Answer: First multiply the numbers you have! 45 x 128 = 5760 miles ! Hope this helps!~
S The intensity of a sound wave at a fixed distance from a speaker vibrating at a frequency f is I . (b) Calculate the intensity if the frequency is reduced to f / 2 and the displacement amplitude is doubled.
The intensity if the frequency is reduced from f to f / 2 and the displacement amplitude doubled is I.
What do you mean by frequency?The frequency of a repeated event is its number of instances per unit of time. In some cases, it is also referred to as temporal frequency or ordinary frequency to underline differences with spatial and angular frequencies, respectively. One (event) per second is equal to one hertz (Hz), which is how frequency is stated. The period is the reciprocal of the frequency since it is the length of time for one cycle in a repeating occurrence. For instance, the period, T—the space between beats—of a heart beating at a frequency of 120 beats per minute (2 hertz), is equal to 0.5 seconds (60 seconds divided by 120 beats).
I=P/4πr²
Given:
Initial frequency, f = f
Initial Intensity, I = I
Final Frequency, [tex]f^{'}=\frac{f}{2}[/tex]
We know that, The intensity of the speaker is,
[tex]I = \frac{1}{2}\rho \omega^{2}S_{max} ^{2}v[/tex]
Substitute the [tex]\omega[/tex] value in the above equation,
[tex]I = \frac{1}{2}\rho (2\pi f)^{2}S_{max} ^{2}v\;\;\;\;-----equation(1)[/tex]
Therefore, Final intensity of the speaker is,
[tex]I^{'} = \frac{1}{2}\rho (2\pi f^{'} )^{2}S_{max} ^{2}v\;\;\;\;-----equation(2)[/tex]
By dividing the equation (1) and (2), We get
[tex]\frac{I}{I^{'}} = \frac{\frac{1}{2}\rho (2\pi f)^{2}S_{max} ^{2}v}{\frac{1}{2}\rho (2\pi f^{'} )^{2}S_{max} ^{2}v}[/tex]
By taking constant parameters in to account, We get,
[tex]\frac{I}{I^{'}} = \frac{(f)^{2}(S_{max}) ^{2}}{(f^{'} )^{2}(S_{max} )^{2}}[/tex]
By solving the above equation, We get
[tex]\frac{I}{I^{'}} = \frac{(f)^{2}}{4(f^{'} )^{2}}[/tex]
Substitute the final intensity value in the above equation,
[tex]I^{'} = I[\frac{4(\frac{f}{2})^{2}}{f^{2} }][/tex]
By solving the above equation, We get,
[tex]I^{'} = I[/tex]
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a jet engine emits sound uniformly in all directions, radiating an acoustic power of 2.11×105 w. find the intensity ???? of the sound at a distance of 50.3 m from the engine and calculate the corresponding sound intensity level ????.
The sound intensity of a jet engine radiating an acoustic power of 2.11×105 w sound at a distance of 50.3 m from the engine is approximately 6.64 [tex]W/m^2[/tex].
The intensity means the amount of loudness in it. The actual definition of intensity is the amount of power a sound has per unit area.
Mathematically, the intensity can be written as:
[tex]I=\frac{Power}{Area}[/tex]
The given data:
Power, P = [tex]2.11\times 10^5 W[/tex]
Area, A = [tex]4\pi d^2=4\pi (50.3)^2 m^2[/tex]
So using the formula, we have:
[tex]I=\frac{2.11\times 10^5}{4\pi (50.3)^2} \approx 6.64 W/m^2[/tex]
Hence, the intensity of a jet engine is approximately 6.64 [tex]W/m^2[/tex].
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If a signal can travel in a cable at 80% of the speed of light, what length of cable, in inches, represents 1 ns?
According to a signal velocity, the cable length is 9.45 inches.
We need to know about the velocity to solve this problem. The velocity can be determined as the total distance divided by the total time. It can be written as
v = d / t
where v is velocity, d is distance and t is time.
From the question above, we know that
v = 80%c = 0.8c = 2.4 x 10⁸ m/s
t = 1 ns = 1 x 10¯⁹ s
The length of cable can be represented by the distance
v = d / t
d = v . t
d = 2.4 x 10⁸ . 1 x 10¯⁹
d = 0.24 m
Convert to inches (1m = 39.37 inches)
d = 0.24 m
d = 0.24 x 39.37 inches
d = 9.45 inches
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The highest speed achieved by a standard non racing sports car is 3.60 x 10² km/h. Assuming that the car accelerates at a constant rate to reach this maximum speed for 25.0 s and covers a distance of 1.50 km while accelerating, what was the initial velocity of the car?
The car has a constant acceleration of 1.95m/s2 and reaches a top speed of 41.0m/s. The boat has a constant acceleration of 6.50m/s2 .
What is acceleration ?When it comes to mechanics, acceleration refers to how quickly an object's velocity changes over time. Acceleration is a vector quantity (in that they have magnitude and direction). The direction of the net force acting on an item determines its acceleration.
According to Newton's Second Law, an object's acceleration is a sum of two factors:
The size of the net balance of all external forces acting on that thing is directly proportional to the net resultant force; the magnitude of the object's mass, depending on the materials from which it was created, is inversely related to the mass.
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how much work is done while pushing a box mass of 35kg at a distance of 20m?
Answer: 6867 N.m
Explanation:
Work Done= (35*9.81)*20 = 6867 N.m
derive an expression for the total range of a projectile launched at an angle that reaches ground that is the same height at the launch position. give your answer in terms of the angle launched and initial velocity.
H= 2gu 2sin 2 is the expression for the total range of a projectile launched at an angle that reaches ground that is the same height at the launch position.
Let's imagine that a projectile is moving at a velocity of u at an angle of to the horizontal. After time t, the velocity will be v=v x i+v y j+v=ucos i+(usingt) j (because v y = usingt).
The projectile's only horizontal component at maximum height is vx =ucosv y 2u y2 =2ayv y =0(atm ax heightH)u y =usin ay=gH.
To put these values into context,
0=(usin) 2 2gH
H= 2gu 2sin 2
Projectile angular momentum is equal to mu cos h, where h stands for height. In the case of angular projection, the angle between the velocity and acceleration ranges from 0 to 180 degrees.
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A particle's location is measured and specified as being exactly at x = 0 , with zero uncertainty in the x direction. How does that location affect the uncertainty of its velocity component in the y direction? (a) It does not affect it. (b) It makes it infinite. (c) It makes it zero.
It does not affect the uncertainty of the velocity component in the y direction.
Any of a number of mathematical inequalities known as the uncertainty principle establishes a fundamental upper bound on the precision with which initial conditions can be used to forecast the values of some pairs of physical properties of a particle, such as location and momentum.
The measured and stated location of a particle is at x = 0 with zero uncertainty in the x direction.
According to the uncertainty principle, positional and velocity uncertainty are related along the same axis. The velocity component's x-directional component is infinitely uncertain due to the zero uncertainty in location along the x-axis, while the y-directional component is unaffected.
The correct option is (a).
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for the same charge q, the electric field strength measured at point x is the electric field measured at point y. the distance of point x from the charge is how many times the distance of point y from the charge?
Due to a single charge and the additional distance =2r, the electric field is E r times the distance of point y from the charge
New intensity is consequently equal to E/4.
Where is electric field?From the point charge, the electric field extends in all directions. Spherical equipotential surfaces are represented by the circles. The vector sum of the individual fields may be used to compute the electric field from any number of point charges.
Volts per metre (V/m) is the electrical field's SI unit. The Newtons per coulomb are the same as this unit. These units have their roots in Newton, which stands for force, and Coulomb, which stands for charge.
Being a vector quantity, the electric. We understand that the electric field is defined by the force to test charge ratio.
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a 6.96 nc charge is located 1.82 m from a 4.02 nc point charge. (a) find the magnitude of the electrostatic force that one charge exerts on the other. n (b) is the force attractive or repulsive? attractive repulsive
The electric force is 7.60 x 10¯⁸ N.
We need to know about the electrostatic force to solve this problem. The electrostatic force produced by charges interacting each other, whose strength is given by the equation
F = k.Q1 . Q2/r²
where F is the electrostatic force, Q1 and Q2 is the charge and r is the radius.
From the question above, we know that
k = 9 x 10⁹ Nm²/C²
Q1 =e = 6.96 x 10¯⁹ C
Q2 = e = 4.02 x 10¯⁹ C
r = 1.82 m
The electrostatic force will attract each other when the charges are different and will repel each other when the charges are same.
F = k.Q1 . Q2/r²
F = 9 x 10⁹ . 6.96 x 10¯⁹ . 4.02 x 10¯⁹/1.82²
F = 7.60 x 10¯⁸ N
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Which equation is perpendicular to the line
(1901
y = 3 and passes through the point (- 1, 3).
a. x = 3
b. y = 3
c. y = -1
d. X = -1
The equation perpendicular to the line is y=3.
The slope of the line [tex]$3 x+y=3$[/tex] is [tex]$m=-3$[/tex]
Hence slope of the perpendicular line is [tex]$\mathrm{m}^{\prime}=\frac{1}{3}$[/tex]
Therefore the equation of a perpendicular line is
Therefore the equation of a perpendicular line is
[tex]$(\mathrm{y}+1)=\frac{1}{3}(\mathrm{x}-3) $[/tex]
[tex](y+3)=\frac{1}{3}(x-1)[/tex]
Switch sides
[tex]\frac{1}{3}(x-1)=(y+3)[/tex]
[tex]$\frac{1}{3}(x-1)=y+3$[/tex]
Multiply both sides by 3
[tex]$3 \cdot \frac{1}{3}(x-1)=3 y+3 \cdot 3$[/tex]
Simplify
[tex]$x-1=3 y+9$[/tex]
Add 1 to both sides
[tex]$$x-1+1=3 y+9+1$$[/tex]
Simplify
[tex]$$x=3 y+10$$[/tex]
y= 3.33 (Approx 3)
The two different lines that cross each other at a 90° angle are called perpendicular lines. Have you observed any similarities between the walls' intersecting corners, such as the letter "L"? They are parallel lines, which are straight lines that cross each other at the proper angle.
If two lines cross at a 90° angle, we say that they are perpendicular to one another.
the vertex's matching angle is a right angle. All crossing lines are not necessarily perpendicular to one another, but perpendicular lines always cross each other. Perpendicular lines have two key characteristics.
In every case, perpendicular lines cross or intersect.
Any two perpendicular lines will always intersect at an angle of 90 degrees.
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How long would it take a 1000W heater to melt 1.00kg of ice at -20.0°C, assuming all the energy from the heater is absorbed by the ice? (a) 4.18 s(b) 41.8 s (c) 5.55 min (d) 6.25min(e) 38.4min
Answer:
Heat for -20 to zero = .48 * 1000 = 480 calories
Heat to melt ice = 1000 * 79.7 = 79700 calories
Total calories required = 80,200 calories
80,200 cal * 4.19 J/cal = 336,000 J
336000 J / 1000 J/sec = 336 sec
336 sec / 60 sec/min = 5.6 min
(c - 5.55 min)
a holistic overview of underground hydrogen storage: influencing factors, current understanding, and outlook raza
a holistic overview of underground hydrogen storage is all three.
What is the best way to store hydrogen?Physically, hydrogen can be kept as either a gas or a liquid. Usually, high-pressure tanks are needed for gas storage (5000–10,000 psi tank pressure). Since hydrogen's boiling point at one atmosphere of pressure is -252.8°C, storage of hydrogen as a liquid necessitates cryogenic temperatures.
Method to store hydrogen :There are different ways and ways of storing hydrogen: 1) high-pressure gas cylinders (up to 800 bar), 2) cryogenic tanks with liquid hydrogen at 21 K, 3) hydrogen adsorbed on materials with a large specific surface area (at T100 K), and 4) absorbed on interstitial sites in a host metal (at ambient pressure).
What is the purpose of hydrogen storage?In applications such as fixed power, portable power, and transportation, hydrogen storage is a crucial enabling technology for the development of hydrogen and fuel cell technologies.
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Q|C Spherical waves of wavelength 45.0cm propagate outward from a point source. (b) Explain how the amplitude at a distance of 240cm compares with the amplitude at a distance of 60.0cm.
The difference between the amplitude at a distance of 60.0 cm and 240 cm is I240 = 16×I60
A240=4×I60
Δ∅240=4.Δ∅60
We are given distance of the center of the source for two waves:
D1=240 cm
D2=60.0 cm
b) Calculating how their amplitude compares:
[tex]A_{240} =\sqrt{\frac{I_{240} }{I_{60} } } .A_{60}[/tex]
[tex]=\sqrt{16} .A_{60}[/tex]
[tex]A_{240} = 4. A_{60}[/tex]
How can you determine a wave's phase?
The period, or length of each cycle, is determined by dividing the frequency by 1, so 1/100 corresponds to a period of 0.01 seconds. The phase shift equation is given by ps = 360 * td / p, where td is the time interval between waves, p is the wave period, and ps is the phase shift in degrees.
Phase: The "Phase" of a waveform refers to the location of the moving particle and is expressed in "Radians or degrees."
Phase difference, also known as "Phase angle," is the amount of time that one wave precedes or follows another.
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What is the difference between “q” and “Q” in physics?
Answer:
Big Q represents the source charge which creates the electric field. Little q represents the test charge which is used to measure the strength of the electric field at a given location surrounding the source charge.
The source charge, or Big Q, is what generates the electric field. Little q stands for the test charge, that is used to gauge the intensity of the electromagnetic field around the source charge at a certain position.
What is electric charge?Charged material experiences a force when it is exposed to an electromagnetic field because of the physical characteristic of electric charge.
You can have a positive or negative electric charge. Unlike charges attract one another, while like charges repel one another. Neutral refers to an object that carries no net charge.
Classical electrodynamics, the name given to early understanding of how charged particles interact, is still accurate for issues that do not call for taking into account quantum phenomena.
Electric current is a conserved attribute, meaning that the net charge—that is, the sum of the positive and negative charges in an isolated system—cannot change.
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An ion rocket engine produces 1 newton of thrust. What acceleration can it give to a space probe with a mass of 1000kg?.
The ion rocket engine give an acceleration to the space probe of: 0.001 m/s²
To solve this exercise, the formula and procedure to be applied is:
F = m * a
Where:
m = massF = Forcea = accelerationInformation about the problem:
F= 1 N1 N = kg * m/s²m = 1000kga= ?Applying the force formula and isolating the acceleration, we get:
F = m * a
a = F/m
a = 1 N /1000kg
a = 1 kg * m/s² / 1000kg
a = 0.001 m/s²
What is force?It is the physical magnitude that expresses the effort necessary to move the mass of one kilogram with an acceleration of one meter per second squared, this is expressed in units of the international system in Newton.
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The charge imbalance that results from this movement of charge will generate an additional electric field in the region within the rod. In what direction will this field point?.
It will point to the left and oppose the initially applied field the correct option is B.
What is an electric field?The term "electric field" refers to the physical field that surrounds electrically charged particles and pulls or attracts all other charged particles nearby. Additionally, it describes the physical environment of a system of charged particles.
Let the electric field point to the right and the charge be positive. A positive charge will build to the right and the overly positive charge will be present there when the charge moves to the right in the field. In opposition to the external electric field, this new charge distribution will produce a field to the left.
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Because most particles fired at metal foil passed straight through, rutherford concluded that.
Answer:
Rutherford deduced that atoms were mostly empty space
Explanation:
how was mount Everest made? Please i am handing out 100 points
Answer:
Mount Everest formed from a tectonic smashup between the Indian and Eurasian tectonic plates tens of millions of years ago.
Explanation:
a commercial airliner flew 20,000 km nonstop from seattle to kuala lumpur at an average speed of 900 km/hr. if its average mass was 140,000 kg, what was its average kinetic energy? (we take an average because the mass of the airplane changes as it exhausts burnt fuel.)
2.5 10 9 J of the 1.034 10 10 J total energy is kinetic energy, and 7.84 10 9 J is potential energy.
Is kinetic energy at a constant temperature?The average kinetic energy of the particles in an item is measured by its temperature. These particles move more quickly as the temperature rises. It is not the worst definition, but it is also not the finest.
The average kinetic energy (K) is determined by multiplying the RMS speed (vrms) by the square of the mass (m) of each gas molecule.
Thus, it may be inferred that the temperature is the single factor affecting the average kinetic energy of the molecules in a thermalized sample of gas.
A substance's temperature is directly related to the average kinetic energy of its particles. Because the particles' mass remains constant, they must travel faster as the planet warms.
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a toaster uses a nichrome heating coil and operates at 120 v. when the toaster is turned on at 20oc, the current in the cold coil is 1.5 a. when the coil warms up, the current has a value of 1.3 a. if the thermal coefficient of resistivity for nichrome is 4.5 x 10-4 1/co, what is the temperature of the coil?
If the thermal coefficient of resistivity for nichrome is 4.5 x 10-4 1/co, the temperature of the coil of the coil is 0.56 a.
What is resistivity?Resistivity is a central property of a material, and it shows how unequivocally the material opposes or transmits electric flow. A low resistivity is an obvious sign of a material which promptly permits electric flow. The resistivity increments implies that the conductivity of the material abatements. For metals or transmitters, it is said that they have a positive temperature co effective. The worth α is positive. Electrical resistivity is a property interesting to each material, which is fundamental to comprehend prior to making and planning electrical and electronic frameworks.
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a pot of stew is placed on a stove to heat. the temperature of the liquid reaches 170°f, and then the pot is taken off the burner and placed on a kitchen counter. the temperature of the air in the kitchen is 76°f. if k
If k = 0.34, the temperature of the liquid after 7 hours will be T(t) = 84.7°F.
We can solve the above problem using Newton's Law of Cooling.
According to this Law, the rate at which a hot body loses heat is directly proportional to the difference between the temperature of the hot body and that of its surroundings.
T(t) = [tex]T_{s}[/tex] + ([tex]T_{0}[/tex] - [tex]T_{s}[/tex])[tex]e^{-kt}[/tex]
where,
t= time
T(t) = temperature of the given body at time t
[tex]T_{s}[/tex] = surrounding temperature
[tex]T_{o}[/tex] = initial temperature of the body
k = constant
Substituting the values we get,
T(t) = 76 + (170-76)[tex]e^{(-0.34)(7)}[/tex]
T(t) = 84.7°F
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A conductor carrying a current I = 15.0 A is directed along the positive x axis and perpendicular to a uniform magnetic field. A magnetic force per unit length of 0.120 N/m acts on the conductor in the negative y direction. Deter- mine (a) the magnitude
The magnitude of the magnetic field in the region through the current passes is 8×10⁻³ T.
What is a magnetic field?The magnetic field is defined as the field the magnetic materials generate or when an electric charge moves in a field region that generates the magnetic field.
As we know:
F = ilB
F is the magnetic force
i is the current
l is the length
B is the magnitude of the magnetic field
Here F/l = 0.120 N/m
i = 15 A
B = (F/l)(1\i)
B = (0.120)(1/15)
B = 0.120/15
B = 8×10⁻³ T
Thus, the magnitude of the magnetic field in the region through the current passes is 8×10⁻³ T.
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A ball starts from rest and rolls down a 5.0m long frictionless ramp. It accelerates at 3.5m/s^. when it reaches the bottom, it rolls across a frictionless horizontal surface at a constant speed for an additional 3.0 s before striking a wall. what is the total distance travelled by the ball
Using uniform motion equation , the total distance travelled by the ball is 22.74m.
It is known as uniform motion when an object moves in a straight path at a constant speed. This indicates that the body's velocity stays constant as it travels the same distance in the same amount of time. The body will not accelerate in the case of uniform rectilinear motion. In this case, the object's average speed will be equal to its real speed.
Using equation of motion ;
[tex]s = ut +\frac{1}{2} at^{2}[/tex]
plugging in the values we get:
s = 22.74m
Therefore, using uniform motion equation , the total distance travelled by the ball is 22.74m.
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Two identical loudspeakers are placed on a wall 2.00 m apart. A listener stands 3.00m from the wall directly in front of one of the speakers. A single oscillator is driving the speakers at a frequency of 300 Hz.(b) What If? What is the frequency closest to 300 Hz to which the oscillator may be adjusted such that the observer hears minimal sound?
283 Hz is the frequency closest to 300 Hz to which the oscillator may be adjusted such that the observer hears a minimal sound.
Δr = 1/2λ
= v/2f
f = v / 2Δr
= 343 / 2(√13 - 3.00)
= 283 Hz.
Frequency is a vital parameter used in technological know-how and engineering to specify the temporal fee of exchange located in oscillatory and periodic phenomena, including mechanical vibrations, audio signals (sound), radio waves, and light.
The wide variety of intervals or cycles consistent with 2d is referred to as frequency. The SI unit for frequency is the hertz (Hz). One hertz is the same as one cycle in keeping with 2nd.
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which phrase best describes the structure of an atom
A. a solid ball of protons, neutrons, and electrons
B. A nucleus surrounded by an electron cloud
C. A nucleus by electrons in set orbits
D. A core of protons surrounded by an electron cloud
The phrase which best describes the structure of an atom from the answer choices given above is a nucleus surrounded by an electron cloud.
The correct answer choice is option b
This means that an atom consist of a centrally placed nucleus in which electrons revolves around it. The nucleus of any given atom consist of protons and neutrons. Electrons revolve round the nucleus of any atoi
What is an atom?An atom is a smallest particle of an element that takes part in chemical reaction.
Atom is divided into three basic parts:
Protons: They are positively charged subatomic particle forming part of the nucleus of an atom and determining the atomic number of an element, composed of two up quarks and a down quark.Neutrons: This is a subatomic particle forming part of the nucleus of an atom and having no charge; it is a combination of an up quark and two down quarks.Electrons: It is a subatomic particle having a negative charge and orbiting round the nucleus of any given atom of an element; the flow of electrons in a conductor constitutes electricity.So therefore, the phrase which best describes the structure of an atom from the answer choices given above is a nucleus surrounded by an electron cloud.
The correct answer choice is option b
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Jaronda is a member of a dance team. As a fundraiser, she and the other members of the team decide that she will use the team’s money to buy flowers in bulk, sell the flowers individually to students with her school’s permission, and return the team’s money plus any profits she makes. What is the MOST accurate name for Jaronda’s role?
A.
project manager
B.
network facilitator
C.
data manager
D.
systems operator
The role described here is that of a project manager.
Who is a project manager?A project manager is one who is saddled with the responsibility of seeing to the actualization of a project. The project manager is the one that plans, manages and executes the project.
Looking at the description of Jaronda’s role, we can see that she is in charge of the planning, execution and implementation of the project. This means that she has taken up the role of the project manager.
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Bubba-Joe carries out a careful investigation to determine the melting point of salicylic acid, and concludes that the value
is 161.4 degrees Celcius.
The melting point of salicylic acid is known very well as 158.6 degrees Celcius.
What is Bubba's percent error?
Bubba-Joe carries out a careful investigation to determine the melting point of salicylic acid, and concludes that the value is 161.4 degrees Celsius. The melting point of salicylic acid is known very well as 158.6 degrees Celsius. Bubba's percent error will be 1.74 %
Percentage error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words, the percent error is the relative error multiplied by 100.
estimated value of melting point = 161.4 °C
true value of melting point = 158.6 °C
percent error = ((true value - expected value) / expected value) * 100
= ((158.6 - 161.4 ) / 161.4 ) * 100
= 1.74 %
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Suppose you are transported to a planet with twice the mass of earth, but the same radius of earth. Your weight would __________ by a factor of __________.
According to gravitational force, the weight would be greater by a factor of 2.
We need to know about gravitational force to solve this problem. The gravitational force is the force caused by two masses objects. The magnitude of gravitational force can be determined as
F = G.m1.m2 / R²
where F is the gravitational force, G is the gravitational constant (6.674 × 10¯¹¹ Nm²/kg²), m1 and m2 are the mass of the object and R is the radius.
From the question above, we know that
m1 = m
m2 = 2m1 = 2m
R1 = R2 = R
Gravitational force is proportional to mass
F1 ~ M
Hence, the ratio of weight is
F2 / F1 = m2 / m1
F2 / F1 = 2m / m
F2 / F1 = 2
Hence, the weight would be greater by factor of 2 .
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Once its rockets have ceased firing, an intercontinental ballistic missile will follow a path that is best described as.
Once its rockets have ceased firing, an Intercontinental Ballistic Missile will follow a path that is best described as an ellipse with the center of the Earth at one focus.
As the ellipse is the set of points, on a plane whose distance from two fixed points sums up to constant, in That describes all free-fall paths near Earth, it got The Major Axis which is the longest diameter and the widest part of the ellipse it basically starts from one side of the ellipse crossing the center to the other side and the Minor Axis which is the shortest diameter and present at the narrowest part of the ellipse.As the ellipse explains all free-fall paths near Earth (free-fall is referred to as the acceleration of objects toward the Earth when dropped at rest)
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A particle with electric charge q moves along a straight line in a uniform electric field →
E with speed u . The electric force exerted on the charge is qE . The velocity of the particle and the electric field are both in the x direction.(a) Show that the acceleration of the particle in the x direction is given bya = du/dt = qE/m (1 - u²/c²)³/²
A physical field called an electric field surrounds electrically charged particles and attracts or repels all other charged particles nearby. The physical field of a system of charged particles can also be referred to as the electric field.
In a uniform electric field E, a particle with electric charge q moves in a straight line. The speed of the particle is u.
The electric force exerted in the charge is qE.
The electric field and the velocity of the particle are both in the x direction.
Now, the momentum of the particle at any speed is given as:
p = γ mu = mu / √[ 1 - (u/c)²]
By Newton's law,
F =qE
F = dp/dt
qE = (d/dt) [ mu [ 1 - (u/c)²]^(-1/2)
qE = m [ 1 - (u²/c²)]^{-1/2} du/dt + (1/2) mu[1 - (u²/c²)]⁻³/² (2u/c²) du/dt
Therefore,
qE/m = (du/dt) [( 1 - (u²/c²) + (u²/c²) ) / ( 1 - (u²/c²)⁻³/²
Now,
a = (du/dt) = (qE/m) (( 1 - (u²/c²) )⁻³/²
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