The cost of gas is $1.27 per liter and the gallon of gas costs $4.80. where 1 gallon is equal to 3.78541 liters.
To convert the cost of gas from dollars per liter to dollars per gallon, The conversion factor between liters and gallons.
1 gallon is equal to 3.78541 liters (the exact conversion factor is 3.785411784).
Given the cost of gas is $1.27 per liter, let's calculate the cost per gallon:
Cost per gallon = Cost per liter × Liters per gallon
Cost per gallon = $1.27 × 3.78541
Cost per gallon = $4.80
So, a gallon of gas costs $4.80.
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A long rope is fixed at one end, and the free end is made to oscillate in one plane at right angles to the rope with frequency 5Hz. The successive crests are 60cm apart. What is the speed of the waves? For what frequency would the wavelength be 0.4m?
Answer:
See below
Explanation:
speed = freq * wavelength
= 5 Hz * .6 m = 3 m/s
speed = freq * wavelength
3 = freq * .4 m freq = 7.5 hz
1. The speed of the waves is 3 m/s. 2. for a wavelength of 0.4 m, the frequency would be 7.5 Hz.
To find the speed of the waves, we can use the equation:
[tex]\[ \text{Speed} = \text{Frequency} \times \text{Wavelength} \][/tex]
Given that the frequency is 5 Hz and the distance between successive crests (wavelength) is 60 cm, we need to convert the wavelength to meters:
[tex]\[ \text{Wavelength} = 60 \, \text{cm} = 0.6 \, \text{m} \][/tex]
Plugging in the values, we have:
[tex]\[ \text{Speed} = 5 \, \text{Hz} \times 0.6 \, \text{m} = 3 \, \text{m/s} \][/tex]
Therefore, the speed of the waves is 3 m/s.
Now, to find the frequency at which the wavelength is 0.4 m, we rearrange the equation:
[tex]\[ \text{Frequency} = \frac{\text{Speed}}{\text{Wavelength}} \][/tex]
Substituting the given values:
[tex]\[ \text{Frequency} = \frac{3 \, \text{m/s}}{0.4 \, \text{m}} = 7.5 \, \text{Hz} \][/tex]
Thus, for a wavelength of 0.4 m, the frequency would be 7.5 Hz.
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An emf source with a magnitude of E = 120.0 V, a resistor with a resistance of R = 89.0 Ω, and a capacitor with a capacitance of C = 6.00 μF are connected in series. A) As the capacitor charges, when the current in the resistor is 0.950 A , what is the magnitude of the charge on each plate of the capacitor?
For an emf source with a magnitude of E = 120.0 V, is mathematically given as
Q=136.63uC
What is the magnitude of the charge on each plate of the capacitor?Parameters
E = 120.0 VR = 89.0 ΩC = 6.00 μFGenerally, the equation for voltage on the resistor is mathematically given as
Vr=IR
Therefore
Vr=71*0.95
Vr=67.45V
voltage on capacitor
Vc=120-67.45
Vc=52.55V
In conclusion,
Q=CVc
Therefore
Q=52.55*2.60
Q=136.63uC
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What are significant figures?
Answer:
The term significant figures refers to the number of important single digits (0 through 9 inclusive) in the coefficient of an expression in scientific notation.
Hope its helpful!
Answer:
The term significant figures refers to the number of important single digits (0 through 9 inclusive) in the coefficient of an expression in scientific notation.
Explanation:
A housefly with a mass of 0.00100 kilograms zooms through the room at a rate of 2.20 m/s. How much kinetic energy does it have?
0.00110 J
0.00220 J
0.00242 J
The height of the fly above the ground must be known to answer this question.
Considering the definition of kinetic energy, the housefly has a kinetic energy of 0.00242 J.
Kinetic energyKinetic energy is a form of energy. It is defined as the energy associated with bodies that are in motion and this energy depends on the mass and speed of the body.
Kinetic energy is defined as the amount of work necessary to accelerate a body of a given mass and in a rest position, until it reaches a given speed. Once this point is reached, the amount of accumulated kinetic energy will remain the same unless there is a change in speed or the body returns to its rest state by applying a force to it.
The kinetic energy is represented by the following expression:
Ec= ½ mv²
Where:
Ec is the kinetic energy, which is measured in Joules (J).m is the mass measured in kilograms (kg).v is the speed measured in meters over seconds (m/s).Kinetic energy of a houseflyIn this case, you know:
m= 0.00100 kgv= 2.2 m/sReplacing in the definition of kinetic energy:
Ec= ½ ×0.00100 kg× (2.20 m/s)²
Solving:
Ec= 0.00242 J
Finally, the housefly has a kinetic energy of 0.00242 J.
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A big rock falls from a height towards water below, and hits water at a speed of 12 m/s. Rock was at a height of 15 m before falling and weighs 65 kg.
a) What was the average force of air resistance (e.g., friction) acting on the rock?
b) What is the force of friction underwater if the rock reaches a depth of 2.5 m before stopping and there is a buoyant force of 650 N [upward] acting on the rock once underwater.
The frictional force of air resistance is; 949N while the force of friction underwater is; 1859N.
What is the Frictional force of air resistance?The frictional force on the action rock can be evaluated as follows;
F - W = ma
However, the acceleration of fall a can be evaluated as follows;
a = (12² -0²)/2× 15
a = 144/30 = 4.8m/s².
a) Hence, the air resistance, frictional force, F = (65×9.8) + (65 ×4.8)
F = 949N.
b) When reaches a depth of 2.5m, it follows that the acceleration is;
a = (0²-12²)/(2×2.5)
a = 144/5 = 28.8m/s².
On this note, the force balance is;
F + 650 = 65(9.8 + 28.8)
F = 2509 - 650
F = 1859N.
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A 2.0 kg block on a frictionless table is connected to two ideal massless springs with spring constants k1 and k2 whose opposite ends are fixed to walls. What is angular frequency of the oscillation if k1= 9.5 N/m and k2= 5 N/m?
The angular frequency of the oscillation is determined as 2.7 rad/s.
Angular frequency of the block
ω = √k/m
With respect to spring constant k1 and k2
k1 + k2 = 9.5 N/m + 5 N/m = 14.5 N/m
ω = √14.5/2 = 2.7 rad/s
Thus, the angular frequency of the oscillation is determined as 2.7 rad/s.
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The electric field in a region points to the northeast. What is the direction of the acceleration of an electron
placed in this region? Consider only the electric force.
northeast
None of the other answers are correct.
northwest
southwest
southeast
Answer:
Southwest. The electric force on this electron would point southwest (opposite to the direction of the electric field.)
Explanation:
Consider a position in an electric field. A positive point charge placed at that position would experience an electric force from this field. By definition, the direction of this field at that position would be the same as the direction of electric force that the field exerts on the positive point charge placed at that position.
It is given that the electric field in this question points to the northeast in this region. Thus, a positive point charge placed in this region would experience an electric force in the same direction- to the northeast.
Electrons are negatively charged. The direction of electric force on an electron would be opposite to that on a positive point charge placed at the same position. The electric force on a positive point charge in this region points to the northeast (same as the direction of the electric field). The opposite of northeast is southwest. Hence, the electric force on an electron at this position would point to the southwest.
What is the mass of mars
Answer:
6.39 × 10^23 kg
.........
what role do supernovae explosions play in galactic recycling?
Explanation:
Supernovae play a fundamental role in a great cosmic recycling program. We believe that almost all of the elements in the Universe that are heavier than hydrogen and helium are created either in the centres of stars during their lifetimes or in the supernova explosions that mark the demise of larger stars.
a jet of water of cross section area and velocity v impinges normally on a stationary flat plate the mass per unit volume of water ρ
by dimensional analysis determine and expression for the force f exerted by the jet against the plate.
Explained in the attachment !
Hope it helps you!!A crane lifts up two boxes. A picture of a crane with a cable hanging down labeled Rope 1, which is attached to a box labeled A. Box A is attached to a cable labeled Rope 2, which is attached to a box labeled B. Which free body diagram shows the forces acting on block A? A free body diagram with two force vectors, the first pointing downward labeled F Subscript g A Baseline, the second pointing upward labeled F Subscript T 1 Baseline. A free body diagram with three force vectors, the first pointing downward labeled F Subscript g A Baseline, the second pointing upward labeled F Subscript T 1 Baseline, and the third pointing downward labeled F Subscript g B. A free body diagram with three force vectors, the first pointing downward labeled F Subscript g A Baseline, the second pointing upward labeled F Subscript T 1 Baseline, and the third pointing downward labeled F Subscript T 2. A free body diagram with three force vectors, the first pointing downward labeled F Subscript g A Baseline, the second pointing upward labeled F Subscript T 1 Baseline, and the third pointing upward labeled F Subscript T 2.
The free body diagram showing the forces acting on block A is diagram 3; option C.
What are free body diagrams?Free body diagrams are simple diagrams which are used to illustrate the magnitude and direction of the forces acting on the body.
The diagram of the crane and boxes as well as the free body diagrams are shown in the attached image.
Three forces are acting on A as follows:
The force of gravity acting downward, represented by [tex]F_{gA}[/tex]The tension in the rope 1, pulling block A upwards, represented by [tex]F_{T1}[/tex]The tension in the rope 2, due to the weight of block B, pulling block A downwards, represented by [tex]F_{T2}[/tex]Therefore, diagram 3 is correct.
In conclusion, free body diagram shows the forces acting on a body as well as their direction of action.
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Answer:
I think C is the correct answer
Explanation:
two object of masses 80kg and 50kg are separated by a distance 0.2m. If the gravitational constant is 6.6 × 10^-11 Nm^2 kg^-2, calculate the gravitational attraction between them.
The gravitational attraction between them will be 6.6 × 10 ⁻⁶ N.
What is Newton's law of gravitation?Newton's law of gravity states that each particle having mass in the universe attracts each other particle with a force known as the gravitational force.
Given data
Mass of object 1,m = 80 kg
Mass of object 2,M = 50 kg
Gravitational constant,G = 6.6 × 10⁻¹¹ kg⁻² m²
Distance of seperation,R = 0.2 m
The gravitational force is proportional to the product of the masses of the two bodies and inversely proportional to the square of their distance.
[tex]\rm F = G\frac{mM}{R^ 2} \\\\ F = 6.6 \times 10^{-11 }\times \frac{80 \times 50 }{(0.2)^2} \\\\F = 6.6 \times 10^{-6 } \ N[/tex]
Hence the gravitational attraction between them will be 6.6 × 10 ⁻⁶ N.
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Hydroelectric plants are used to produce electricity. Electric generators are used in such plants that are linked to water-wheels. As these water-wheels rotate, electricity is generated. Which of the following best explains the relationship between energy and motion in the process described
Hydroelectric plants are used to produce electricity is the statement that best explains the relationship between energy and motion.
Explains the relationship between energy and motion in the process?There is direct relationship between energy and motion in the process because if we increase the motion of the turbines, more electricity is produced in the generator and vice versa.
So we can conclude that the relationship between energy and motion in the process is directly proportional to each other.
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Question 4
Newton's first law of motion is also known as the law of inertia. Which of the following BEST
describes inertia?
Inertia depends on an objects mass and velocity
Objects at rest stay at rest until an outside force acts on them
An unbalanced force causes an object to move
An object's tendency to resist change in motion
Answer:
It is the tendency
of an object to resist any change in its state of motion .
Explanation:
if I am right mark my answer as brainliest
A water wave has a frequency of 6 Hz and a wavelength of 3 m. (a) What is the period of these waves? (b) What is the wave velocity?
The period or time duration of these waves is 0.16 sec. While the wave velocity is 18m/sec.
What is Wavelength?Wavelength may be defined as the space between equivalent points in the contiguous cycles of a waveform signal propagated in the area or along a wire.
The time duration of these waves is calculated by the given formula:
T = [tex]\frac{1}{F}[/tex] = [tex]\frac{1}{6}[/tex] = 0.16 seconds.
The velocity is calculated by the given formula:
V= Wavelength × Frequency = 6Hz × 3m = 18m/sec.
Therefore, it is well described above.
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Many television sets show 25 images, called 'frames, each second. What is the time interval between one
frame and the next?
Answer:
Given,
Frame rate = 25 frames per second
To find,
Time interval between one frame and the next.
Solution,
We can simply solve this numerical problem by using the following process.
Now,
Number of frames = 25
Total time taken to display the given number of frames (ie. 25 frames) = 1 second
To calculate the time interval between one frame and next, we need to divide the time taken to display total number of frames by total number of frames.
So,
Time interval between one frame and next :
= Time taken to display total number of frames / Total frames
= 1/25
= 0.04 second
Hence, time interval between one frame and next is 0.04 second.
Assuming barber wants to setup a saloon in a measuring length of 3m by 3m. He has a simple wooden chairs,3 large mirror and one bulb. Using the knowledge of shadows and reflection, advice the barber on how to arrange a good saloon using the only item he has. Without adding more source of light, how can he enhance the lighting system in his saloon?
The best way to arrange the salon to best use what he has is:
Place the bulb in the middle of the wallDirectly face the chair and mirror in front of the bulb for proper lighting and reflectionPlace the chairs side by side of each otherEach mirror should be facing each chaiWhat is Reflection?This refers to the change in direction of a wavefront between two different media so that the wavefront returns to its originating medium.
Hence, we can see that from our knowledge of shadows and reflection, we can note that mirrors reflect and light helps to bring detail in a dark area and the chairs should be facing the mirrors directly so the customer can see his hair and how it is being cut by the barber.
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calculate the pressure of water in a will if the deep of the water is 10 m
Answer:
98,000 pa
Explanation:
The formula for water pressure is as follows:
[tex]pressure = pgh[/tex]
Where p is the density of water (in kg/m3), g is the gravitational field strength, and h is the height of the water.
The density of water is 1000kg/m3, the gravitational field strength is 9.8, and the height is 10. Substituting in these values:
[tex]pressure = 1000 \times 9.8 \times 10[/tex]
[tex]pressure = 98000[/tex]
A 0.145 kg ball moving in the +x direction at 14 m/s is hit by a bat. The ball's final velocity is 20.0 m/s in the -x direction. The bat acts on the ball for a duration of 0.010 s.
Find the average force exerted on the ball by the bat. Include the sign of the force to indicate the direction of the force.
Answer:
Approximately [tex](-4.9\times 10^{2}\; {\rm N})[/tex] (rounded to two significant figures.)
Explanation:
The impulse [tex]\mathbf{J}[/tex] on an object is equal to the change in the momentum [tex]\mathbf{p}[/tex] of this object. Dividing impulse by duration [tex]\Delta t[/tex] of the contact would give the average external force that was exerted on this object.
If an object of mass [tex]m[/tex] is moving at a velocity of [tex]\mathbf{v}[/tex], the momentum of that object would be [tex]\mathbf{p} = m\, \mathbf{v}[/tex].
Let [tex]m[/tex] denote the speed of this ball. Let [tex]\mathbf{v}_{0}[/tex] denote the velocity of this ball before the contact, and let [tex]\mathbf{v}_{1}[/tex] denote the velocity of the ball after the contact.
Momentum [tex]\mathbf{p}_{0}[/tex] of this ball before the contact: [tex]\mathbf{p}_{0} = m\, \mathbf{v}_{0}[/tex].
Momentum [tex]\mathbf{p}_{1}[/tex] of this ball after the contact: [tex]\mathbf{p}_{1} = m\, \mathbf{v}_{1}[/tex].
Impulse, which is equal to the change in momentum:
[tex]\mathbf{J} = \mathbf{p}_{1} - \mathbf{p}_{0} = m\, \mathbf{v}_{1} - m\, \mathbf{v}_{0}[/tex].
Since the velocity of the ball after the contact is in the [tex](-x)[/tex] direction, [tex]\mathbf{v}_{1} = -20.0\; {\rm m\cdot s^{-1}}[/tex]. The average external force on this ball would be:
[tex]\begin{aligned} \mathbf{F} &= \frac{\mathbf{J}}{\Delta t} \\ &= \frac{m\, \mathbf{v}_{1} - m\, \mathbf{v}_{0}}{\Delta t} \\ &= \frac{m\, (\mathbf{v}_{1} - \mathbf{v}_{0})}{\Delta t} \\ &= \frac{0.145\; {\rm kg} \times ((-20.0\; {\rm m\cdot s^{-1}}) - 14\; {\rm m\cdot s^{-1}})}{0.010\; {\rm s}} \\ &\approx -4.9 \times 10^{2}\; {\rm N}\end{aligned}[/tex].
(Rounded to two significant figures.)
Which graph describes the motion of a car that moves at constant speed, stops for some time and then moves again at a slower speed?
a. A
b. B
c. C
d. D
A motor has coils with a resistance of 10.0 ohms and is supplied by a voltage of V = 1.20 x 102 V. When the motor is running at its maximum speed, the back emf is 70.0 V. Find the current in the coils (a) when the motor is first turned on and (b) when the motor has reached its maximum rotation rate.
Hi there!
a)
When the motor is first turned on, the coils are initially stationary. Thus, there is no change in magnetic flux and, consequently, no induced emf.
Therefore:
[tex]iR = \epsilon - \epsilon_{back}[/tex]
Since there's no back emf:
[tex]iR = \epsilon[/tex]
Solving for i using Ohm's Law:
[tex]i = \frac{\epsilon}{R}\\\\i = \frac{120}{10} = \boxed{12.0 A}[/tex]
b)
We are given that at max speed, the back EMF is 70.0 V.
Using the same equation as above:
[tex]iR = \epsilon - \epsilon_{back}[/tex]
Plugging in the values:
[tex]10i = 120 - 70 \\\\10i = 50 \\\\[/tex]
Solving for current:
[tex]i = \frac{50}{10} = \boxed{ 5.0 A}[/tex]
A section of a high speed test track is circular with a radius of curvature R = 1860 m.
At what angle of θ should the track be inclined so that a car traveling at 61.0 m/s (136 mph) would keep moving in a circle if there is oil on that section of the track, i.e., it would not slip sideways even with zero friction on that section. (Hint: The car's vertical acceleration is zero)
From the calculation, the banking angle is obtained as 11.5°.
What is the banking angle?The banking angle refers to the angle at which the vehicle must be inclined so that it does not skid off the road.
Now we have;
θ = ?
v = 61.0 m/s
r = 1860 m
g = 9.8 m/s^2
θ = tan-1(61^2/ 1860 * 9.8)
θ = tan-1(3721)/18228
θ = 11.5°
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When a mass of m = 29 kg is hung from the middle of a fixed straight aluminum wire, the wire sags to make an angle of 12∘ with the horizontal as shown in (Figure 1) . The elastic modulus for aluminum is 7.0×1010N/m2. Determine the radius of the wire
The solution to the given question is that the radius of the wire will be 0.378 millimetre approximately
At equilibrium,
Lets assume Tension T in the wire
mass of the block is given as 29 Kg
T sin 12° + T sin 12° = mg
T sin 12° + T sin 12° = 29 × 9.8
2T sin 12° = 29 × 9.8
T = ( 29 × 9.8 )/2 sin 12°
T = 141.1 / sin 12°
T = 141.1 / 0.2
T = 705.5 Newton
Stress = K × Strain
where K is the elastic modulus of the metal
elastic modulus is given as 7.0 × 10¹⁰ N/m²
T/A = 7.0 × 10¹⁰ × (Δl/l)
A = T × (l/Δl) × (1/ (7.0 × 10¹⁰) )
A = π r² = T / ( (7.0 × 10¹⁰) × ( (1/cos 12°) - 1) )
π r² = 705.5 / ( (7.0 × 10¹⁰) × 0.02234 )
r = √( 705.5 / ( π × (7.0 × 10¹⁰) × 0.02234 ) ) metre
r = √( 705.5 / ( 4910.33 × 10⁶ ) ) metre
r = √( 0.1436 × 10⁻⁶ ) metre
r = ( 0.378 × 10⁻³ ) metre
r = 0.378 millimetre
Thus we have find the radius of the wire by applying stress strain relation which came out to be 0.378 millimetre.
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(15 Points)
1. Two builders carry a sheet of drywall up a ramp.
Assume that W = 1.80 m, L = 3.30 m, θ = 24.0°, and that the lead builder carries a (vertical) weight of 147.0 N (33.0 lb). What is the (vertical) weight carried by the builder at the rear? (First Figure)
2. The builder at the rear gets tired and suggest that the drywall should be held by its narrow side. What is the weight (in N) he must now carry? (Second Figure)
The vertical weight carried by the builder at the rear end is F = 308.1 N
Calculations and ParametersGiven that:
The weight is carried up along the plane in rotational equilibrium condition
The torque equilibrium condition can be used to solve
We can note that the torque due to the force of the rear person about the position of the front person = Torque due to the weight of the block about the position of the front person
This would lead to:
F(W*cosθ) = mgsinθ(L/2) + mgcosθ(W/2)
F(1cos20)= 197/2(3.10sin20 + 2 cos 20)
Fcos20= 289.55
F= 308.1N
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1. Is it reasonable to expect that anyone would be able to make good sense of a filing system such as this new one? Why or why not?
It reasonable to expect that anyone would be able to make good sense of a filing system as it reduces the overall storage space occupied by the records.
What is Filing?This is the process of keeping document safely and being able to easily retrieve them.
The new filing system is based on their volume which is why the space is reduced thereby reducing the ambiguity.
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the density of gas is 1.775kg/m^3 at 27 degree celcius and pressure of 10^-5n/m^2. if the specific heat capacity at constant pressure is 846 jkg^-1k^-1 calculate the ratio of specific heat capacity at constant pressure to tht constant volume
Answer:
76.52
Explanation:
the density of gas is 1.775kg/m^3 at 27 degree celcius and pressure of 10^-5n/m^2. if the specific heat capacity at constant pressure is 846 jkg^-1k^-1, the ratio of specific heat capacity at constant pressure to tht constant volume is 76.52
what is density?Density is the mass of a unit volume of a material substance. The formula for density is represented by d = M/V, where d is density, M is mass, and V is volume.
It is commonly represented in units of grams per cubic centimeter. Density can also be expressed as kilograms per cubic meter .
Density can used to define how different materials interact when mixed together. For example Wood floats in water because it has a lower density, while an anchor sinks because the metal has a higher density.
density can be applied in pipe design, shipbuilding, helium balloons, weight distribution in the aeroplane, and the fact that ice floats on water.
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Two people are dragging a canoe on a beach using light ropes. Person 1 applies a
force of 60.0N [Forward] and person 2 applies a force of 90.0N [Forward]. The
friction exerted by the beach on the canoe is 85.0N. Determine the net force of the
canoe.
a) 50.0 N [forward]
Ob) 6.50 N [backward]
c) 6.50 N [forward]
d) 65.0 N [forward]
The net force on the canoe is obtained as 65.0 N [forward]
What is the frictional force?The frictional force is the force that opposes motion. We know that the net force is the actual force that moves the canoe in a given direction.
Hence, the total force acting in the forward direction = 60.0N + 90.0N = 150 N and the total backwards force = 85.0N
Net force = 150 N - 85.0N = 65.0 N [forward]
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Example No. 10
In a worst-case design scenario, a 2000 kg elevator with broken cables is
falling at 8.0 m/s when it first contact a cushioning spring at the bottom
of the shaft. The spring is supposed to stop the elevator, compressing 3.0
m as it does so. Determine what the force constant of the spring should
be.
The force constant of the spring is determined as 14,222.2 N/m.
Force constant of the springApply the principle of conservation of energy,
K.E = U
where;
K.E kinetic energy of the elevatorU is elastic potential energy of the spring¹/₂mv² = ¹/₂kx²
mv² = kx²
k = mv²/x²
Where;
m is mass of the elevatorv is speedx is compression of the springk = (2000 x 8²)/(3²)
k = 14,222.2 N/m
Thus, the force constant of the spring is determined as 14,222.2 N/m.
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Which includes the definition of both Behaviorism and Psychoanalysis approaches?
Behaviorism approach centers on giving absolute prominence to the outside characters of individuals
What is Psychoanalysis approaches?Psychoanalysis approach centers on fact the fact that the unconscious has the potential to drive our behavior
Interestingly, the behaviorists and psychoanalysts share some common norms and values in such away that
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A voltmeter of 600ohms resistance reads 200v when connected across a battery of 3ohms internal resistance. Calculate the emf of the battery
The emf of the battery will be 2.955 V. The rate of change of magnetic flux linked with the coil is responsible for generating emf.
What is induced voltage?Electromagnetic induction is what causes the induced voltage. Electromagnetic induction generates emf (induced voltage) by subjecting a conductor to a magnetic field.
Given data;
Voltage,v = 200 v
Resistance, r=600 ohms
Internal resistance,R = 3 ohms
The EMF of the battery is found as follows;
E = {vR}/{R+r}
E = 200×3/(3 + 200)
E = 2.955 V
Hence, the emf of the battery will be 2.955 V.
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