Explanation:
(A) Electric field for the parallel plate capacitor is given by :
[tex]E=\dfrac{\sigma}{2\epsilon_o}[/tex]
It is clear that the electric field does not depend on the separation of the plates.
(B) The relation between the electric field and the electric potential is given by :
[tex]V=Ed[/tex]
d is the separation between plates. So, if the separation of the plates is increased, the potential difference increases.
(C) The capacitance of the parallel plate capacitor is given by :
[tex]C=\dfrac{A\epsilon_o}{d}[/tex]
So, the capacitance decreases when the separation of the plates is increased.
(D) The energy stored in the capacitor is given by :
[tex]E=\dfrac{1}{2}CV^2[/tex]
[tex]E=\dfrac{1}{2}C(Ed)^2[/tex]
So, the energy stored in the capacitor is increased when the separation of the plates is increased.
Answer:
a)constant
b)constant
c)constant
d) constant
Explanation:
a)
The electric field between the plates remain constant. The Electric field between the plates is given as:
[tex]E=\frac{\sigma}{\epsilon}[/tex]
where:
[tex]\sigma=[/tex] surface charge density
[tex]\epsilon=[/tex] permittivity of the material between the plates
b)
The potential difference between the plates is related as:
[tex]V=\frac{Q}{C}[/tex]
and
[tex]E=\frac{V}{d}[/tex]
where:
d = distance between the plates
Therefore the potential difference remains constant when the capacitor plates distance remains constant.
c)
the capacitance:
[tex]C=\frac{Q}{V}[/tex]
When the charge and potential difference is constant then the capacitance also remains constant.
d)
Energy stored in a capacitor:
[tex]U=\frac{1}{2} C.V^2[/tex]
Since capacitance and potential difference are constant therefore potential difference is also constant.
Stefan's Law says:
A) that doubling the star's temperature would also double its peak wavelength.
B) the energy radiated by a blackbody is proportional to T3.
C) that if the Sun's temperature were doubled, it would give off 16X more energy.
D) the hotter a star's surface, the bluer it looks to us.
E) E =mc2.
Answer:
The Sun's temperature were doubled, it would give off 16X more energy.
Explanation:
The Stefan's law gives the relationship between total energy radiated per unit surface area of a black body and the temperature. It is given by :
[tex]j\propto T^4[/tex]
[tex]j=\sigma T^4[/tex]
[tex]\sigma[/tex] is the constant of proportionality called the Stefan–Boltzmann constant
T is temperature
So, the correct statement regarding Stefan's Law is that if the Sun's temperature were doubled, it would give off 16 X more energy. Hence, the correct option is (C).
Final answer:
Stefan's Law, or the Stefan-Boltzmann law, indicates the power output of a black body like the Sun would increase by a factor of 16 (C) if its temperature were to double, due to the relationship where energy flux is proportional to the fourth power of temperature. Hence, (C) is the correct option.
Explanation:
The correct answer to the statement 'Stefan's Law says' is that if the Sun's temperature were doubled, it would give off 16X more energy.
This relationship is known as the Stefan-Boltzmann law and states that the total energy flux (energy radiated per square meter) from a black body, such as a star, is proportional to the fourth power of its absolute temperature, as expressed in the formula [tex]F = \sigma\T4[/tex] (with sigma being the Stefan-Boltzmann constant).
Therefore, if the temperature of the Sun were to double from its current temperature (approximately 5800 K to 11600 K), its power output, or radiated energy, would increase by a factor of 24 or 16.
Describe the total momentum of billiard balls before and after the cue ball collides with another ball.
Answer:
The Total Momentum before and after collision remains the same.
Explanation:
Note that the balls have the same masses.
A moving cue ball has an initial momentum. After every collision with another stationary ball, the momentum, which is the product of their mass and velocity, of the balls is conserved. This simply means that the total momentum before the collision is the same as the total momentum after the collision.
This also means that the energy must be conserved as well. The balls cannot fling away from each other with more energy than you give them.
Answer:
Total momentum is conserved before and after collusion and it's elastic.
Explanation:
For two colliding balls, the general vector equation for conservation of linear momentum is giving as
Ma*V1a = Ma*V2a + Mb*V2b
Where Ma=mass of que ball = Mb = mass of billiard ball so therefore
V1a= velocity of que ball before impact, V2a = velocity of que ball after impact, V2b = velocity of billiard ball after impact.
So therefore:
V1a = V2a + V2b
Which Earth system spheres are involved in this particular scientific investigation on hydraulic fracturing? Choose one or more: a.biosphere b.atmosphere c.hydrosphere d.cryosphere e.geosphere
Hydraulic fracturing involves several of Earth's system spheres including the geosphere (with drilling into rock formations), the hydrosphere (with extensive use of water), and the biosphere (potential impacts on ecosystems).
Explanation:The scientific investigation on hydraulic fracturing involves several of Earth's systems, specifically the biosphere, the hydrosphere, and the geosphere. The geosphere is involved as hydraulic fracturing involves the extraction of natural gas from deep underground rock formations. The hydrosphere is engaged as large quantities of water are used in the process, potentially affecting water resources. Finally, the biosphere is implicated as there could possibly be impacts on local ecosystems and wildlife from the operation and waste produced from the process.
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the New England Merchants Bank Building in Boston is 152 mm high. On windy days it sways with a frequency of 0.12 HzHz , and the acceleration of the top of the building can reach 2.3 %% of the free-fall acceleration, enough to cause discomfort for occupants. what is______________
Answer:
The question is incomplete or some details are missing. The last part of the question says ; What is the total distance, side to side, that the top of the building moves during such an oscillation? Express your answer to two significant figures and include the appropriate units.
Total distance (x) = 0.3972m
Explanation:
The detailed steps is as shown in the attachment
Which of the following is a scalar quantity
A. Distance
B. Displacement
C. Velocity
D. Acceleration
Answer :
I think it is A. Distance
Answer:
A. Distance
Explanation:
Velocity, Acceleration, and displacement all require a magnitude and direction to be measured.
At a certain time a particle had a speed of 18 m/s in the positive x direction, and 2.4 s later its speed was 30 m/s in the opposite direction. What is the magnitude of the average acceleration of the particle during this 2.4 s interval?
m/s2
a) in the initial direction of motion
b) opposite the initial direction of motion
c) direction changes continuously
Answer:
(a) (18m/s/t₁)m/s²
(b) -12.5m/s²
(c) -20mls²
Explanation:
(a) Let t₁ be the initial time
a = v-u/t
acc = (18m/s/t₁)m/s²
(b) acc = -30m/s/2.4
= -12.5m/s²
(c)The particle was at a speed of 18m/s in the positive x-direction and later after 2.4s ≡Δt, it was at speed of -30m/s in the negative x-direction.
so this imply that the velocity was first v₁ =18m/s and later v₂ = -30m/s.
The average acceleration is then:
Aavg = Δv
Δt
= v₂-v₁/Δt
= -30-18/2.4 = -20mls²
"Electromagnetic radiation travels or propagates through space in the form of a wave but can interact with matter as a particle of energy called a photon. This dual nature is referred to as":____________
Answer:
"Electromagnetic radiation travels or propagates through space in the form of a wave but can interact with matter as a particle of energy called a photon. This dual nature is referred to as" Wave particle duality (answer)
Explanation:
Electromagnetic radiation is created when an atomic particle, such as an electron, is accelerated by an electric field, causing it to move, and it is a form of energy that spreads as both magnetic and electrical waves that travels in vessels of energy called photons.
All types of electromagnetic radiation travel at the speed of light, radiation can be also described in terms of particles of energy, called photons. Electromagnetic radiation is generated when an electrical charge is accelerated. The acceleration produces oscillating electric and magnetic fields. Electromagnetic radiation ranges from gamma rays with very short wavelength to long radio waves. Electromagnetic radiation has the dual nature: its exhibits wave properties and photon properties.
Waves are characterized by frequency, wavelength, speed and phase, where as, a photon is the basic unit of all light. Wave particle duality can be explained as when an entity exhibits a wavelike and a particlelike properties though these properties never appear simultaneously.
What is the difference between series and parallel circuits? Specify in words and algebraic formula, if possible, the relationships between current, voltage, and resistance in each type of circuit.
Series Circuit.
There is only one path in which electrons can flow in a circuit.
Algebraic Formulas (for n number of components)
I = I1 = I2 = I3 =In
V= V1 + V2 + V3 + - - - + Vn
Req = R1 + R2 + R3 + - - - + Rn
Vn = I Rn
Parallel Circuit.
There is more than one path in which electrons can flow in a circuit.
Algebraic Formulas
I = I1 + I2 + I3 = - - - - - +In
V= V1 = V2 = V3 + - - - - - = Vn
1/Req = 1/R1 + 1/R2 + 1/R3 + - - - - - + 1/Rn
V = In Rn
A hammer is used to drive a nail into a board. Work is done in the act of driving the nail. Compared to the moment before the hammer strikes the nail, the mechanical energy of the hammer after its impact will be:
A. Greater, because the hammer has done work.
B. Greater, because work has been done on the hammer.
C. Less, because the hammer has done work.
D. Less, because work has been done on the hammer.
When a hammer drives a nail into a board, it does work on the nail, resulting in the hammer's mechanical energy being less after the impact due to the transfer of kinetic energy. The correct answer is C. Less, because the hammer has done work.
The question relates to mechanical energy and work in a physics context, specifically during the interaction between a hammer and a nail. When a hammer drives a nail into a board, it transfers some of its kinetic energy to the nail, doing work on the nail. As the kinetic energy is transferred from the hammer to the nail, the hammer's mechanical energy decreases. Therefore, the correct answer is C. Less, because the hammer has done work. This is due to an inelastic collision where some of the kinetic energy is not conserved in form of kinetic energy but could be converted into other forms such as thermal energy or energy needed to deform the nail and the wood.
What frequencies (in Hz) will a 1.85 m long tube produce in the audible range (20 Hz - 20,000 Hz) at 18.0°C for the following cases?
Answer:
The lowest frequency is 45.01 Hz.
The second lowest frequency is 135.03 hz.
The highest frequency is 19993.4 Hz.
Explanation:
Given that,
Length = 1.85 m
Range of frequency = 20 hz - 20000 Hz
Temperature = 18.0°C
Suppose, the tube is closed at one end lowest frequency , second lowest frequency and highest frequency
We need to calculate the velocity of sound
Using formula of sound velocity
[tex]v=v_{0}+0.61\times T[/tex]
Put the value into the formula
[tex]v=332+0.061\times18[/tex]
[tex]v=333.09\ m/s[/tex]
(a). For closed end,
We need to calculate the lowest and second lowest frequency
Using formula of frequency
[tyex]f_{n}=(2n+1)\times\dfrac{v}{4l}[/tex]
If n =0
[tex]f_{0}=\dfrac{v}{4l}[/tex]
Put the value into the formula
[tex]f_{0}=\dfrac{333.09}{4\times1.85}[/tex]
[tex]f_{0}=45.01\ Hz[/tex]
If n = 1
[tex]f_{1}=\dfrac{3v}{4l}[/tex]
Put the value into the formula
[tex]f_{1}=\dfrac{3\times333.09}{4\times1.85}[/tex]
[tex]f_{1}=135.03\ Hz[/tex]
Now, The maximum audible range is 20000 Hz.
We need to calculate the value of n
Using formula of frequency
[tex]f_{n}=(2n+1)\dfrac{v}{4l}[/tex]
Put the value into the formula
[tex]20000=(2n+1)\times45.01[/tex]
[tex]20000=2n\times45.01+45.01[/tex]
[tex]n=\dfrac{20000-45.01}{2\times45.01}[/tex]
[tex]n=221.6[/tex]
We need to calculate the maximum frequency
Using formula of frequency
[tex]f_{n}=(2n+1)\dfrac{v}{4l}[/tex]
Put the value into the formula
[tex]f_{221.6}=(2\times221.6+1)\times45.01[/tex]
[tex]f_{221.6}=19993.4\ Hz[/tex]
Hence, The lowest frequency is 45.01 Hz.
The second lowest frequency is 135.03 hz.
The highest frequency is 19993.4 Hz.
Final answer:
To find the resonant frequencies of a 1.85 m long tube, calculate the speed of sound at 18.0°C, and determine the wavelengths for both an open and closed tube. Use these to calculate the fundamental frequencies, which are 92.5 Hz for the open tube and 46.3 Hz for the closed at one end tube, with higher harmonics also possible in the audible range.
Explanation:
The question involves calculating the resonant frequencies of a tube at a certain temperature, which relates to the physics concept of standing waves in air columns. Specifically, a 1.85 m long tube will produce different frequencies based on whether it's closed at one end or open at both ends, due to the formation of nodes and antinodes. At 18.0°C, the speed of sound in air can be calculated using the formula v=331.4 + 0.6T, where T is the temperature in degrees Celsius. This gives 331.4 + 0.6(18.0) = 342.2 m/s for the speed of sound. The wavelength λ for the fundamental frequency (for a tube open at both ends) is 2L, where L is the length of the tube. Thus, λ = 2(1.85 m) = 3.70 m. The frequency can then be calculated using f = v/λ, resulting in approximately 92.5 Hz. For a tube closed at one end, the fundamental frequency has a wavelength of 4L, because only quarter-wavelengths can fit in the tube, making the fundamental frequency approximately 46.3 Hz. Higher harmonics can also be calculated for both cases, but they will depend on the number of nodes and antinodes that can fit within the tube for closed and open situations respectively.
Show that the effective force constant of a series combination is given by 1keff=1k1+1k2. (Hint: For a given force, the total distance stretched by the equivalent single spring is the sum of the distances stretched by the springs in combination. Also, each spring must exert the same force. Do you see why?
Answer:
1keff=1k1+1k2
see further explanation
Explanation:for clarification
Show that the effective force constant of a series combination is given by 1keff=1k1+1k2. (Hint: For a given force, the total distance stretched by the equivalent single spring is the sum of the distances stretched by the springs in combination. Also, each spring must exert the same force. Do you see why?
From Hooke's law , we know that the force exerted on an elastic object is directly proportional to the extension provided that the elastic limit is not exceeded.
Now the spring is in series combination
F[tex]\alpha[/tex]e
F=ke
k=f/e.........*
where k is the force constant or the constant of proportionality
k=f/e
[tex]f_{eff} =f_{1} +f_{2}[/tex]............................1
also for effective force constant
divide all through by extension
1) Total force is
Ft=F1+F2
Ft=k1e1+k2e2
F = k(e1+e2) 2)
Since force on the 2 springs is the same, so
k1e1=k2e2
e1=F/k1 and e2=F/k2,
and e1+e2=F/keq
Substituting e1 and e2, you get
1/keq=1/k1+1/k2
Hint: For a given force, the total distance stretched by the equivalent single spring is the sum of the distances stretched by the springs in combination.
Suppose an object starts out electrically neutral. Through some process, 11 electrons are removed from the object. What is the electric charge of the object afterward? ANSWER
1. Unselected It has a net charge somewhere between the charge of 11 electrons and 11 protons, but we can’t tell exactly how much.
2. Unselected The stated situation isn’t possible.
3. Unselected It has the same net charge as 11 protons.
4. Unselected It has the same net charge as 11 electrons.
Answer:
3. It has the same net charge as 11 protons.
Explanation:
An electrically neutral object contains the same number of protons and electrons. Therefore, if 11 electrons are removed from it, there will be 11 more protons compared to the number of electrons in the object. Thus, the object It has the same net charge as 11 protons.
Atoms are electrically neutral, but removing electrons results in a charged object with a net charge equivalent to the number of protons present.
Atoms are electrically neutral, meaning that the overall electric charge is zero because the number of protons (positive charge) equals the number of electrons (negative charge). When an atom loses electrons, it becomes positively charged, and when it gains electrons, it becomes negatively charged. In this case, removing 11 electrons from a neutrally charged object will result in a net charge equivalent to having the same net charge as 11 protons.
Four identical metallic spheres with charges of +8.2 µC, +9.0 µC, −7.8 µC, and −8.8 µC are placed on a piece of paper. The paper is lifted on all corners so that the spheres come into contact with each other simultaneously. The paper is then flattened so that the metallic spheres become separated.
a. What is the resulting charge on each sphere?
b. How many excess or absent electrons (depending on the sign of your answer to part (a)) correspond to the resulting charge on each sphere?
Answer:
a) 0.15 μC b) 9.4*10¹¹ electrons.
Explanation:
As the total charge must be conserved, the total charge on the spheres, after being brought to contact each other, and then separated, must be equal to the total charge present in the spheres prior to be put in contact:
Q = +8.2μC +9.0 μC +(-7.8 μC) + (-8.8 μC) = +0.6 μC
As the spheres are assumed perfect conductors, as they are identical, once in contact each other, the excess charge spreads evenly on each sphere, so the final charge, on each of them, is just the fourth part of the total charge:
Qs = Qt/4 = 0.6 μC / 4 = 0.15 μC.
b) As the charge has a positive sign, this means that each sphere has a defect of electrons.
In order to know how many electrons are absent in each sphere, we can divide the total charge by the charge of one electron, which is the elementary charge e, as follows:
[tex]N =\frac{0.15e-6C}{1.6e-19C} = 9.4e11 electrons[/tex]
The Earth and the Moon are attracted to each other by universal gravitation. The Earth is much more massive than is the Moon. Does the Earth attract the Moon with a force that is greater, smaller, or the same size as the force with which the Moon attracts the Earth?
Answer:
Earth attract the Moon with a force that is greater.
Explanation:
According to the law of gravitation, the gravitational force between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Mathematically, F1 = Gm1m2/r²... 1
Let m1 be the mass of the earth and m2 be that of the moon
If the Earth is much more massive than is the Moon, the new force of attraction between them will become;
F2= G(2m1)m2/r²
F2 = 2Gm1m2/r² ... (2)
Dividing eqn 1 by 2 we have;
F1/F2 = (Gm1m2/r²)÷(2Gm1m2/r²)
F1/F2 = Gm1m2/r²×r²/2Gm1m2
F1/F2 = 1/2
F2=2F1
This shows that that the earth will attract the moon by a force 2times the initial force of the masses(i.e a much greater force)
If an object which weighs 100 lbs on the Earth's surface were placed on a planet with 3 times the radius of the Earth and with 5 times the Earth's mass, how much would that object weigh? Enter answer to nearest 0.1 lbs.
The object's weight on the other planet is determined by the force of gravity on that planet, which depends on the planet's mass and radius. The object's weight can be found by plugging these values into the formula for gravitational force, once the actual mass of the object is obtained by dividing its weight on Earth by the Earth's gravitational acceleration.
Explanation:To find the weight of the object on the other planet, we need to calculate the gravitational pull on that planet. The force of gravity is given by the formula F = G * (m1 * m2) / r^2, where G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between the centers of the two objects (which in this case is the radius of the planet).
On Earth, the object weighs 100 lbs. This is its mass times the gravity of Earth, which is roughly 9.8 m/s^2. So we can find the mass of the object by dividing the weight (100 lbs) by the acceleration due to gravity (9.8 m/s^2).
The planet in question is stated to have 3 times the Earth's radius and 5 times its mass. So we substitute these values into the formula along with the mass of the object we calculated, and solve for F, the force, which will be the weight of the object on the other planet.
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Four equal masses m are so small they can be treated as points, and they are equally spaced along a long, stiff wire of neglible mass. The distance between any two adjacent masses is l. What is the rotational inertia I_cm of this system about its center of mass?
1) 1/2 ml^2
2) 3 ml^2
3) ml^2
4) 2 ml^2
5) 4 ml^2
6) 7 ml^2
7) 5 ml^2
8) 6 ml^2
Answer: 5m/L^2
Explanation:
Inertial I = mr^2 where r = distance from axis of rotation, while m is the mass of the object.
I = 2[m(1L/2)^2] + 2[m(3L/2)^2] = 2m×. 25/L^2+ 3m×2. 25/L^2= 0. 5m/l^2 +4. 5m/l^2
= 5m/l^2.
The power rating on a light bulb indicates how much power it would dissipate when it is hooked up to the standard household voltage of 120 V (this rating does not mean that the light bulb always dissipates the same amount of power, assume that the resistance is constant in this case).
A. How much power is dissipated in a light bulb that is normally rated at 75 W, if instead we hook it up to a potential difference of 60 V?
B. How much power is dissipated in a light bulb that is normally rated at 75 W, if instead we hook it up to a potential difference of 120 V?
Answer:
A. P = 18.75 watts
B. P = 75 watts
Explanation:
V = 120 Volts
P = VI
I = P/V = 75/120 = 0.625 Amps
V = IR
R = V/I
R = 120/0.625 = 192 Ω
So the resistance of the bulb is 192 Ω and it does not change as it is given in the question.
A. How much power is dissipated in a light bulb that is normally rated at 75 W, if instead we hook it up to a potential difference of 60 V?
As P = VI and I = V/R
P = V*(V/R)
P = V²/R
P = (60)/192
P = 18.75 watts
As expected, it will dissipate less power (18.75 watts) than rated power due to not having rated voltage of 120 Volts.
I = V/R = 60/192 = 0.3125 Amps
or I = P/V = 18.75/60 = 0.3125 Amps
Since the resistance is being held constant, decreasing voltage will also decrease current as V = IR voltage is directly proportional to the current.
B. How much power is dissipated in a light bulb that is normally rated at 75 W, if instead we hook it up to a potential difference of 120 V?
P = V*(V/R)
P = V²/R
P = 120/192 = 75 watts
I = P/V = 75/120 = 0.625 Amps
As expected, it will dissipate rated power of 75 watts at rated voltage of 120 Volts.
For a light bulb rated at 75 W at 120 V, the power dissipated at 60 V is 18.75 Watts and at 120 V, it would dissipate its rated power of 75 Watts.
Explanation:The power dissipated by a resistor (in this case, a light bulb) can be calculated using the formula P = V² / R, where P is the power, V is the potential difference (or voltage), and R is resistance.
A. With a potential difference of 60 V (half of its normal voltage), we expect the bulb to dissipate a quarter of its normal power. Hence, the power in this case would be (60V)²/R = 75W/4 = 18.75 Watts.
B. The rating on the bulb is 75 W assuming a household voltage of 120 V. So, if we hook it up to a potential difference of 120 V, it should dissipate its normal rated power of 75 Watts.
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anna litical is practicing a centripetal force demonstration at home. she fills a bucket with water, ties it to a strong rope, and spins it in a circle. Anna spins the bucket when its half- full of water and when it is quater- full of water. In which case is more force required to stop spin the bucket circle.
Answer:
half filled bucket requires more force to stop
Explanation:
When spinning a bucket half filled it is clear that is has greater mass of water than the quarter filled bucket.
While revolving any mass tied about a fixed point we have a centripetal force acting on the bucket which makes it take the circular path during the motion.
This is centripetal force is given as:
[tex]F_c=m.\frac{v^2}{r}[/tex]
where:
[tex]m=[/tex] mass of the revolving body
[tex]v=[/tex] tangential velocity
[tex]r=[/tex] radius of revolution
From the above equation we observe that centripetal force is directly proportional to mass and square of the velocity but inversely proportional to the radius of the revolution which is same as the length of the rope between the hand and the bucket (more precisely the distance between the center of revolution and the center of mass of the revolving body). While this force acts inward to the circular path and not along the tangential direction.The revolving mass has to be brought to rest in this case the momentum of the heavier mass will be greater and from the Newton's second law of motion we have the the rate of change in momentum directly proportional to the force applied.
Mathematically:
[tex]F=\frac{d}{dt}(m.v)[/tex]
here the mass is constant so,
[tex]F=m.\frac{d}{dt} v[/tex]
Therefore if the length of the rope, and the speed of revolution is same in both the case then the half filled bucket whose mass is greater than the quarter filled bucket will require more force to stop the circular motion of the bucket.
Answer: so there is potiental enrgy need to stop spinning the bucket
Explanation:The Force of and bucket outcome is determed by the force of that i uesd to
Technician A says that the starter motor used to crank diesel engines can draw up to 400 amps of current. Technician B says that high resistance on the insulated side of a starter motor circuit would cause higher than specified starter motor current draw. Who is correct?a. Technician A
b. Technician B
c. Both Technician A and Technician B
d. Neither Technician A nor Technician B
Answer: Option A : Technician A
Explanation:
The statement/observation, "that the starter motor used to crank diesel engines can draw up to 400 amps of current" made by Technician A is correct.
A diesel engine uses up to 400+ Amperes of electricity to start up a diesel engine in the ignition chamber of motor engine.
What tension must a 42.1 cm length of string support in order to whirl an attached 1,000.0 g stone in a circular path at 2.85 m/s?
Answer:
Tension in the string will be 19.293 N
Explanation:
We have given length of the string r = 42.1 cm = 0.421 m
Mass of the stone m = 1000 gram
We know that 1000 gram = 1 kg
Velocity in the circular path v = 2.85 m/sec
We have to find the tension in the string
Tension in the string will be equal to centripetal force
So tension [tex]T=\frac{mv^2}{r}[/tex], here m is mass, v is velocity and r is length of the string
So tension in the string [tex]T=\frac{1\times 2.85^2}{0.421}=19.293N[/tex]
So tension in the string will be equal to 19.293 N
The height of an object dropped from the top of a 64-foot building is given by h(t)=-16t^2+64. How long will it take the object to hit the ground?
Answer:
1.86 s
Explanation:
Given the expression
h(t) = -16t²+ 64...................... Equation 1
Where h = height of the object, t = time it will take the object to hit the ground.
Given: h = 64 foot.
We have to concert from foot to meters
If 1 foot = 0.3048 meters
Then, 64 foot = 0.3048×64 = 19.51 meters.
We substitute the value of h into equation
119.51 = -16t²+64
-16t² = 199.51-64
-16t² = 55.51
t² = 55.51/-16
t² = 3.469
t = √3.469
t = 1.86 s.
Hence it will take the object 1.86 s to hit the ground.
To prepare 400 ml of a 40% (w/v) solution of sodium bicarbonate, how many grams of solute are needed?
Answer : The mass of solute needed are, 40 grams.
Explanation :
As we are given that 40 % (w/v) solution of sodium bicarbonate (solute) that means 40 grams of sodium bicarbonate present in 100 mL of solution.
Now we have to calculate the mass of solute needed.
As, 100 mL of solution needs mass of solute = 10 g
So, 400 mL of solution needs mass of solute = [tex]\frac{400mL}{100mL}\times 10g=40g[/tex]
Thus, the mass of solute needed are, 40 grams.
To prepare a 400 ml of 40% (w/v) solution of sodium bicarbonate, multiply the percentage (40%) by the total volume (400 ml) and divide by 100. You will need 160 grams of sodium bicarbonate for this solution.
Explanation:To prepare 400 ml of a 40% (w/v) solution of sodium bicarbonate, you need to understand the meaning of (w/v). It stands for weight/volume, and it means that for every 100 ml of solution, you have the given percentage in grams of the solute. So, for a 40% (w/v) solution, 100 ml of the solution will contain 40 grams of sodium bicarbonate. Therefore, we need to calculate the amount of sodium bicarbonate for 400 ml of solution:
First, determine the total weight of sodium bicarbonate needed for 100 ml: 40 grams (from the definition of 40% w/v).Next, because you need 400 ml, which is four times the amount of 100 ml, you multiply the amount needed for 100 ml by 4.This results in 40 grams x 4 = 160 grams.To prepare a 400 ml of 40% (w/v) sodium bicarbonate solution, you would need 160 grams of sodium bicarbonate.
Students in Mr. Jackson's class built two containers designed to keep Ice pops cold for a
penod of time. Both containers had the same dimensions, but were constructed from
diferent materials. They put one Ice pop in each container, kept the surrounding
temperature constant, and measured how long it took for each ice pop to melt. The table
shows their results.
Container Time it took the Ice Pop to Melt (min)
1-25
2-32
Which container was most likely made with a material that had a low specific heat?
A. Container 1 because it took the shortest amount of time for the ice pop to melt, and
materials with low specific heat are poor Insulators
B. Container 1 because it took the shortest amount of time for the Ice pop to melt, and
materials with low specific heat are good Insulators
C. Container 2 because it took the longest amount of time for the Ice pop to melt, and
materials with low specific heat are poor insulators
D. Container 2 because it took the longest amount of time for the ice pop to melt, and
materials with low specific heat are good insulators
The ice in first container melts fastly because the container is made of material with low specific heat capacity. The material is a poor insulator.
What is specific heat capacity ?The heat energy required to raise the temperature of a substance by one degree Celsius per one gram of that substance is called its specific heat capacity. It is an intensive property.
Less the specific heat, heat energy required by the material is less to increase the temperature. If a substance is having higher specific heat it requires more heat energy and it is a poor conductor.
To melt a substance heat energy is required to absorb by the substances to weaken the intermolecular forces. If the ice in container melts easily than the ice in other container, the material of the first container is made with material of less specific heat.
The material with less specific heat is a thermal conductor. Therefore, option A is correct.
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What percent is the air density at the summit of Mount Everest relative to the air density at sea level?
Answer:
43.76%
Explanation:
The air density at the sea level ρ_s = 1.25 kg/m^3.
also, air density at the top of the mountain where ρ_t = 0.547 kg/m^3.
taking temp as --50° C and pressure as 1/3 of P_atm.
therefore, t percent is the air density at the summit of Mount Everest relative to the air density at sea level
= [tex]\frac{\rho_t}{\rho_s}\times100[/tex]
=[tex]\frac{0.547}{1.25}\times100[/tex]
=43.76 %
Why is designing a successful service operation often more difficult than a successful design of a tangible product?
A. Strong element of customer involvement
B. Lack of computer-aided design
C. Tangible products are more personalized
D. More challenging inventory considerations
Answer:
A. Strong element of customer involvement
Explanation:
A service operation involves managing and performing the activities that are necessary to deliver services at a good level of quality to customers. Service operation tends to be more difficult than a successful design of a tangible product because the process involves high customer contact because customers are consumers of the product but in the case of the services, they are also part of its production and this is more difficult to control. According to this, the answer is that a successful service operation is more difficult because it has a strong element of customer involvement.
Two football players with mass 75kg and 100kg run directly toward each other with speeds of 6 m/s and 8 m/s respectively, If they grab each other as they collide, the combined speed of the two players just after the collision would be:
Answer:
2 m/s
Explanation:
From the law of conservation of momentum,
Total momentum before collision = total momentum after collision
mu+m'u' = V(m+m') .................................Equation 1
Where m = mass of the first player, u = initial speed of the first player, m' = mass of the second player, u' = initial speed of the second player, V = combined speed of both players.
Making V the subject of the equation,
V = (mu+m'u')/(m+m')................ Equation 2
Note: Taking the direction of the first player as positive.
Given: m = 75 kg, m' = 100 kg, u = 6 m/s, u' = -8 m/s (opposite the first player),
Substituting into equation 2
V = [(75×6)+(100×(--8))]/(75+100)
V = (450-800)/175
V = 350/175
V = - 2 m/s.
Note: The negative signs tells that the combined speed is in the direction of the second player.
Hence the combined speed of the two players = 2 m/s
Final answer:
The question involves using the conservation of momentum to calculate the combined speed of two football players after they collide and cling together. By applying the formula (m1*v1 + m2*v2) / (m1 + m2), the resulting velocity can be obtained, considering the direction of the players' velocities.
Explanation:
The question involves a physical interaction between two football players, which is described by the conservation of momentum, a fundamental concept in physics. When two objects, in this case football players, collide and stick together, the total momentum before the collision equals the total momentum after the collision, provided no external forces act on the system. The formula to find the combined velocity just after the collision is derived from the conservation of momentum principle: (m1*v1 + m2*v2) / (m1 + m2), where m1 and m2 are the masses and v1 and v2 are the velocities of the two players respectively.
Therefore, to find the combined speed of the two players just after the collision, we would use their given masses and initial speeds: (75kg*6m/s + 100kg*-8m/s) / (75kg + 100kg). The negative sign indicates that the second player is running in the opposite direction. After solving, we'd get the resulting velocity, which represents the speed and direction of the two players immediately after the collision.
A sailboat moves north for a distance of 10.00 km when blown by a wind 30° east of south with a force of 5.00×10^4 N . How much work was done by the wind?
Answer:
-433 MJ of work
Explanation:
Given:
Displacement of the sailboat is, [tex]d=10.00\ km[/tex] towards north
Force applied by the wind is, [tex]F_w=5.00\times 10^4\ N[/tex]
Direction of the force is, [tex]\theta=30(Towards\ East\ of\ South)[/tex]
The vector diagram representing the given scenario is shown below.
We know that, work done by a force is the dot product of force and displacement and is given as:
[tex]W=F\cdot d=Fd\cos x[/tex]
Where, 'x' is the angle between the tails of the vectors 'F' and 'd'.
Now, from the figure below, we can find 'x'.
[tex]x=180-\theta=180-30=150[/tex]
Now, plug in all the given values and solve for 'W'.
[tex]W=(5.00\times 10^4\ N)(10.00\times 10^3\ m)(\cos 150)\\\\W=-433012702\ J =-433\ MJ[/tex]
Therefore, the work done by the wind is nearly 433 MJ. The negative sign implies that the force acts in the direction opposite to the displacement.
Since you've determined that the power supply is a 700W dual rail, what does that make the maximum output power?
700 makes the maximum output power.
Explanation:
In physics, power is the rate of doing work or of transferring heat, i.e. the amount of energy transferred or converted per unit time. The output power of a motor is the product of the torque that the motor generates and the angular velocity of its output shaft.
A joule is equal to one Newton-meter, which is the amount of work needed to move a 1 Newton force a distance of 1 meter. When you divide work by time, you get power, measured in units of joules per second. This is also called a Watt. 1 Watt = 1 Joule Sec. This is the formula to calculate output power.
The maximum output power of a 700W dual rail power supply is 700W. 'Dual rail' refers to how the power is distributed, it does not increase the total output.
Explanation:Having determined that the power supply is a 700W dual rail, this refers to the maximum amount of power that the power supply can output. The power supply's maximum output power is its total capacity, which in this case is 700W. It's important to remember that 'dual rail' refers to the way the power is distributed and doesn't increase the overall power. Simply put, a dual rail power supply divides its power between two ‘rails’ or circuits, but the maximum output power remains 700W.
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When we look at an object that is 1,000 light-years away we see it _________.
a. as it is right now, but it appears 1,000 times dimmer
b. as it was 1,000 light-years ago
c. as it was 1,000 years ago
d. looking just the same as our ancestors would have seen it 1,000 years ago
Answer:
c. as it was 1,000 years ago
Explanation:
since the object is one thousand light years away, it means what ever light is comes from the object (is reflected off the object) would take 1,000 years to get to us, meaning we would be seeing the object as it was 1,000 years ago.
What is the best wavelength to use if an astronomer wants to study the composition of planets and stars
Answer: a. gamma rays
Explanation:
Scientists are able to use gamma rays to determine the composition of planets and other celestial bodies.
Special equipment exists that can measure gamma rays emitted by atoms on a planet's surface when it is struck by cosmic rays thus enabling us (humans) to understand more of the universe.
Answer:
Wrong its actually radio waves
Explanation: