional to the mass about one mole of its elements in grams. Despite the fact that mass can be stated as either amu or g/mol, g/mol.
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A hot rod of mass 2000 kg, starting from rest
reaches a speed of 120 m/s in only 24.8 s.
What is the average output power?
The power of the hot rod of mass 2000 kg is 580645.16 W.
What is power?Power is the rate at which work is done.
To caculate the power output of the hot rod, we use the formula below.
Formula:
P = mv²/2t.......................... Equation 1Where:
P = Power output of the hot rodm = Mass of the hot rod = 2000 kgv = Velocity of the hot rod = 120 m/st = Time = 24.8 sSubstitute these values into equation 1
P = (2000×120²)/(2×24.8)P = 580645.16 WHence, the power is 580645.16 W.
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A closed piston-cylinder system contains air (molecular weight M = 28.97 kg/kmol) at a temperature of 27'C and an absolute pressure of 100 kPa.
(a) Determine the specific volume of air, in m'/kg. Air in the cylinder is heated without changing its temperature until its volume doubles.
(b) Does the specific volume of air in the cylinder decrease, increase, or remain the same? Justify with quation(s).
c) Does the pressure of air in the cylinder decrease, increase, or remain the same? Justify with equation(s).
(a) The specific volume of air in the cylinder is heated without changing its temperature until its volume doubles is 0.861 m³/kg.
(b) Specific volume of air in the cylinder increases.
(c) The pressure of air in the cylinder decrease.
What is Specific volume?The amount of cubic metres that one kilogramme of matter takes up is known as the specific volume. It is the reciprocal of density and the ratio of a substance's volume to mass. In other words, specific volume is inversely related to density. Any state of matter may be measured or calculated for specific volume, but calculations involving gases are where it is most frequently applied.
Though it can also be expressed in terms of millilitres per gramme (mL/g) or cubic feet per pound (ft³/lb), the standard unit for specific volume is cubic metres per kilogramme (m³/kg).
(a) Specific volume =
[tex]$ \mathrm{ \hat V = \frac{V}{m} = \frac{RT}{P} }[/tex]
[tex]$ \mathrm{ =\frac{\overline RT}{mP} }[/tex]
[tex]$ \mathrm{ = \frac{8.314 \times 300}{28.97 \times 100} }[/tex]
[tex]$ \mathrm{ \hat V = 0.861 \ m^3/kg }[/tex]
(b) Mass will remain constant so on doubling the volume, specific volume will also be doubled i.e.
[tex]$ \mathrm{ \hat V_2 = 2\hat V_1 }[/tex]
Thus, specific volume increases.
(c) Since, T = constant
[tex]$ \mathrm{ P\hat V_1 = P\hat V_2}[/tex]
[tex]$ \mathrm{ \frac{P_2}{P_1} = \frac{\hat V_1 }{\hat V_2 } }[/tex]
[tex]$ \mathrm{ \frac{P_2}{P_1} = \frac{\hat V_1 }{2\hat V_1 } }[/tex]
[tex]$ \mathrm{ \frac{P_2}{P_1} = \frac{1 }{2 } }[/tex]
[tex]$ \mathrm{ P_2= \frac{1}{2} \times 100}[/tex]
[tex]$ \mathrm{ P_2=50}[/tex]
Thus pressure decrease in this case.
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Complete question:
Which vector goes from (4, 0) to (1, -3)?
A. a
B. c
C. b
D. d
Answer:
B. Vector c
Explanation:
You have to look for these two points (4,0) and (1,-3) on your graph (x, y) , and then you have to find which vector connects them together and that must be vector c
The electric potential V is given as a function of distance x (metre) by V=(5x 2−10x−9) volt. Value of electric field at x=1m is:
Value of electric field at x=1m is
electric field E= [tex]\frac{-dV}{dx} =[/tex] [tex]- \frac{-d(5x^{2} -10x - 9)}{dx}[/tex]
electric field E= -(10x-10)
electric field E= 0
An electric field is a physical phenomenon that surrounds electrically charged particles and exerts force on any other charged particles nearby, either attracting or repelling them. It can also refer to the physical field surrounding a system of charged particles.Electric charges and time-varying electric currents are the building blocks of electric fields. The electromagnetic field, one of the four fundamental interactions (also known as forces) of nature, manifests itself in both electric and magnetic fields.Electrical technology makes use of electric fields, which are significant in many branches of physics. For instance, in atomic physics and chemistry, the electric field acts as an attracting force to hold atoms' atomic nuclei and electrons together.
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A 500 g squirrel with a surface area of 895 cm2 falls from a 5.6-m tree to the ground. Estimate its terminal velocity. (Use the drag coefficient for a horizontal skydiver. Assume that the squirrel can be
approximated as a rectanglar prism with cross-sectional area of width 11.3 cm and length 22.6 cm. Note, the squirrel may not reach terminal velocity by the time it hits the ground. Give the squirrel's
terminal velocity, not it's velocity as it hits the ground.)
x m/s
What will be the velocity of a 50.0 kg person hitting the ground, assuming no drag contribution in such a short distance?
x m/s
8.3 m/s is the terminal velocity of the squirrel can be calculated using the equation for terminal velocity and 10.8 m/s is the velocity of a 50.0 kg person hitting the ground.
What is velocity?
Velocity is a measure of the speed of an object's motion in a particular direction. It is a vector quantity, meaning it has both magnitude and direction. Velocity is usually measured in meters per second (m/s).
The terminal velocity of the squirrel can be calculated using the equation for terminal velocity of an object in a fluid, which is given by Vt = (2×m×g)/(ρ×Cd×A). Here, m is the mass of the object, g is the acceleration due to gravity, ρ is the density of the fluid, Cd is the drag coefficient, and A is the reference area of the object. The drag coefficient for a horizontal skydiver is 0.8, and the density of air is 1.225 kg/m^3. Therefore, the terminal velocity of the squirrel can be calculated as Vt = (2×500×9.8)/(1.225×0.8×895) = 8.3 m/s.
The velocity of a 50.0 kg person hitting the ground can be calculated using the equation for the velocity at the end of a fall, which is given by Vf = sqrt(2×g×h). Here, g is the acceleration due to gravity and h is the height of the fall. Therefore, the velocity of the person hitting the ground can be calculated as Vf = sqrt(2×9.8×5.6) = 10.8 m/s.
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Which of the following equations correctly represent the conversions between the different units of temperature? Select all that apply. A. degrees Fahrenheit = ( 9/5 x degrees Celsius) + 32
B. Kelvin = degrees Celsius + 273.15
C. degrees Celsius= ( 5/9 x degrees Fahrenheit) -32
D. degrees Fahrenheit = ( Kelvin -273.15) x 5/9
These energy between the various temperature units are accurately represented by formulae in Degrees Celsius = (9/5 x Degrees Fahrenheit) + 32
How is 9 5 converted to a temperature?The Formula for Converting Temperature We employ the same conversion formulas found in the majority of textbooks. To convert temperatures from degrees Fahrenheit to degrees Celsius, multiply the result by.5556 (or 5/9) after subtracting 32. When converting from celsius to Degrees, multiply the result by 1.8 (about 9/5) then by 32.
How do you translate Class 9 in Fahrenheit from Celsius?The formula for converting degrees Celsius to degree Fahrenheit, which would be given by the equation F=95(C)+32, must be used in this situation. Therefore, we must divide the stated temperature by nine, multiply it.
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a bar rotates horizontally about its centre, reaching a maximum angular velicity in 6 complete raotaions from rest. the bar has a constant angular acceleratino of .110 radians
A bar rotates horizontally about its center, reaching a maximum angular velocity in 6 complete rotations from rest and has a constant angular acceleration of 0.110 radians.
What is angular acceleration?
The angular acceleration is the rate at which the angular velocity of an object is changing.
Therefore, since the angular acceleration of the bar is constant, this means that the angular velocity of the bar is increasing at a constant rate.
To find the angular velocity at any given time, we can use the equation: angular velocity = angular acceleration x time.
To find the final angular velocity, we can use the equation: final angular velocity = initial angular velocity + angular acceleration x time.
Therefore, the final angular velocity of the bar after 6 complete rotations is: 0 + 0.110 radians/s x (6 x 2π) = 6.832 radians/s.
To find the angle that the bar has rotated through, we can use the equation: angle = angular velocity x time
Therefore, the angle that the bar has rotated through after 6 complete rotations is: 6.832 radians/s x (6 x 2π) = 42.5 radians.
It's worth noting that angular velocity is a vector quantity, it's magnitude is given in radians/s and its direction is given by the right hand rule.
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Complete question is:
A bar rotates horizontally about its center, reaching a maximum angular velocity in 6 complete rotations from rest and has a constant angular acceleration of 0.110 radians. The movement of the interia of the bar about the raxis of the rotation is about 0.0216kgm^.
a. Show the final angular velocity of the bar is 3 radians.
b. Draw the variation with time t of the angular displacement 0 of the bar during the acceleration .
c. Calculate the torque acting on the bar while it is accelerating.
d. The torque is removed. The bar comes to rest in 30 complete rotations with constant angular deceleration. Determine the time taken for the bar to come to rest.
What is the minimum speed with which a meteor strikes the top of Earth’s stratosphere (about 40.0 km above the surface), assuming that the meteor begins as a bit of interplanetary debris far from Earth and stationary relative to Earth? Assume that the drag force is negligible until the meteor reaches the stratosphere. Mass of Earth is 5.974 × 1024 kg; radius of Earth is 6.371 × 106 m; and gravitational constant is 6.674 × 10−11 N·m2/kg2.
Answer: v = 11149.3 m/s
Explanation:
Assuming that the values in your question were supposed to have exponents.
v = minimum speed
r = distance from center of earth
= radius of earth + height above the surface
= (6.371 * 10^6 m) + (0.40 * 10^5 m)
= 6.411 x 10^6 m
M = mass of earth = 5.974 x 10^24 kg
m = mass of meteor
Using conservation of energy
GMm/r = (0.5) m v^2
GM/r = (0.5) v^2
(6.67 * 10^-11)(5.974 * 10^24)/(6.411 * 10^6) = (0.5) v^2
62153455 = (0.5)v^2
Divide both sides by 0.5
124306910 = v^2
Square root both sides
v = 11149.3 m/s
For a reaction for which the activation energies of forward and reverse reactions are equal:A.ΔH=0B.ΔS=0C.the order is zeroD.there is no catalyst
When the activation energies of the forward and backward processes are equal, the energy of the reactant and product becomes equal.
Therefore, E=EAEB=0. The reaction has reached equilibrium when the forward and reverse reaction rates are equal to one another. When the rate of the forward reaction equals the rate of the reverse reaction, a system is said to be in chemical equilibrium. The activation energy () of the reverse reaction is the SUM of the activation energy of the forward reaction AND the energy released from the forward reaction, according to the information provided.
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✓
Question 3:
A small cube of mass m₁ slides down a circular track of radius,
cut into a large block of mass m₂ = 2m₁ as shown in the figure
below. The large block rests on a table, and both blocks movė
without friction. The blocks are initially at rest, and m₁ starts
from the top of the path. Find the magnitude of velocity of the
cube as it leaves the block.
The velocity 'v' of the cube as it leaves the block would be, v=[tex]\sqrt{\frac{2gR}{1+m/M} }[/tex].
What is Conservation of mechanical energy?Conservation of mechanical energy is a principle that states that the total mechanical energy of a closed system remains constant as long as no energy is added or removed from the system. In this case, the system consists of the two blocks and the table on which they rest. Since there is no friction and no external force acting on the system, the total mechanical energy (potential energy + kinetic energy) remains constant as the cube slides down the track. This allows us to use the initial potential energy of the cube to calculate its final kinetic energy, and thus its velocity as it leaves the block.
The magnitude of velocity of the cube as it leaves the block can be found using Conservation of mechanical energy.
Initially, the cube is at rest at the top of the track and has only potential energy, given by m₁gh, where g is the acceleration due to gravity and h is the height of the track. As the cube slides down the track, it loses potential energy and gains kinetic energy.
we have
mu=mv−−(1)
wall=Δk
mgR = [tex]\frac{1}{2} mv^{2} + \frac{1}{2} mu^{2}[/tex]
mgR = [tex]\frac{1}{2} mvH_{2}[/tex] + [tex]\frac{1}{2} (\frac{mv}{M} ) ^{2}[/tex] × M
mgR= [tex]\frac{1}{2} mv^{2} + \frac{1}{2} \frac{m^{2} v^{2}}{M}[/tex]
So, v²=[tex]\frac{2gR}{1+m/M}[/tex]
So, v= [tex]\sqrt{\s{\frac{2gR}{1+m/M} }}[/tex].
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Dimensional / Projectile motion (mass has no effect)A 200g ball is thrown up at 25 m/s at 40 degrees.a. How high will it reach? (Hint Vfy=0 at peak)b. How much time will it take to reach peak heightc. How much time will it take to fall back to the ground?(Hint: symmetrical parabola)d. How far will it fall? (Dx=Vox* tair)
The ball of mass 200g reaches a height of 17.2m when it is thrown up at 25 m/s at 40 degrees, the time taken to reach peak height is 1.86s and the total time taken to fall back is 3.72s.
Given mass of the ball (m) = 200g
Initial speed of ball (u) = 25m/s
The angle at which ball is thrown = θ = 40 degrees
The horizontal velocity of ball = uxsinθ = 25 x sin 40 = 18.6m/s
The vertical velocity of ball = uycosθ = 25 x cos 40 = -16.6m/s
(a) Maximum height reached (h) = ux^2sin^2θ/2g where g is the gravitational acceleration.
Then h = (18.6)^2/2 x 10 = 17.2m
(b) The final velocity at maximum height (Vfy) = 0
We know that from Newtons laws of motion v = u + at then
Vy = uxsinθ + (-gt)
then t = uxsinθ/g = 18.6/10 = 1.86s
(c) The amount of time required for an upward and downward route is equal. So, total time taken by the ball to return to the ground = 1.86+1.86 = 3.72s.
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find a unit vector perpendicular and describe geometrically what th eocllection of all such vectors look like.
A unit vector perpendicular to a given vector is a vector of the same length but with a direction that is 90 degrees to the given vector. Geometrically, the collection of all such vectors forms a circle.
What is vector?
Vector is a mathematical object used to represent magnitude and direction. It is composed of a magnitude and a direction that can be represented in Euclidean space by an ordered pair of numbers. A vector can also be represented by a directed line segment to indicate the direction of the vector and its magnitude. Vectors can be used to represent many physical quantities such as velocity, force, acceleration, and electric and magnetic fields. Vectors are also used in calculus to represent derivatives of functions, enabling us to calculate the rate of change of the function.
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the star betelgeuse is about 600 light-years away. if it explodes tonight, the star betelgeuse is about 600 light-years away. if it explodes tonight, we'll know because it will be brighter than the full moon in the sky. we'll know because debris from the explosion will rain down on us from space. we won't know about it until about 600 years from now.
It is exactly because of the expanding cosmos that we can see objects that are up to 46.1 billion light-year away. The range of objects we can perceive and potentially reach will always be constrained.
Why can't we observe a galaxy that is 15 billion years old?
Answer and justification According to prevailing opinion, we can't see a galaxy 15 billion light-years away because the universe is thought to be less than 14 billion years old.
Why can we observe objects 13 billion light-years away?
Since light travels at a finite speed, if we witness an object 13 billion light years distant, the light has been moving in our direction for 13 billion years. In essence, we perceive that item as
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. learning over the first year of life, for example the emerging understanding of gravity and stability or the relationship between weight and size
Babies learn to concentrate their eyesight, stretch out, explore, and learn about the world around them during their first year. Cognitive development, often known as brain development, refers to the process of acquiring memory, language, thinking, and reasoning.
What is the significance of the first year of life?The period of infancy is critical for brain development. Children who do not have a healthy first attachment are less likely to grow up to be happy, independent, and resilient individuals.
One of the primary causes is the rapid growth of the brain beginning before birth and continuing throughout early life.
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Instantaneous power output of a 3-phase 60 Hz generator will not be constant under following condition:
A. The load draws only real power. B. The load is unbalanced. C. None of the other choices D. The load draws only reactive power. E. The load draws both real and reactive power.
Instantaneous power output of a 3-phase 60 Hz generator will not be constant under following condition when the load is balanced.
Instantaneous power output of a single phase 60 hz generator will be constant under reactive power.
Responsive power is otherwise called: ghost power. One more method for making sense of this is that responsive power is the resultant power in watts of an air conditioner circuit when the ongoing waveform is out of stage with the waveform of the voltage, normally by 90 degrees assuming the heap is simply receptive and is the consequence of either capacitive or inductive burdens. A model is fueling a brilliant light, in a responsive burden energy stream toward the heap a fraction of the time, though in the other half power streams from it, which gives the deception that the heap isn't dispersing or consuming power. Receptive power is one of the three kinds of force present in stacked circuits.
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in the town of centralburg (figure 1), which is laid out in a uniform block grid, the grocery store is three blocks east and four blocks north of the post office. which of the following is a correct equation for the quantities represented in this scenario?
A correct equation for the quantities represented in this scenario is
tan Θ=[tex]\frac{d_{n} }{d_{e} }[/tex].
Now, according to the question,
tanΘ=[tex]\frac{opp.\: side}{adj.\: side}[/tex]
Now, by the figure mention,
The side opposite to the angle Θ is [tex]d_{n}[/tex] and the adjacent sides is [tex]d_{e}[/tex].
The three primary trigonometric functions—Sine, Cosine, and Tangent—are based on a right-angled triangle.
Triangle with the opposite side, adjacent side, and hypotenuse can be declared by:
The terms "opposite" and "adjacent" refer to the angle's opposing and adjacent, respectively.
The long one is "Hypotenuse."
Now, put these values in the formula,
which gives the equation,
tanΘ=[tex]\frac{d_{n} }{d_{e} }[/tex]
Now, from the options given it is clearly seen that option-1 is correct.
Question: in the town of centralburg (figure 1), which is laid out in a uniform block grid, the grocery store is three blocks east and four blocks north of the post office. which of the following is a correct equation for the quantities represented in this scenario
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