Answer:
Part 1
The vector can be expressed as follows;
r = 12, θ = 72°, ·v = (12, ∠72°), ·v ≈ 3.71·\(\mathbf{\hat i}\) + 11.41·\(\mathbf{\hat j}\) or
\(\mathbf{\cdot v}=\begin{bmatrix}3.71\\ 11.41\end{bmatrix} = \begin{pmatrix}3.71\\ 11.41 \end{pmatrix}\)
Part 2
The angle of the vector is 56.31°
Explanation:
Part 1
The given parameters are;
The direction of the vector = 72°
The vector magnitude = 12
Therefore, the vector can be described in the following forms;
Polar form
1) Direct notation;
r = 12, θ = 72°
2) Ordered set
·v = (12, ∠72°)
Rectangular vector notation;
1) Unit vector notation
·v = vₓ\(\mathbf{\hat i}\) + \(v_y\)\(\mathbf{\hat j}\)
Where;
vₓ = 12 × cos(72) ≈ 3.71
\(v_y\) = 12 × sin(72) ≈ 11.41
Therefore;
·v ≈ 3.71·\(\mathbf{\hat i}\) + 11.41·\(\mathbf{\hat j}\)
2) Matrix notation
\(\mathbf{\cdot v}=\begin{bmatrix}3.71\\ 11.41\end{bmatrix} = \begin{pmatrix}3.71\\ 11.41 \end{pmatrix}\)
Part 2
The given vector is V = 2·x + 3·y
Therefore, the angle of the vector, θ = tan⁻¹(y/x) = tan⁻¹(3/2) ≈ 56.31°
The angle of the vector = 56.31°.
Melissa was putting on her makeup when she accidentally ran into a stopped car at a red light, 11. 01 m in front of her. Melissa's 1,219 kg car was moving at 8. 133 m/s and came to a complete stop in 0. 3994 seconds. What is the magnitude of the force that stopped Melissa's car?
a
2. 970E4 N
b
1. 535E4 N
c
1. 934E4 N
d
4. 550E4 N
e
4. 295E4 N
f
3. 400E4 N
g
3. 821E4 N
h
2. 482E4 N
The required magnitude of the force that stopped Melissa's car is 118608.7 N.
What are 1st 2nd and 3rd laws of motion?According to the first law, unless a force acts on an object, it will not alter its motion. According to the second law, an object's force is determined by multiplying its mass by its acceleration. According to the third law, when two objects interact, they exert equal-sized and opposite-direction forces upon one another.
According to question:An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line unless acted on by an unbalanced force.
Given,
speed=8.133 m/s
final velocity=0 (due to impact)
time=0.3994 seconds
distance=11.01m
Then,
S = ut + (at^2)/2
a = 2(s - ut)t^2
a = 97.3 m/s^2
So,
Force = ma
Force = 1219(97.3)
Force = 118608.7 N
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Choose all correct statements: Refractive index of medium A with respect to medium B is 4/3 and refractive index of medium A with respect to medium C is 3/2. Medium B is denser than medium C When light travels from B to C light bends away from the normal Refractive index of C with respect to B is 8/9 Ratio of speed of light in medium B to the speed of light in medium A = 4/3
Answer:
Medium B is denser than medium C
When light travels from B to C light bends away from the normal .
Refractive index of C with respect to B is 8/9
Ratio of speed of light in medium B to the speed of light in medium A = 4/3
Explanation:
Refractive index of medium A / Refractive index of medium B = 4/3
Refractive index of medium A / Refractive index of medium C = 3/2
Dividing ,
Refractive index of medium B / Refractive index of medium C
= 3/2 x 3/4
= 9 / 8
Refractive index of medium B > Refractive index of medium C
Refractive index of C with respect to B is 8/9
speed of light in medium B / the speed of light in medium A
= refractive index of A / refractive index of B = 4 / 3
2x+4y
GCF for the polynomial
Answer:
\(\boxed{2}\)
Explanation:
The GCF is the greatest common factor of the polynomial.
\(2x = 1, \ 2, \ x\)
\(4y=1, \ 2, \ 4,\ y\)
The greatest common factor is 2.
the plates of a parallel-plate capacitor are connected to a battery. if the distance between the plates is halved, the energy of the capacitora. a. Increases by a factor of 4b. Doublesc. Remains the samed. Is halvede. Decreases by a factor of 4
Cantilever beam capacitance at time t, expressed as C= U's rate of change is therefore inversely proportional to x 2.
What are capacitance and its measure?Date Updated: 27 June 2022. (00 : 00) Solution: A capacitor's capacitance is determined by dividing the amount of charge on either of its conductor plates by the potential difference between its conductors.
QpropV or C=(Q)/(V). The coulomb per volt and farad is the SI unit for capacitance (F).
The formula for capacitors is what?The fundamental equation for capacitors is charge (= capacitance x voltage, or Q = C x V. We gauge capacitance by series or in parallel, which is the capacity that holds one coulomb (specified as the charge delivered by one ampere inside one minute) of charge per one farad.
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if ablock is at verge of motion
If a block is on the verge of motion, Limiting friction acts on the block.
Friction refers to the force that acts on a body to oppose any motion. These are of the following types:
Static Friction: This friction acts on the body when it is at rest. This friction doesn't have a fixed value and is adjustable with force acts.Limiting Friction: This is the highest amount of friction that acts on the body just before it is in motion or the body is on the verge of motion. This friction acts on the body when it is at rest.Kinetic Friction: This friction acts on the body when it is in motion. This friction acts on the body when it is at rest. It has a fixed value independent of force acting on the body.Learn more about Friction:
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However, the complete question should be: What type of friction, acts on the block, if a block is on the verge of motion?
Wave 1
a) How many waves are there in this wave train?
b) Wavelength cm c) Amplitude
cm
Answer:
see below
Explanation:
a wave means one complete wave which is 1 period
so a) 5 complete waves
wavelength is the shortest distance between any two points in phase
so wavelength = 1 CM
amplitude of a wave is the maximum displacement of a particle from its rest position
so amplitude = 3 CM
hope this helps
A block of mass 2.0kg experiences the following steady forces while moving a displacement of 3.0m to the left (there may be additional forces on the block). Each square on the grid has a side of 1.0N. What is the work done by the sum of these 3 forces
The total work done by the sum of the three forces is -18.0 Joules. Each individual force contributes a negative amount of work due to the opposite direction of the displacement.
To calculate the work done by a force, we can use the formula:
Work = Force * Displacement * cos(Ф)
Where:
- Force is the magnitude of the force applied,
- Displacement is the magnitude of the displacement,
- theta is the angle between the force and the displacement.
Since the displacement is given as moving 3.0m to the left, we can assume the angle theta to be 180 degrees (or pi radians) because the force and displacement are in opposite directions.
Let's calculate the work done by each force and then sum them up:
Force 1: 2.0N
Work 1 = 2.0N * 3.0m * cos(180°) = -6.0 Joules
Force 2: 3.0N
Work 2 = 3.0N * 3.0m * cos(180°) = -9.0 Joules
Force 3: 1.0N
Work 3 = 1.0N * 3.0m * cos(180°) = -3.0 Joules
The total work done by the sum of these three forces is the sum of their individual works:
Total Work = Work 1 + Work 2 + Work 3
= -6.0 Joules + (-9.0 Joules) + (-3.0 Joules)
= -18.0 Joules
Therefore, the total work done by the sum of these three forces is -18.0 Joules.
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The force that always opposes the motion of an object is called _________.
inertia
acceleration
friction
The force that always opposes the motion of an object is called friction. Friction is the force that resists the motion of two surfaces that are in contact with each other.
What is force?Force is an external influence that can cause an object to accelerate, decelerate, change direction, maintain its current state, or experience a combination of these effects. Forces can be either contact forces, such as friction, normal force, and applied force, or non-contact forces, such as gravity, magnetic force, and electrical force. The magnitude of a force is measured in terms of its strength, while the direction of a force is measured in terms of its direction. Force is an integral part of physics and is used to explain and predict a wide range of physical events. Force is a fundamental concept for understanding how the physical universe works.
It is caused by the interaction of the two surfaces as they interact with each other. Friction can be static, which is the force that resists the motion of two surfaces that are in contact with each other but not moving, or kinetic, which is the force that resists the motion of two surfaces that are in contact with each other and moving.
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A truck pulls a trailer on a flat stretch of road. The forces acting on the trailer are
the force due to gravity (250 000 N downward), the force exerted by the road
(250 000 N upward), and the force exerted by the cable connecting the wailer to
the truck (20 000 N to the right). The forces acting on the truck are the force due to
gravity (80 000 N downward), the force exerted by the road (80 000 N upward), the
force exerted by the cable (20 000 N to the left), and the force causing the truck to
move forward (26 400 N to the right).
The net vertical force on the trailer is 0, while the net horizontal force on the trailer is 20,000 N to the right.
The net vertical force on the truck is 0, while the net horizontal force on the truck is 6,400 N to the right.
The given parameters;
the trailer:
force on the trailer due to gravity, Fg = 250,000normal force on the trailer due to the road, N = 250,000 Nhorizontal force on the trailer, Fx = 20,000 N to the rightthe truck:
force on the truck due to gravity, Fg = 80,000 Nnormal force on the truck due to the road, N = 80,000 Nleft horizontal force on the truck, Fx = 20,000 Nright horizontal force on the truck, Fx = 26,400 NThe net force on each vehicle is calculated as follows;
for the trailer:
Net vertical force is calculated as;
\(\Sigma F_y = 250, 000 \ N - 250,000 \ N = 0\)
Net horizontal force is calculated as;
\(\Sigma F_x = 20,000 \ N\)
for the truck;
Net vertical force is calculated as;
\(\Sigma F_y =80,000 \ N - \ 80,000 \ N = 0\)
Net horizontal force is calculated as;
\(\Sigma F_x = 26,400 \ N - \ 20,000 \ N = 6,400 \ N \ to \ the \ right\)
"Your question is not complete, it seems to be missing the following information;"
find the net force on each vehicle.
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if we compare light photons and energetic electrons which have constant velocity independent of energy
Light photons always travel at a constant speed (the speed of light) regardless of their energy, while the velocity of electrons is not constant and can vary with their energy.
Light photons and energetic electrons do not have constant velocities independent of energy. Light photons, which are particles of electromagnetic radiation, travel at a constant speed in a vacuum, which is approximately 299,792 kilometers per second (or about 186,282 miles per second) in a vacuum, denoted as the speed of light (c). This speed is a fundamental constant of nature and remains constant regardless of the energy of the photons. In other words, all photons, regardless of their energy, travel at the same speed in a vacuum.
On the other hand, energetic electrons do not have a constant velocity independent of their energy. According to classical physics, the velocity of an electron can vary depending on its energy. In classical mechanics, the kinetic energy of an object is related to its velocity. However, in the microscopic world of quantum mechanics, the behavior of particles such as electrons is described differently.
In quantum mechanics, the concept of particle velocity becomes less straightforward. Instead of velocity, quantum particles are described by wavefunctions, which represent the probability distribution of finding the particle at a certain location. The wavefunction of an electron evolves over time according to the Schrödinger equation, and it does not directly correspond to a well-defined classical velocity.
However, in certain situations, such as in electron beams or particle accelerators, electrons can be accelerated to high energies. In these cases, the energy of the electrons is related to their speed, but it is not a constant relationship. As the energy of the electrons increases, their speed can also increase, but it is not independent of their energy.
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1 Which requires more work, lifting a 10kg sack of
coal or lifting a 15kg bag of feathers?
the grand coulee dam is 1270. m long and 170. m high. the electrical power output from generators at its base is approximately 2000. mw. how many cubic meters of water must flow from the top of the dam per second to produce this amount of power if 92% of the work done on the water by gravity is converted to electrical energy? (each cubic meter of water has a mass of 1000. kg .)
Hence, 127.2 m3/s per second is the required water flow rate from the dam's crest.
What is a second?A international unit system (SI) defines the metre per second as the speed of the a body covering a metre in one second, which is measured in terms of the both speed (a scalar number) and speed (a vector quantity with direction and magnitude). m/s, m/s1, m/s, or ms are the SI unit symbols.
How do you calculate a second?Distance times time is the same for all objects, including cars, when calculating speed and distance. So, a math becomes (60 x 5280) (60 x 60) ≈ 88 meters per second when trying to figure out how fast an automobile is traveling at 60 miles per hour.
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what is the period t0 between successive ticks of the clock in its rest frame? express your answer in terms of variables given in the introduction. use c for the speed of light.
The period t0 between successive ticks of the clock in its rest frame can be expressed using the variables given in the introduction. Let's assume that the clock is moving with a constant velocity v relative to the rest frame.
According to special relativity, time dilation occurs when an object is moving relative to an observer. The equation for time dilation is:t = t0 / sqrt(1 - (v^2 / c^2))where t is the time interval measured by the observer and t0 is the time interval measured in the rest frame of the clock.In this case, since we are interested in the period t0 between successive ticks of the clock in its rest frame, we can rewrite the equation as:
the period t0 between successive ticks of the clock in its rest frame is equal to the time interval measured by the observer (t). This explanation shows that the period remains the same and does not change due to the clock's motion.
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Express 48 m/s in terms of
1.km/h
2.m/min
3.km/s
4.km/minutes
48 m/s in terms of km/h is 720.8 km/h. In terms of m/min is 2880 m/min, in terms of km/s is 0.048 km/s and in terms of km/min is 2.88 km/min.
To solve this question, we need to understand some terms. The unit of velocity is measured in m/s. It can be expressed in different units of velocity.
1 km (kilometer) = 1000 meter
1 h (hour) = 3600 seconds
1 minutes = 60 seconds
To convert m/s into km/h,
48 m/s * 3600/1000 = 172.8 km/h
To convert m/s into m/min,
48 m/s * 60 = 2880 m/min
To convert m/s into km/s,
48 m/s ÷ 1000 = 0.048 km/s
To convert m/s into km/minutes,
48 m/s * 60 / 1000 = 2.88 km/min
Therefore, the 48 m/s expressed is 172.8 km/h, 2880 m/min, 0.048 km/s and 2.88 km/min.
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48 m/s is equivalent to 172.8 km/h, 2880 m/min, 0.048 km/s, and 2.88 km/minute.
To express 48 m/s in different units of velocity:
km/h (kilometers per hour):
To convert m/s to km/h, we can use the conversion factor of 3.6 since 1 m/s is equal to 3.6 km/h.
48 m/s * (3.6 km/h / 1 m/s) = 172.8 km/h
Therefore, 48 m/s is equivalent to 172.8 km/h.
m/min (meters per minute):
To convert m/s to m/min, we can use the conversion factor of 60 since there are 60 seconds in a minute.
48 m/s * (60 m/min / 1 s) = 2880 m/min
Therefore, 48 m/s is equivalent to 2880 m/min.
km/s (kilometers per second):
Since 1 kilometer is equal to 1000 meters, to convert m/s to km/s, we divide the value by 1000.
48 m/s / 1000 = 0.048 km/s
Therefore, 48 m/s is equivalent to 0.048 km/s.
km/minute (kilometers per minute):
To convert m/s to km/minute, we first need to convert m/s to km/s (as calculated in the previous step) and then multiply by 60 to convert seconds to minutes.
0.048 km/s * 60 = 2.88 km/minute
So, 48 m/s is equivalent to 2.88 km/minute.
Hence, 48 m/s is equivalent to approximately 172.8 km/h, 2880 m/min, 0.048 km/s, and 2.88 km/minute.
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The rotation of Earth on its axis is gradually slowing. This change in rotation rate will most likely cause the
The rotation of Earth on its axis is gradually slowing. This change in rotation rate will most likely cause the length of a day to increase over time.
The gradual slowing of Earth's rotation on its axis is caused by various factors such as tidal forces, changes in atmospheric and oceanic circulation patterns, and the redistribution of mass within the planet. As a result of this slowing, the length of a day is increasing by a fraction of a second every year. This change in rotation rate could potentially cause a variety of effects on Earth such as changes in climate, alterations in the distribution of land and water, and disruptions in ecosystems and migratory patterns of animals. However, these effects are expected to be very gradual and may not be noticeable within our lifetimes.
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3. a capacitor is connected across an oscillating emf. the peak current through the capacitor is 2.0 a. what is the peak current if: a. the capacitance c is doubled? b. the peak emf e0 is doubled? c. the frequency v is doubled?
Doubling the capacitance would halve the peak current, but the changes in peak emf and frequency would not directly impact the peak current without additional information about the circuit configuration.
To determine the effects on the peak current in a capacitor when certain parameters are changed, we can analyze each scenario separately:
a. If the capacitance (C) is doubled:
The peak current (I) through a capacitor in an oscillating circuit is given by the equation:
I = C * dV/dt
Where dV/dt represents the rate of change of voltage across the capacitor.
Doubling the capacitance while keeping the rate of change of voltage constant would result in a halving of the peak current. Therefore, the peak current would become 1.0 A.
b. If the peak emf (E0) is doubled:
The peak current (I) in an oscillating circuit is also influenced by the peak emf. The relationship between peak current and peak emf depends on the circuit parameters and is determined by Ohm's Law and the impedance of the circuit.
Without specific information about the circuit configuration, it is difficult to determine the exact relationship between the peak current and peak emf. Therefore, we cannot determine the new value of the peak current without additional information.
c. If the frequency (v) is doubled:
Doubling the frequency in an oscillating circuit would not directly affect the peak current through the capacitor. The peak current is primarily determined by the capacitance, voltage, and circuit impedance. Therefore, doubling the frequency would not change the peak current.
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CAN ANY OF YALL ANSWER DIS PLS!!!!!!!! I AM GIVING 20 POINTS BTW!!!!!!!
Select all the correct answers.
An unmanned spacecraft leaves for Venus. Which statements about the spacecraft's journey are true?
O
The weight of the spacecraft keeps changing.
The mass of the spacecraft keeps changing.
The weight of the spacecraft remains the same.
The mass of the spacecraft remains the same.
The gravitational pull on the spacecraft remains the same.
An unmanned spacecraft leaves for Venus. The statements, The weight of the spacecraft keeps changing and The mass of the spacecraft remains the same. This 2 statements A and D are true.
What is Spacecraft ?A spaceship is a machine or vehicle built to travel through space. Spacecraft are a form of artificial satellite utilised for a wide range of tasks, such as communications, Earth observation, meteorology, navigation, space colonisation, planetary exploration, and freight and person transfer. All spacecraft, with the exception of single-stage-to-orbit vehicles, need a launch vehicle (carrier rocket) to get into space.
A spacecraft that is performing a sub-orbital spaceflight launches into space and then lands without gaining enough momentum or energy to complete a full orbit of the Earth. Spacecraft enter confined orbits around the Earth or other celestial bodies for orbital spaceflights. Only humans are carried on human spacecraft either as crew or guests from launch or while in orbit (space stations).
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Petroleum is a non -renewable resource. Therefore, its use needs
to be planned so that present and future use can be adequately met.
Explain how the optimal level of use of petroleum can be
achieved.
Petroleum is a non-renewable resource, which means that it cannot be replenished. Because of this, its usage needs to be planned properly to make sure that there is sufficient availability for present and future needs
The optimal level of use of petroleum can be achieved by several ways which are listed below:
1. Reduce wastage: The optimal level of petroleum use can be achieved by reducing wastage. We should aim to use petroleum products efficiently to minimize wastage and ensure that the resource is not used up too quickly.
2. Develop alternative energy sources: Another way to achieve the optimal level of petroleum use is to develop alternative energy sources. Renewable energy sources like solar, wind, and hydro can be developed to supplement petroleum.
3. Increase efficiency: The third way to achieve the optimal level of petroleum use is to increase efficiency. We can achieve this by improving the efficiency of vehicles and machinery that consume petroleum products.
4. Conservation: Conservation can also help achieve the optimal level of petroleum use. We can conserve petroleum by using it judiciously and avoiding unnecessary use. We can also reduce our reliance on petroleum products by using alternatives like public transport or bicycles.
5. Develop sustainable transportation: Developing sustainable transportation can also help achieve the optimal level of petroleum use. We can develop transportation systems that are more efficient, rely on alternative energy sources, and reduce the amount of petroleum consumed.
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What is the mass of an object traveling at 30. m/s if it has 33,750 J of energy?
Answer:
\(30 \div 33750 = 0.008888\)
"The LPI mechanism inflates the BCD with air from my scuba cylinder.
a. True
b. False
"
The LPI mechanism inflates the BCD with air from my scuba cylinder. The statement is b. False.
The LPI (Low-Pressure Inflator) mechanism is not responsible for inflating the BCD (Buoyancy Control Device) with air from a scuba cylinder. The LPI mechanism is typically found on the scuba regulator and is used to control the flow of air to the diver. It is used for adjusting the buoyancy and controlling the ascent or descent of the diver by adding or releasing air from the BCD.
To inflate the BCD, divers typically use a separate inflator mechanism connected to the BCD, which allows them to introduce air from the scuba cylinder into the BCD's air bladder. The BCD inflator usually has a dedicated button or lever for inflation, and it is this mechanism that enables divers to add air to the BCD and achieve buoyancy control underwater.
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A truck falls off a cliff. If the cliff is 45 m high, how much time for the truck to reach the bottom?
Which latitude receives the most direct rays of the sun year-round?.
The latitude that receives the most direct rays of the sun year-round is the equator, which has a latitude of 0 degrees.
Due to the Earth's axial tilt, the sun's rays strike the Earth at different angles at various latitudes throughout the year. Near the equator, the sun's rays are nearly perpendicular to the Earth's surface, resulting in a more direct and intense sunlight.
At the equator, the sun is positioned directly overhead at least once a year during the equinoxes (around March 21st and September 21st). This means that the equator receives the most direct and concentrated sunlight throughout the year compared to other latitudes.
As one moves away from the equator towards higher latitudes, the angle at which the sun's rays hit the Earth becomes progressively steeper, resulting in less direct and more diffuse sunlight. This is why regions closer to the poles experience more significant variations in daylight and seasonal changes in sunlight intensity.
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a solid cylinder with center-of-mass inertia 1 2 m r2 rolls without slipping on a horizontal surface at constant center-of-mass velocity. vcm what is the ratio between its rotational and center-of-mass kinetic energies?
The ratio of rotational and kinetic energy of center-of-mass is, 1/2.
If a solid cylinder is placed at top of inclined plane due to mgsinθ linear velocity increases and friction apply torque so angular velocity increases.
If cylinder is performing rolling without friction then displacement of point of contact is zero so work done by friction is zero so mechanical energy is conserved here.
So it's kinetic energy = (1/2) m v²
And rotational energy is, (1/2) I ω²
The moment of inertia is, I = (1/2) m r², and the angular velocity, ω = v/r.
Using these values, rotational energy is,
\(\dfrac{1}{2} \times \dfrac{1}{2} \times m r^2 ({\dfrac{v}{r}})^2\\= \dfrac{1}{4} \times m v^2\)
Now, the ratio of rotational and kinetic energy is, 1/2.
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1. A capacitor is made of 2 rectangular metal plates with side length of 3cmx6cm separated by a distance of 2. 36cm with water in between the plates. The capacitor has a voltage of 110v and is not connected to a battery. Calculate the capacitance. What is the new capacitance if we replace water with a new dielectric material with a constant of 3. 75 in between the plates? What is the new voltage? What is the charge on each plate?
2. A capacitor of 3. 23µF has an area of 6. 35mm^2. Determine the separation distance between the two plates. If the new capacitance is now 5. 63mF, what is the value of the dielectric inserted to the capacitor? What is the new voltage if the capacitor is connected to a 110 volts source? If the electric field created by two plates 8. 99x10^4 N/C and a working voltage of 63 volts. Will the capacitor experience a dielectric breakdown? Prove your answer.
USE GRESA
the electric field is more than the threshold value and the capacitor will experience dielectric breakdown.
1. Given values are,
side length of metal plates, a = 3 cm and b = 6 cm
distance between the plates, d = 2.36 cm
voltage, V = 110 V
dielectric constant of water, k = 80.4
dielectric constant of new material, k2 = 3.75
a) To calculate the capacitance of capacitor, the formula is, C=εA/d ……………… (1)
where A = area of plate, ε = permittivity, and d = separation distance between two plates.
We know that the permittivity of vacuum is given as, ε0 = 8.854 x 10^-12 F/m
The capacitance of capacitor can be expressed as,
C1 = ε0 (kA/d) …………….. (2)
where, ε0 = permittivity of vacuum, k = dielectric constant and A = area of plate.
Substituting the given values in equation (2),
C1 = 8.854 x 10^-12 x 80.4 x (0.03 x 0.06)/0.0236
C1 = 0.000132 F
Therefore, the capacitance of capacitor is 0.000132 F.
b) To calculate the new capacitance, the formula is given as,
C2 = k2ε0A/d ……………… (3)
where k2 is the dielectric constant of new material.
Substituting the given values in equation (3),
C2 = 3.75 x 8.854 x 10^-12 x (0.03 x 0.06)/0.0236
C2 = 0.000263 F
Therefore, the new capacitance is 0.000263 F.
c) The new voltage can be calculated as,
V2 = V1(C1/C2) …………… (4)
Substituting the given values in equation (4),
V2 = 110 (0.000132/0.000263)
V2 = 55 V
Therefore, the new voltage is 55 V.
d) The charge on each plate is given as,
Q = CV ………….. (5)
Substituting the given values in equation (5),
Q = 0.000132 x 110
Q = 0.0145 C
Therefore, the charge on each plate is 0.0145 C.
2. Given values are,
capacitance, C = 3.23 µF
area of plate, A = 6.35 mm^2
separation distance between two plates, d = ?
new capacitance, C2 = 5.63 mF
new dielectric constant, k2 = ?
voltage, V = 110 V
electric field between two plates, E = 8.99 x 10^4 N/C
working voltage, Vw = 63 V
a) The separation distance between two plates can be calculated as,
C1/C2 = d2/d1 …………….. (6)
where d1 and d2 are the initial and final separation distance, respectively.
Substituting the given values in equation (6),
3.23 x 10^-6/5.63 x 10^-3 = d2/d1
d2 = 5.63 x 10^-3 x (d1/3.23 x 10^-6)
Area of plate, A = 6.35 mm^2 = 6.35 x 10^-6 m^2
The capacitance can be expressed as,
C = εA/d
d = εA/C
where ε = permittivity of dielectric material.
Therefore, substituting the given values in above equation,
d1 = ε x 6.35 x 10^-6/3.23 x 10^-6
d1 = 12.50 ε
Substituting the value of d1 in equation (6),
5.63 x 10^-3 = d2/12.50 ε
d2 = 70.38 ε
The separation distance between two plates is 70.38 ε.
b) The new dielectric constant can be calculated as,
C2 = k2ε0A/d2
k2 = C2d2/ε0A
Substituting the given values in above equation,
k2 = 5.63 x 10^-3 x 70.38 ε/(8.854 x 10^-12 x 6.35 x 10^-6)
k2 = 3.95
Therefore, the new dielectric constant is 3.95.
c) The new voltage can be calculated as,
V2 = V1(C1/C2)
Substituting the given values in above equation,
V2 = 110(3.23 x 10^-6/5.63 x 10^-3)
V2 = 0.063 V
Therefore, the new voltage is 0.063 V.
d) The electric field can be expressed as,
E = V/d
d = V/E
Substituting the given values in above equation,
d = 63/8.99 x 10^4
d = 7.01 x 10^-4 m
The voltage, V = 110 V > working voltage, Vw = 63 V
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The flag pole is mounted on a universal joint at O and help to the ground with two cables. Solve the reaction force
Without additional information such as the height and weight of the flag pole, we cannot provide an accurate solution for the reaction force.
However, we can provide a general approach to solving the problem. First, we need to draw a free-body diagram of the flag pole and cables. We can assume that the weight of the flag pole acts at its center of gravity, which is typically located at the midpoint of the pole. We can also assume that the tension forces in the cables act at angles of 45 degrees with the horizontal axis, as this is a common setup for flag poles. Next, we can apply Newton's laws of motion to determine the reaction force. Since the system is in equilibrium, the net force acting on the flag pole must be zero. This means that the sum of the tension forces in the cables must be equal to the weight of the flag pole. To solve for the tension forces, we can use trigonometry to decompose the forces into their horizontal and vertical components. Once we have these components, we can use the equations of equilibrium to solve for the tension forces. Overall, the solution for the reaction force depends on the weight and height of the flag pole, as well as the angle and tension of the cables. Without this information, we cannot provide a specific solution.
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If the force causing a mass to accelerate is multiplied by a number while keeping the mass the same, what happens to the acceleration of the object?
Answer: If mass remains constant and you double the force you will double the acceleration.
At what conditions acceleration of a body is zero?
Answer:
when there is uniform velocity the acceleration of a body is zero
contraposition: every container having no more than one item implies that there are at most as many items as containers.
The contrapositive of the statement "Every container having no more than one item implies that there are at most as many items as containers" would be: "If there are more items than containers, then there exists a container with more than one item."
In other words, if the number of objects is greater than the number of containers then there must be at least one container that contains more than one thing. The original statement and the counterfactual statement are logically equivalent, thus if one is true, then the other must also be true. This helps demonstrate the relationship between the number of items and containers and shows that it is impossible for each container to store only one item when there are more items than containers.
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WILL MARK BRAINLIEST IF RIGHT
Commander M.J. Jordan loses track of time, in the excitement of the Chicago Bulls winning their sixth NBA championship, and uses up all of the remaining fuel in his jetpack. Stranded in space, with nothing but his lucky basketball, how can Commander M.J. Jordan safely return to the space station?
A. While facing the space station, pass the basketball towards the space station.
B. Keeping his back to the space station, pass the basketball into space away from the space station.
B. Keeping his back to the space station, pass the basketball into space away from the space station.
By passing the basketball into space away from the space station, Commander M.J. Jordan would experience a reactive force in the opposite direction due to Newton's third law of motion. This reactive force would cause him to move in the direction opposite to that of the basketball's movement, providing him with propulsion to propel himself towards the space station.
On the other hand, if Commander M.J. Jordan were to pass the basketball towards the space station while facing it, the reactive force would push him further away from the space station, making it more difficult for him to return safely.
Therefore, option B is the correct choice for safely returning to the space station.
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