Stokes’ law describes sedimentation of particles in liquids and can be used to measure viscosity. Particles in liquids achieve terminal velocity quickly. One can measure the time it takes for a particle to fall a certain distance and then use Stokes’ law to calculate the viscosity of the liquid. Suppose a steel ball bearing (density 7.8 \times 10^3~\text{kg/m}^37.8×10 3 kg/m 3 and diameter 3.0~\text{mm}3.0 mm) is dropped in a container of motor oil. It takes 12 s to fall a distance of 0.60 m. Calculate the viscosity of the oil.
Answers
Answer:
The viscosity is \(\eta = 0.76243 \ kg/ m \cdot s \)
Explanation:
From the question we are told that
The density is \(\rho = 7.80 *10^{3} \ kg/m^3\)
The diameter is \(d = 3.0 \ mm =0.003 \ m\)
The time taken is \(t = 12 \ s\)
The distance covered is \(d = 0.60 \ m\)
Generally the velocity of the ball is
\(v = \frac{d}{t}\)
=> \(v = \frac{0.60}{12}\)
=> \(v = 0.05 \ m/s \)
Generally the mass of the steel ball is
\(m = \rho * V\)
Here V is the volume and this is mathematically represented as
\(V = \frac{4}{3} * \pi * [\frac{d}{2} ]^3\)
=> \(V = \frac{4}{3} * 3.142 * [\frac{0.003}{2} ]^3\)
=> \(V = 1.414 *10^{-8} \ m^3\)
So
\(m = 7.80 *10^{3} * 1.414 *10^{-8}\)
\(m = 0.00011 \ kg \)
Generally the viscosity is mathematically represented as
\(\eta = \frac{m * g}{6\pi * r * v }\)
Here r is the radius represented as
\(r = \frac{d}{2}\)
=> \(r = \frac{0.003}{2}\)
\(r = 0.0015 \ m \)
So
\(\eta = \frac{0.00011 * 9.8}{6 * 3.142 * 0.0015 * 0.05 }\)
=> \(\eta = 0.76243 \ kg/ m \cdot s \)
Related Questions
A car travels from point A to B in 3 hours and returns back to point A in 5 hours. Points A and B are 150 miles apart along a straight highway. Calculate: a) Total distance and total displacement (in mile and meter) b) Average speed and Average velocity (in mile/hr and m/s
Answers
The total distance covered by the car is 300 miles.
The total displacement covered by the car is zero.
The average speed of the car is 17.88 m/s.
The average velocity of the car is also zero.
Distance between the points A and B, d = 150 miles
Time taken by the car to travel from A to B, t₁ = 3 hours
Time taken by the car to travel from B to A, t₂ = 5 hours
a) Given that the car travelled from A to B and then back to A.
Therefore, the total distance covered by the car is,
Distance = 2 x d
Distance = 2 x 150
Distance = 300 miles
Since the car is travelling from A to B and then returning back to the initial point A, the total displacement covered by the car is zero.
b) The speed with which the car travelled from A to B is,
v₁ = d/t₁
v₁ = 150/3
v₁ = 50 miles/hr
v₁ = 22.35 m/s
The speed with which the car travelled from B to A is,
v₂ = d/t₂
v₂ = 150/5
v₂ = 30 miles/hr
v₂ = 13.41 m/s
Therefore, the average speed of the car is,
v = (v₁ + v₂)/2
v = (22.35 + 13.41)/2
v = 17.88 m/s
As, the total displacement of the car is zero, the average velocity of the car is also zero.
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A sample of gas in a cylinder is compressed by a piston at a constant pressure of 0.800 atm. The volume of the cylinder decreases from 8.50 L to 2.00 L, while at the same time 320 J of energy leaves the gas by heat.
(a)
What is the work done on the gas (in J)?
Answers
The work done on the gas 526.89 Joule.
What is work done?The amount of force multiplied by the distance the thing travelled in the direction of the applied force is how much work is done on an object.
Work is equal to force times distance.
Given parameters:
Constant pressure of the gas: p = 0.800 atm.
Initial volume of the cylinder: V₁ = 8.50 L.
Final volume of the cylinder: V₂ = 2.00 L.
Energy leaves the gas by heat: E = 320 J.
So, the work done by the gas (W) = pΔV = p(V₂ - V₁)
= 0.800(2.00 - 8.50) atm-lit
= - 5.2 atm-lit
= - 5.2×101.325 Joule
= - 526.89 Joule.
Hence, The work done on the gas 526.89 Joule.
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When light travels from air into water, how are its velocity, frequency, and wavelength affected?
A. it’s velocity changes, but it’s frequency and wavelength do not change.
B. it’s velocity, wavelength, and frequency all change.
C. it’s frequency changes, but it’s velocity and wavelength do not change.
D. it’s wavelength changes, but it’s velocity and frequency do not change.
W. it’s velocity and wavelength change, but it’s frequency does not change.
Answers
Answer:
E
Explanation:
It's velocity and wavelength change, but its frequency does not
when 82.5 calories of heat are given to a metallic rod of mass 150g its temperature raises from 20 degree celcius to 25 degree Celsius. what is the specific heat of the metal.
Answers
A 150-g metallic rod with a specific heat of 0.11 cal/g.°C absorbs 82.5 calories of heat and its temperature increases from 20 °C to 25 °C.
What is specific heat?It is the heat required to raise the temperature of the unit mass of a given substance by a given amount (usually one degree).
A metallic rod of mass 150 g (m) absorbs 82.5 cal of heat (Q) and its temperature raises from 20 °C to 25 °C. We can calculate the specific heat (c) of the metal using the following expression.
Q = c × m × ΔT
c = Q / m × ΔT
c = 82.5 cal / 150 g × (25 °C - 20 °C) = 0.11 cal/g.°C
A 150-g metallic rod with a specific heat of 0.11 cal/g.°C absorbs 82.5 calories of heat and its temperature increases from 20 °C to 25 °C.
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An aeroplane is circling above an airport in a horizontal circle at a speed of 400 kmh-1.The banking angle of the wings is 20.What is the radius of the circular path?
Answers
Answer: the radius of the circular path is approximately 1637.58 meters.
Explanation:
The centripetal force acting on the airplane is provided by the component of the gravitational force that acts towards the center of the circular path. This component is given by:
F_c = m * g * tan(banking angle)
Where:
F_c is the centripetal force
m is the mass of the airplane
g is the acceleration due to gravity
tan(banking angle) is the tangent of the banking angle
Now, the centripetal force is also given by the formula:
F_c = (m * v^2) / r
Where:
v is the speed of the airplane
r is the radius of the circular path
Equating the two expressions for F_c, we get:
(m * g * tan(banking angle)) = (m * v^2) / r
Canceling out the mass (m) on both sides of the equation, we have:
g * tan(banking angle) = v^2 / r
Solving for r, we get:
r = (v^2) / (g * tan(banking angle))
Substituting the given values:
v = 400 km/h = 400,000 m/h
g = 9.8 m/s^2
banking angle = 20°
Converting the speed to m/s:
v = 400,000 m/h * (1/3600) h/s = 111.11 m/s
Converting the banking angle to radians:
banking angle = 20° * (π/180) rad/° = 0.3491 rad
Now, substituting the values into the formula:
r = (111.11^2) / (9.8 * tan(0.3491))
r ≈ 1637.58 meters
Therefore, the radius of the circular path is approximately 1637.58 meters.
PLS HELP
A marble rolls off a table with a horizontal velocity of 8 m/s and the cliff has a height of
2.71 m. How far does the marble land from the base of the table? Round your answer to
two decimal places.
Answers
Two blocks, 1 and 2, are connected by a massless string that passes over a massless pulley. 1 has a mass of 2.25 kg and is on an incline of angle 1=42.5∘ that has a coefficient of kinetic friction 1=0.205. 2 has a mass of 5.55 kg and is on an incline of angle 2=33.5∘ that has a coefficient of kinetic friction 2=0.105
. The figure illustrates the configuration.
A system of two blocks connected by a rope passing over a pulley. The system sits atop a scalene triangle whose long edge forms the base. The pulley is attached to the apex of the triangle. Box M subscript 1 rests on the triangle edge to the left of the pulley, which makes an angle of theta subscript 1 with the base of the triangle. The coefficient of friction between box M sub 1 and the surface is mu subscript 1. Box M subscript 2 rests on the triangle edge to the right of the pulley, which makes an angle of theta subscript 2 with the base of the triangle. The coefficient of friction between box M sub 2 and the surface is mu subscript 2.
Answers
The force acting on the system of two blocks connected by a rope passing over a pulley is -13.26 N.
The system of two blocks connected by a rope passing over a pulley are M1 and M2, where M1 rests on the triangle edge to the left of the pulley, which makes an angle of theta subscript 1 with the base of the triangle. The coefficient of friction between box M1 and the surface is mu subscript 1. M2 rests on the triangle edge to the right of the pulley, which makes an angle of theta subscript 2 with the base of the triangle.
The coefficient of friction between box M2 and the surface is mu subscript 2. The system sits atop a scalene triangle whose long edge forms the base. The pulley is attached to the apex of the triangle.M1 has a mass of 2.25 kg and is on an incline of angle 1=42.5∘ that has a coefficient of kinetic friction 1=0.205. M2 has a mass of 5.55 kg and is on an incline of angle 2=33.5∘ that has a coefficient of kinetic friction 2=0.105.The free-body diagram of M1 shows that the weight of M1 acts straight downwards (vertically) and the normal force acts perpendicular to the slope.
The force of friction opposes the motion and acts opposite to the direction of motion.M1 = 2.25 kgTheta subscript 1 = 42.5 degreesMu subscript 1 = 0.205g = 9.81 m/s²In the free-body diagram of M2, the normal force acts perpendicular to the incline of the slope, the weight of the object acts vertically downwards and parallel to the incline, and the force of friction opposes the motion and acts opposite to the direction of motion.M2 = 5.55 kgTheta subscript 2 = 33.5 degreesMu subscript 2 = 0.105g = 9.81 m/s²The tension in the string is the same throughout the rope. Since the masses are being pulled by the same rope, the acceleration of the objects is the same as the acceleration of the rope.
The tension in the string is directly proportional to the acceleration of the objects and the rope.A system of two blocks connected by a rope passing over a pulley has a total mass of M. The acceleration of the system is given by the formula below:a = [(m1-m2)gsin(θ1) - μ1(m1+m2)gcos(θ1)] / (m1 + m2)Where, μ1 = 0.205 is the coefficient of friction of block M1θ1 = 42.5 degrees is the angle of the incline of block M1M1 = 2.25 kg is the mass of block M1M2 = 5.55 kg is the mass of block M2g = 9.81 m/s² is the acceleration due to gravitysinθ1 = sin 42.5 = 0.67cosθ1 = cos 42.5 = 0.75The acceleration of the system is:a = [(2.25-5.55)(9.81)(0.67) - (0.205)(2.25+5.55)(9.81)(0.75)] / (2.25 + 5.55)a = -1.7 m/s² (the negative sign indicates that the system is accelerating in the opposite direction).
The force acting on the system is given by:F = MaWhere M is the total mass of the system and a is the acceleration of the system. The total mass of the system is:M = m1 + m2M = 2.25 + 5.55M = 7.8 kgThe force acting on the system is:F = 7.8(-1.7)F = -13.26 N (the negative sign indicates that the force is acting in the opposite direction).
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What is the significance of the discovery of exoplanets?
a. they may possibly be inhabited or harbor life.
b. they can provide natural resources for the future.
c. they help our understanding of the formation of planetary bodies.
d. they help calibrate gps satellites.
e. they help understand the nature of the expansion of the universe.
Answers
Answer:
C. the help our understanding of the formation of planetary bodies.
Explanation:
this is the answer of PLATO
A boat on a river is moving with a steady speed. The engine is running.
What would happen if the engine was turned off?
Answers
If the engine of a boat on a river is turned off while the boat is moving with a steady speed, several things would happen Loss of propulsion,Drifting,Loss of steering control and Potential hazards.
Loss of propulsion: Without the engine running, the boat would lose its power source for propulsion. The boat would gradually slow down and eventually come to a stop unless other external forces, such as currents or wind, continue to move it.
Drifting: Once the boat comes to a stop, it would start to drift with the current of the river or be affected by wind forces. The direction and speed of the drift would depend on the strength and direction of the current or wind.
Loss of steering control: When the engine is turned off, the boat's steering mechanism, such as a rudder, would also lose power. Without the ability to steer, the boat would follow the course determined by the river's current or the wind direction.
Potential hazards: Depending on the surroundings and the current conditions, there could be potential hazards for a boat that is no longer under power. These hazards might include other vessels, obstacles, shallow areas, or strong currents. The boat's crew would need to take appropriate actions to ensure the safety of the boat and its occupants.
It's important to note that the specific behavior of the boat after the engine is turned off can vary depending on factors such as the size and design of the boat, the strength and direction of the current, and the presence of wind or other external forces.
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An object floats with half its volume beneath the surface of the water. The volume of the object is 3.5 m. What is the weight of the object? The density of water is 1000 kg/m3
Answers
Answer:
Since the object is floating, the buoyant force equals the weight of the water displaced:
W = d g v where d is the density of water and v = V/2 where v is the volume of the water displaced and v = V/2 where V is the volume of the object.
W = 1000 kg/m^3 * 9.8 m/s^2 * (3.5 /2 m^3)
W = 17150 kg m / s^2 = 17150 N
When an object floats with half its volume beneath the surface of the water. If the volume of the object is 3.5 m,then the weight of the object would be 17167.5 N if the density of water is 1000 kg/m3
What is density?It can be defined as the mass of any object or body per unit volume of the particular object or body. Generally, it is expressed as in gram per cm³ or kilogram per meter³.
The density is the reciprocal of the specific volume of any substance.
The mathematical formula for density is given below
ρ =m /V
where ρ is the density of the substance
m is the mass of the substance
V is the volume of the substance
As given in the problem an object floats with half its volume beneath the surface of the water. The volume of the object is 3.5 m
The density of water is 1000 kg/m3
According to the Archimedes principle, the buoyancy force acting on the floating object is equal to the weight of the fluid displaced by it
W = ρ g V
Given the object floats with half its volume beneath the surface of the water means the volume of the water displaced is half of the volume of the object
V=3.5/2 m³
W = 1000×9.81×3.5/2
= 17167.5 N
Thus, the weight of the object is 17167.5 N
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The half-life of cesium-137 is 30 years. Suppose that we start with 60 grams of cesium-137 in a storage pool.
How many half-lives will it take for there to be 10 grams of cesium-137 in the storage pool? (Round answer to two decimal places.)
How many years is that? (Round answer to one decimal place.)
Answers
9514 1404 393
Answer:
2.58 half-lives77.5 yearsExplanation:
The remaining amount, in terms of t half-lives, is ...
q(t) = 60·(1/2)^t
We want t when q(t) = 10, so ...
10 = 60·(1/2)^t
1/6 = (1/2)^t . . . . . . divide by 60
log(1/6) = t·log(1/2) . . . . take logs
t = log(1/6)/log(1/2) = -0.778151/-0.30103 ≈ 2.58496
It will take about 2.58 half-lives for there to be 10 grams remaining.
In years, that is 2.58×30 = 77.5 years.
A block on the end of a spring is pulled to position x = A and released. In one full cycle of its motion, through what total distance does it travel? A. A / 2 B. A C24 ) 0.4A
Answers
The total distance traveled by the block in a one full or complete cycle is 2A.
option C.
What is the total distance travelled by the block?If a block on the end of a spring is pulled to position x = A and released. In one full cycle of its motion, it will travel the following distance as shown below;
x = A cos (ωt)
where;
A is the amplitude of the motionω is the angle speed of the block = 2πft is the period of the motionDuring a half cycle the block will travel a total distance of A.
During another half cycle the block will travel a total distance of A.
The total distance traveled by the block in a one full or complete cycle is calculated as follows;
distance = A + A
distance = 2A
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If a human were to produce tears in space, what of the following would happen?
A) The tears would freeze, braking off for the face and floating away
B) The tears would stick to said face, never moving from below the eyes
C) The tears would sing Never Gonna Give You Up
D) The tears would immediately decompose, leaving nothing but a grainy dust
*This is a serious question for a quiz, and if a mod needs me to take off the Rick mention WHICH IS ON THE QUIZ, then I’d be happy to
Answers
Answer:
The tears would stick to said face,never moving
from below the eyes
Explanation:
This would happen because of newtons 1st law.A object remains in its moment of motion or rest until or unless any external force is applied.
There is no gravity in space .So nothing will pull tears down.No force would have been applied.Hence tears will remain sticked to face .
a surfer talks about riding a 20-foot wave. Which measurement of waves is the surfer describing?
frequency
amplitude
wavelength
speed
60 POINTS!!
Answers
Answer:
C. Amplitude
Explanation: Amplitude is the maximum displacement from the equilibrium of a wave. Basically the height.
An open 1-m-diameter tank contains water at a depth of 0.5 m when at rest. As the tank is rotated about its vertical axis the center of the fluid surface is depressed. At what angular velocity will the bottom of the tank first be exposed
Answers
Answer:
Angular velocity (w) = 8.86 rad/s
Explanation:
Angular velocity (w) = \(\sqrt{} 4ghi/R^{2}\)
g= 9.81 m/s
R= 0.5
hi (initial depth) = 0.5m
Hence= \(\sqrt4* 9.81* 0.5/0.5^{2}\) = 8.86 rad/s
Research help further the biological perspective when they demonstrated that electrical
Answers
Research helps further the biological perspective when they demonstrated that electrical activity in the brain can predict an individual's behaviour.
What is behaviour?Behaviour is the way in which an individual or group acts and reacts to events, people, and their environment. It is the actions of an individual or group and the reactions they cause in others. Behaviour can be conscious or unconscious, voluntary or involuntary, and is often defined in terms of being either adaptive or maladaptive.
This concept, known as neuropsychology, provides evidence that behavior is largely determined by biological processes and can help explain the complex relationships between the brain and behavior. Neuropsychological research has allowed scientists to better understand the neural basis of behavior, allowing a more.
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A flat sheet of paper of area 0.450 m2 is oriented so that the normal to the sheet is at an angle of 600 to a uniform electric field of magnitude 18 N C-1. What is the magnitude of the electric flux through the sheet? A. 3.22 N m2 C-1 B. 21.42 N m2 C-1 C. 5.04 N m2 C-1 D. 11.72 N m2 C-1 E. 4.05 N m2 C
Answers
The magnitude of the electric flux through the sheet is 4.05 N m² C⁻¹ (Option E).
The electric flux through a surface is given by the product of the electric field strength and the area of the surface projected perpendicular to the electric field.
In this case, the electric field strength is 18 N C⁻¹, and the area of the sheet projected perpendicular to the electric field is 0.450 m²
(since the normal to the sheet makes an angle of 60° with the electric field). Multiplying these values gives the electric flux:
Electric flux = Electric field strength × Area
Electric flux = 18 N C⁻¹ × 0.450 m²
Electric flux = 8.1 N m² C⁻¹
In summary, the magnitude of the electric flux through the sheet is 4.05 N m² C⁻¹. This value is obtained by multiplying the given electric field strength by the projected area of the sheet perpendicular to the electric field.
The angle of 60° is taken into account to determine the effective area for calculating the flux.(Option E).
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causes and effect of different types of power
Answers
Answer:
The Earth's magnetic field is generated in the fluid outer core by a self-exciting dynamo process. Electrical currents flowing in the slowly moving molten iron generate the magnetic field.
Explanation:
\(hii\)
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Which items in this image are electrically conductive?
Check all that apply
the power lines themselves
the wooden pole that supports the lines
the rubber soles on the worker's boots
the metal tools the worker uses
the wooden ladder leaning against the lines
Answers
all except the rubber boots.
The answers should be The power lines themselves and The metal tools the worker uses (the 1st and 4th choices).
(For anyone curious, the image I attached to this answer is the image given for this problem.)
Which of the following is one way creativity can help scientists? (20 points) +Brainiest
a
By ensuring they follow the scientific method
b
By increasing the amount of time it takes to complete scientific experiments
c
By making sure they only try things that have already been proven
d
By leading them to ask more questions about the natural world
Answers
In an electromagnet, why must the wire be connected to the battery for the magnet to work?
Answers
Answer:
Some of the copper wire needs to be exposed so that the battery can make a good electrical connection. ... You need to do this because the direction of a magnet field depends on the direction of the electric current creating it. The movement of electric charges creates a magnetic field.
Explanation:
In an electromagnet, it must the wire be connected to the battery for the magnet to work the current is flowing through into the wire once it is introduced.
What is a magnetic field?The magnetic field is defined as the field the magnetic materials generate or when an electric charge moves in a field region that generates the magnetic field.
As we know, the electricity is often used to generate a magnetic field in electromagnets.
The current is flowing through into the wire once it is introduced, from either a battery or maybe another source of electricity. The looped wire is magnetized as if it were a magnetic material as a function of the magnetic field created around it.
Thus, in an electromagnet, it must the wire be connected to the battery for the magnet to work the current is flowing through into the wire once it is introduced.
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2. Explain brightness of light using the wave model of light
Answers
The brightness of light is explained by the wave model of light. Brightness refers to the perceived intensity of light. Brightness is determined by the amplitude or intensity of light waves.
The larger the amplitude, the brighter the light. This can be explained using the wave model of light.Light is a form of electromagnetic radiation that is composed of oscillating electric and magnetic fields. The wave model of light states that light is a transverse wave that propagates through space. The wave model of light states that light travels in straight lines and can be reflected, refracted, and diffracted. Brightness is a measure of the intensity of light waves.
The intensity of light waves is determined by the amplitude of the wave.The amplitude of a wave is the maximum displacement of the wave from its equilibrium position. The larger the amplitude of a wave, the more energy the wave carries. This means that the larger the amplitude of light waves, the brighter the light. The brightness of light can be increased by increasing the amplitude of light waves. This can be achieved by increasing the intensity of light waves. The intensity of light waves can be increased by increasing the power of the light source. Thus, brightness can be explained by the wave model of light as it is determined by the amplitude or intensity of light waves.
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Delta waves occur during
Select one:
O a. awake relaxation.
O b. Stage 1 sleep.
O c. Stages sleep.
O d. wakefulness.
Answers
Imagine a spaceship traveling at a constant speed through outer space. The length of the ship, as measured by a passenger aboard the ship, is 28.2 m. An observer on Earth, however, sees the ship as contracted by 16.1 cm along the direction of motion. What is the speed of the spaceship with respect to the Earth
Answers
\(3.20×10^7\:\text{m/s}\)
Explanation:
Let
\(L = 28.2\:\text{m}\)
\(L' = 28.2\:\text{m} - 0.161\:\text{m} = 28.039\:\text{m}\)
The Lorentz length contraction formula is given by
\(L' = L\sqrt {1 - \left(\dfrac{v^2}{c^2}\right)}\)
where L is the length measured by the moving observer and L' is the length measured by the stationary Earth-based observer. We can rewrite the above equation as
\(\sqrt {1 - \left(\dfrac{v^2}{c^2}\right)} = \dfrac{L'}{L}\)
Taking the square of the equation, we get
\(1 - \left(\dfrac{v^2}{c^2}\right) = \left(\dfrac{L'}{L}\right)^2\)
or
\(1 - \left(\dfrac{L'}{L}\right)^2 = \left(\dfrac{v}{c}\right)^2\)
Solving for v, we get
\(v = c\sqrt{1 - \left(\dfrac{L'}{L}\right)^2}\)
\(\:\:\:\:=(3×10^8\:\text{m/s})\sqrt{1 - \left(\dfrac{28.039\:\text{m}}{28.2\:\text{m}}\right)^2}\)
\(\:\:\:\:=3.20×10^7\:\text{m/s} = 0.107c\)
You move to Mars and as a momento from Earth take your Ma-maw's mercury barometer. You place it outside in the Martian atmosphere and read a very low pressure. Does the pressure reading accurately reflect the atmospheric on the surface of Mars
Answers
Answer:
Explanation:
No, the reading is not expected to be accurate. This is because Relative to Earth, the air on Mars is extremely thin. The Martian atmosphere is primarily carbon dioxide with a much lower surface pressure, and Mars does not have oceans and an Earthlike hydrological cycle so latent heat release is not as important as it is for Earth.
ASAP Even though the force exerted on each object in a collision is the same strength, if the objects have different masses, their will be different. * O changes in velocity O amount of force O speed and direction
Answers
Answer:
it should be changes in velocity
Explanation:
I hope this helps!
What energy is always conserved
Answers
Answer:
Renewable Energy took a test on this not to long ago!
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The principle of cross-cutting relationships states that certain features, such as faults, are than the rock layers they cut through. These features are breaks in Earth’s surface where rock has moved sideways, upward, or downward. formations are made of molten rock that has cooled. Those on Earth’s surface are called . Those beneath Earth’s surface are called .
Answers
a. When the electric field between the plates is 75% of the dielectric strength and energy density of the stored energy is 2800 J/m3, what is the value of the dielectric constant k?
Answers
Answer: The value of the dielectric constant k = 1.8
Explanation:
If C= ε A/d and
Electrostatic energy W = 1/2CV^2
Substitutes C in the first formula into the energy formula.
W = 1/2 ε A/d × V^2
Let us remember that electric field strength E is the ratio of potential V to the distance d. Where V = Ed
Substitute V = Ed into the energy W.
W = 1/2 × ε A/d ×( Ed )^2
W = 1/2 × ε A/d × E^2 × d^2
d will cancel one of the ds
W = 1/2 × ε Ad × E^2
W/Ad = 1/2 × ε × E^2
W/V = 1/2 × ε E^2
Where Ad = volume V
E = dielectric strength
εo = permittivity of free space = 8.84 x 10^-12 F/m
W/V = 2800 J/m^3
Let first calculate the dielectric strength
2800 = 1/2 × 8.84×10^-12 × E^2
5600 = 8.84×10^-12E^2
E^2 = 5600/8.84×10^-12
E = sqrt( 6.3 × 10^14)
E = 25 × 10^7
75% of E = 18.9 × 10^6Jm
The permittivity of the material will be achieved by using the same formula
2800 = 1/2 × ε E^2
2800 = 0.5 × ε × (18.9×10^6)^2
2800 = ε × 1.78 × 10^14
ε = 2800/1.78×10^14
ε = 1.57 × 10^-11
Dielectric constant k = relative permittivity
Relative permittivity is the ratio of the permittivity of the material to the permittivity of the vacuum in a free space. That is
k = 1.57×10^-11/8.84×10^-12
k = 1.776
k = 1.8 approximately
Therefore, the value of the dielectric constant k is 1.8
What force is required to stop a 1600-kg car in a distance of 0.20 m if it is initially moving at 2.2 m/s? What if the car is moving at 4.5 m/s?
Answers
The force required to stop the car of mass 1600 kg is 19360 N.
If the car is moving at 4.5 m/s the force required is 81000 N.
What is force?Force is the product of mass and acceleration.
To calculate the force that will stop the car, we use the formula below.
Formula:
F = m(v²)/2s............................... Equation 1Where:
F = Forcem = Massv =Velocitys = DistanceFrom the question,
Given:
m = 1600 kgv = 2.2 m/ss = 0.2 mSubstitute these values into equation 1
F = 1600(2.2²)/(2×0.2)F = 19360 NIf the car is moving at 4.5 m/s,
F = 1600(4.5²)/(2×0.2)F = 81000 NHence, the force required to stop the car is 19360 N or 81000 N.
Learn morr about force here: https://brainly.com/question/25239010
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