Answer:
a) the geometric optics is adequate (Ray)
b) wave optics should be used for the second case
Explanation:
In general, the approximation of the geometric optics is adequate when the dimensions of the system are much greater than the wavelengths and the wave optics should be used for cases in which the size of the system is from the length of the wave.
Let's apply this to our case
a) in this case the size of the system is d = 26 cm=0.26 m and the wavelength is alm = 530 10⁺⁹ m
in this case
d >>> λ
therefore the geometric optics is adequate (Ray)
b) in this case the system has a size of d = 114 10⁻⁹ m with a wavelength of λ= 722 nm
for this case d of the order of lam
therefore wave optics should be used for the second case
One consequence of turbulence is mixing. Different layers of fluid flow cross over one another very easily, and get blended together. This is another kind of "transport", which lets atoms which might have started out all in one place get uniformly mixed around. Would you expect turbulent mixing to happen most easily in:
A. waterB. motor oilC. airD. honey
Answer:
Turbulence mixing will happen mostly in air
Explanation:
Rotational dynamics about a fixed axis: A solid uniform sphere of mass 1.85 kg and diameter 45.0 cm spins about an axle through its center. Starting with an angular velocity of 2.40 rev/s, it stops after turning through 18.2 rev with uniform acceleration. The net torque acting on this sphere as it is slowing down is closest to:A) 0.149 N m. B) 0.0620N m. C) 0.00593 N m. D) 0.0372 N m. E) 0.0466 N·m
Answer:
D) 0.0372 N m
Explanation:
r = 45/2 cm = 22.5 cm = 0.225 m
As 1 revolution = 2π rad we can convert to radian unit
2.4 rev/s = 2.4 * 2π = 15.1 rad/s
18.2 rev = 18.2 * 2π = 114.35 rad
We can calculate the angular (de)acceleration using the following equation of motion
[tex]-\omega^2 = 2\alpha \theta [/tex]
[tex]- 15.1^2 = 2*\alpha * 114.35[/tex]
[tex]\alpha = \frac{-15.1^2}{2*114.35} = -0.994 rad/s^2[/tex]
The moment of inertia of the solid uniform sphere is
[tex]2mr^2/5 = 2*1.85*0.225^2/5 = 0.0375 kgm^2[/tex]
The net torque acting on this according to Newton's 2nd law is
[tex]T = I\alpha = 0.0375 * 0.994 = 0.0372 Nm[/tex]
Answer:
(D) The net torque acting on this sphere as it is slowing down is closest to 0.0372 N.m
Explanation:
Given;
mass of the solid sphere, m = 1.85 kg
radius of the sphere, r = ¹/₂ of diameter = 22.5 cm
initial angular velocity, ω = 2.40 rev/s = 15.08 rad/s
angular revolution, θ = 18.2 rev = 114.37 rad
Torque on the sphere, τ = Iα
Where;
I is moment of inertia
α is angular acceleration
Angular acceleration is calculated as;
[tex]\omega_f^2 = \omega_i^2 +2 \alpha \theta\\\\0 = 15.08^2 + (2*114.37)\alpha\\\\\alpha = \frac{-15.08^2}{(2*114.37)} = -0.994 \ rad/s^2\\\\\alpha = 0.994 \ rad/s^2 \ (in \ opposite \ direction)[/tex]
moment of inertia of solid sphere, I = ²/₅mr²
= ²/₅(1.85)(0.225)²
= 0.03746 kg.m²
Finally, the net torque on the sphere is calculated as;
τ = Iα
τ = 0.03746 x 0.994
τ = 0.0372 N.m
Therefore, the net torque acting on this sphere as it is slowing down is closest to 0.0372 N.m
An electron follows a helical path in a uniform magnetic field given by:B =(20i^−50j^−30k^)mTAt time t = 0, the electron's velocity is given by:⃗v=(40i^−30j^+50k^)m/sa. What is the angle ϕ between v and B. The electron's velocity changes with time. Do b. its speed c. the angled. What is the radius of the helical path?
Answer:
a) 1.38°
b) 7.53*10^11 m/s/s
c) 6.52*10^-9m
Explanation:
a) to find the angle you can use the dot product between two vectors:
[tex]\vec{v}\cdot\vec{B}=vBcos\theta\\\\\theta=cos^{1}(\frac{\vec{v}\cdot\vec{B}}{vB})[/tex]
v: velocity of the electron
B: magnetic field
By calculating the norm of the vectors and the dot product and by replacing you obtain:
[tex]B=\sqrt{(20)^2+(50)^2+(30)^2}=61.64mT\\\\v=\sqrt{(40)^2+(30)^2+(50)^2}=70.71m/s\\\\\vec{v}\cdot\vec{B}=[(20)(40)+(50)(30)-(30)(50)]mTm/s=800mTm/s\\\\\theta=cos^{-1}(\frac{800*10^{-3}Tm/s}{(70.71m/s)(61.64*10^{-3}T)})=cos^{-1}(0.183)=1.38\°[/tex]
the angle between v and B vectors is 1.38°
b) the change in the speed of the electron can be calculated by the change in the momentum in the following way:
[tex]\frac{dp}{dt}=F_e=qvBsin\theta\\\\\frac{dp}{dt}=(1.6*10^{-19}C)(70.71m/s)(61.64*10^{-3}T)(sin(1.38\°))=6.85*10^{-19}N[/tex]
due to the mass of the electron is a constant you have:
[tex]\frac{dp}{dt}=\frac{mdv}{dt}=6.85*10^{-19}N\\\\\frac{dv}{dt}=\frac{6.85*10^{-19}N}{9.1*10^{-31}kg}=7.53*10^{11}(m/s)/s[/tex]
the change in the speed is 7.53*10^{11}m/s/s
c) the radius of the helical path is given by:
[tex]r=\frac{m_ev}{qB}=\frac{(9.1*10^{-31}kg)(70.71m/s)}{(1.6*10^{-19}C)(61.64*10^{-3}T)}=6.52*10^{-9}m[/tex]
the radius is 6.52*10^{-9}m
Train cars are coupled together by being bumped into one another. Suppose two loaded train cars are moving toward one another, the first having a mass of 260000 kg and a velocity of 0.32 m/s in the horizontal direction, and the second having a mass of 52500 kg and a velocity of -0.14 m/s in the horizontal direction. What is their final velocity?
Answer:
0.243 m/s
Explanation:
From law of conservation of motion,
mu+m'u' = V(m+m')................. Equation 1
Where m = mass of the first car, m' = mass of the second car, initial velocity of the first car, u' = initial velocity of the second car, V = Final velocity of both cars.
make V the subject of the equation
V = (mu+m'u')/(m+m')................. Equation 2
Given: m = 260000 kg, u = 0.32 m/s, m' = 52500 kg, u' = -0.14 m/s
Substitute into equation 2
V = (260000×0.32+52500×(-0.14))/(260000+52500)
V = (83200-7350)/312500
V = 75850/312500
V = 0.243 m/s
Pease circle the statements incompatible with the Kelvin-Planck Statement. (A) No heat engine can have a thermal efficiency of 100%. (B) It is impossible for any device that operates on a cycle to receive heat from a single reservoir and produce a net amount of work without rejecting waste heat to a cool reservoir. (C) The impossibility of having a 100% efficient heat engine is always due to friction or other dissipative effects such as the system is perfectly designed or the material needed for the system design is not available. (D) Any device that violates the Kelvin-Planck statement also violates the Clausius statement, and vice versa.
Answer:
(C) The impossibility of having a 100% efficient heat engine is always due to friction or other dissipative effects such as the system is perfectly designed or the material needed for the system design is not available.
Explanation:
The above option was never stated in the law
The resistance of physiological tissues is quite variable. The resistance of the internal tissues of humans, primarily composed of salty solutions, is quite low. Here the resistance between two internal points in the body is on the order of 100 ohms. Dry skin, however, can have a very high resistance, with values ranging from thousands to hundreds of thousands of ohms. However, if skin is wet, it is far more conductive, and so even contact with small voltages can create large, dangerous currents though a human body. (For example, although there is no specific minimum current that is lethal, currents generally exceeding a couple tenths of Amps may be deadly.)
Assuming that electrocution can be prevented if currents are kept below 0.1 A, and assuming the resistance of dry skin is 100,000 ohms, what is the maximum voltage with which a person could come into contact while avoiding electrocution? (Of course, all bets are off and things become far more dangerous if this person's skin is wet, which can reduce the resistance by more than a factor of 100.)
Given Information:
Current = I = 0.1 A
Resistance = R = 100 kΩ
Required Information:
Voltage = V = ?
Answer:
Voltage = V = 1000 V
Step-by-step explanation:
We know that electrocution depends upon the amount of current flowing through the body and the voltage across the body.
V = IR
Where I is the current flowing through the body and R is the resistance of body.
If electrocution can be avoided when the current is below 0.1 A then
V = 0.1*10×10³
V = 1000 Volts
Therefore, 1000 V is the maximum voltage with which a person could come into contact while avoiding electrocution, any voltage more than 1000 V may result in fatal electrocution.
Also note that human body has very low resistance when the body is wet therefore, above calculated value would not be applicable in such case.
Consider the steel spring in the illustration.
(a) Find the pitch, solid height, and number of active turns.
(b) Find the spring rate. Assume the material is A227 HD steel.
(c) Find the force Fs required to close the spring solid.
(d) Find the shear stress in the spring due to the force Fs.
Answer:
Explanation:
find the answer below
what is the formula for braking force?
Answer:
Explanation:
The braking force in the context of stopping a vehicle involves the frictional force exerted by the brakes, and it's related to the mass and deceleration of the vehicle. Calculations often use Newton's second law, F = ma, for force, or the work-energy principle, W = F * d * cos(θ), to determine stopping distances.
The formula for braking force isn't provided with a single standard equation, as it relates to several physical quantities, such as friction, mass, and acceleration. However, in the context of vehicle braking, we often analyze the frictional force exerted by the brakes on the car's wheels to determine stopping distance or to calculate the deceleration of the vehicle. The basic physics equation used in this context is Newton's second law, F = ma, where F is the force, m is the mass of the vehicle, and a is the acceleration (which will be negative when braking).
Based on the provided contexts, if a car has a mass (m) and applies a braking force (F), and you want to find the stopping distance (d), you can also use energy equations. The work done by the brakes (W) is equal to the change in the car's kinetic energy, which can be calculated using the equation W = F * d * cos(θ), where θ is the angle at which the force is applied - typically 0 degrees, as the force is in the opposite direction of motion.
In 1958, Meselson and Stahl conducted an experiment to determine which of the three proposed methods of DNA replication was correct. Identify the three proposed models for DNA replication. Conservative Semiconservative Dispersive Answer Bank The Meselson and Stahl experiment starts with E. coli containing 15 N / 15 N labeled DNA grown in 14 N media. Which result did Meselson and Stahl observe by sedimentation equilibrium centrifugation to provide strong evidence for the semiconservative model of DNA replication? Both the first and second generation have both 15 N / 15 N DNA and 14 N / 14 N DNA. No hybrid 15 N / 14 N DNA was observed. The first generation has hybrid 15 N / 14 N DNA and the second generation has both hybrid 15 N / 14 N DNA and 14 N / 14 N DNA. No 15 N / 15 N DNA was observed. The first generation has hybrid 15 N / 14 N DNA and the second generation has hybrid 15 N / 14 N DNA. No 15 N / 15 N DNA nor 14 N / 14 N DNA was observed.
Answer:
Explanation:
The original has hybrid 15N/14N DNA, and the second generation has both hybrid 15N/14N DNA and 14N/14N DNA. No 15N/15N DNA was observed. In this experiment:
Nitrogen is a significant component of DNA. 14N is the most bounteous isotope of nitrogen, however, DNA with the heavier yet non-radioactive and 15N isotope is likewise practical.
E. coli was developed for several generations in a medium containing NH4Cl with 15N. When DNA is extracted from these cells and centrifuged on a salt density gradient, the DNA separates at which its density equals to the salt arrangement. The DNA of the cells developed in 15N medium had a higher density than cells developed in typical 14N medium. After that, E. coli cells with just 15N in their DNA were transferred to a 14N medium.
DNA was removed and compared to pure 14N DNA and 15N DNA. Immediately after only one replication, the DNA was found to have an intermediate density. Since conservative replication would result in equal measures of DNA of the higher and lower densities yet no DNA of an intermediate density, conservative replication was eliminated. Moreso, this result was consistent with both semi-conservative and dispersive replication. Semi conservative replication would result in double-stranded DNA with one strand of 15N DNA, and one of 14N DNA, while dispersive replication would result in double-stranded DNA with the two strands having mixtures of 15N and 14N DNA, either of which would have appeared as DNA of an intermediate density.
The DNA from cells after two replications had been completed and found to comprise of equal measures of DNA with two different densities, one corresponding to the intermediate density of DNA of cells developed for just a single division in 14N medium, the other corresponding to DNA from cells developed completely in 14N medium. This was inconsistent with dispersive replication, which would have resulted in a single density, lower than the intermediate density of the one-generation cells, yet at the same time higher than cells become distinctly in 14N DNA medium, as the first 15N DNA would have been part evenly among all DNA strands. The result was steady with the semi-conservative replication hypothesis. The semi conservative hypothesis calculates that each molecule after replication will contain one old and one new strand. The dispersive model suggests that each strand of each new molecule will possess a mixture of old and new DNA.
During a track and field event, a metal javelin (not infinitesimally thin) is thrown due east and parallel to the ground. At the field where the event took place, the magnetic field is running straight up and perpendicular to the ground. In which direction will the current flow in the metal object?
Answer:
There is no induced current
Explanation:
[Find the attachment]
Find the corresponding initial value problem of the following spring-mass systems, that if solved, would give the position u of the mass at any time t. Use 9.8 m/s 2 for the acceleration due to gravity. DO NOT SOLVE THE IVP. A mass of 60 kg stretches a spring 19.6 m. The mass is acted on by an external force of 6 sin(4t) N and moves in a medium that imparts a viscous force of 8 N when the speed of the mass is 16 cm/s. The mass is pushed up 5 cm and set in motion an initial downward velocity of 2 cm/s. Write the IVP so that u would be in meters if solved.
Answer:
Explanation:
The picture attached shows the full explanation
German physicist Werner Heisenberg related the uncertainty of an object's position ( Δ x ) to the uncertainty in its velocity ( Δ v ) Δ x ≥ h 4 π m Δ v where h is Planck's constant and m is the mass of the object. The mass of an electron is 9.11 × 10 − 31 kg. What is the uncertainty in the position of an electron moving at 2.00 × 10 6 m/s with an uncertainty of Δ v = 0.01 × 10 6 m/s ?
According to the information given, the Heisenberg uncertainty principle would be given by the relationship
[tex]\Delta x \Delta v \geq \frac{h}{4\pi m}[/tex]
Here,
h = Planck's constant
[tex]\Delta v[/tex] = Uncertainty in velocity of object
[tex]\Delta x[/tex] = Uncertainty in position of object
m = Mass of object
Rearranging to find the position
[tex]\Delta x \geq \frac{h}{4\pi m\Delta v}[/tex]
Replacing with our values we have,
[tex]\Delta x \geq \frac{6.625*10^{-34}m^2\cdot kg/s}{4\pi (9.1*10^{-31}kg)(0.01*10^6m/s)}[/tex]
[tex]\Delta x \geq 5.79*10^{-9}m[/tex]
Therefore the uncertainty in position of electron is [tex]5.79*10^{-9}m[/tex]
8. In the procedure for measuring the frequency of oscillation, we are instructed to pull downward on the hanging mass about 10 cm. If we performed the experiment a second time and deliberately pulled down on the hanging mass by 15 cm, would our period change? Justify your answer. (5 points)
Answer:
No
Explanation:
The frequency of oscillation of spring mass system is independent of its amplitude.
The frequency of oscillation will not change because it is not a function of amplitude.
What is the spring-mass system?In a real spring-mass system, the spring has a non-negligible mass m. Since not all of the spring's length moves at the same velocity v as the suspended mass M,
To determine the frequency of oscillation, the effective mass of the spring is defined as the mass that needs to be added to M to correctly predict the behaviour of the system.
For vertical springs, however, we need to remember that gravity stretches or compresses the spring beyond its natural length to the equilibrium position. After we find the displaced position
Thus the frequency of oscillation will not change because it is not a function of amplitude.
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A soft-drink manufacturer purchases aluminum cans from an outside vendor. A random sample of 70 cans is selected from a large shipment, and each is tested for strength by applying an increasing load to the side of the can until it punctures. Of the 70 cans, 53 meet the specification for puncture resistance.
Answer:
lol..WHAT IS THE QUESTION?!
Explanation:
A string is wrapped tightly around a fixed pulley that has a moment of inertia of 0.0352 kgm2 and a radius of 12.5 cm. A mass of 423 grams is attached to the free end of the string. With the string vertical and taut, the mass is gently released so it can descend under the influence of gravity. As the mass descends, the string unwinds and causes the pulley to rotate, but does not slip on the pulley. What is the speed (in m/s) of the mass after it has fallen through 1.25 m
Answer:
the speed (in m/s) of the mass after it has fallen through 1.25 m is 1.968 m/s
Explanation:
Given that :
Mass attached to the free end of the string, m = 423 g = 0.423 kg
Moment of inertia of pulley, I = 0.0352 kg m²
Radius of the pulley, r = 12.5 cm = 0.125 meters
Depth of fallen mass, h = 1.25 m
Acceleration due to gravity, g = 9.8 m/s²
Change in potential energy = mgh
= 0.423 × 9.8 × 1.25
=5.18175 J
From the question, we understand that the change in potential energy is used to raise and increase the kinetic energy of hanging mass and the rotational kinetic energy of pulley.
As such;
[tex]5.18175 \ J= \frac{1}{2}mv^2 + \frac{1}{2} I \omega^2[/tex]
where;
[tex]\omega[/tex] is the angular velocity of the pulley
v is the velocity of the mass after falling 1.25 m
where:
[tex]v = r \omega[/tex]
[tex]\omega = \frac{v}{r}[/tex]
replacing [tex]\omega = \frac{v}{r}[/tex] into above equation; we have:
[tex]5.18175 \ J= \frac{1}{2}mv^2 + \frac{1}{2} I( \frac{v}{r})^2[/tex]
[tex]5.18175= (\frac{1}{2} m + \frac{1}{2}* (\frac{I}{r^2})v^2 \\ \\ v^2 = \frac{5.18175}{0.5*0.423+0.5*\frac{0.0352}{0.1252}} \\ \\ v^2 = 3.873047 \\ \\ v = 1.968 \ m/s[/tex]
Thus, the speed (in m/s) of the mass after it has fallen through 1.25 m is 1.968 m/s
the speed (in m/s) of the mass after it has fallen through 1.25 m is 1.968 m/s
SpeedWhat all information we have?
Mass attached to the free end of the string, m = 423 g = 0.423 kg
Moment of inertia of pulley, I = 0.0352 kg m²
Radius of the pulley, r = 12.5 cm = 0.125 meters
Depth of fallen mass, h = 1.25 m
Acceleration due to gravity, g = 9.8 m/s²
Change in potential energyChange in potential energy = mgh
Change in potential energy = 0.423 × 9.8 × 1.25
Change in potential energy =5.18175 J
As such:
5.18175 J= mv²+1w²
where;
w is the angular velocity of the pulley
v is the velocity of the mass after falling 1.25 m
v=rw
w=v/r
Replacing into above equation;
5.18175 J=mv² + 1/2 (w/r²) ²
5.18175 = (m + /* (4) v²
v² = 3.873047
v² =1.968 m/s
Thus, the speed (in m/s) of the mass after it has fallen through 1.25 m is 1.968 m/s.
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When the temperature is at 30∘C, the A-36 steel pipe fits snugly between the two fuel tanks. When fuel flows through the pipe, the temperature at ends A and B rise to 130∘C and 80∘C, respectively. If the temperarture drop along the pipe is linear, determine the average normal stress developed in the pipe. Assume the walls of each tank acts as a spring, each having a stiffness of k=900 MN/m.
In a system where an A-36 steel pipe is snugly fit between two fuel tanks, the rise in fuel temperature will cause thermal stresses in the pipe due to the restraint from the fuel tanks. This is related to the thermal properties of the material and the rate of change due to temperature rising, from which the average normal stress can be calculated.
Explanation:Determining the average normal stress developed in an A-36 steel pipe when fuel flows through it at varying temperatures requires knowledge of thermal expansion and associated stress in materials. This is related to thermal properties and the rate of change due to temperature rise.
When temperature rises along the pipe such as mentioned, from room temperature to 130∘C and 80∘C, the steel pipe expands. However, the pipe is restrained by the fuel tanks acting as springs, leading to development of stress within the pipe. The average normal stress can be calculated by dividing the force exerted by the expansion (or contraction) by the cross-sectional area of the pipe:
F/A = σ
Where, F is the force and A is the cross-sectional area of the pipe. The force can be obtained from Hooke's law for springs (F = k Δx), where k is the stiffness of the tank walls acting as springs, and Δx is the change in length due to thermal expansion.
The average normal stress is a measure of the extent to which the pipe is going through physical changes due to thermal variations.
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A traveling wave on a string can be described by the equation : y = (5.26 ~\text{m}) \cdot \sin \big( (1.65 ~\frac{\text{rad}}{\text{m}})x - (4.64 ~\frac{\text{rad}}{\text{sec}})t +(1.33 ~\text{rad}) \big)y=(5.26 m)⋅sin((1.65 m rad )x−(4.64 sec rad )t+(1.33 rad)) How much time will it take for a peak on this traveling wave to propagate a distance of 5.00 meters along the length of the string?
Answer:
t = 1.77 s
Explanation:
The equation of a traveling wave is
y = A sin [2π (x /λ -t /T)]
where A is the oscillation amplitude, λ the wavelength and T the period
the speed of the wave is constant and is given by
v = λ f
Where the frequency and period are related
f = 1 / T
we substitute
v = λ / T
let's develop the initial equation
y = A sin [(2π / λ) x - (2π / T) t +Ф]
where Ф is a phase constant given by the initial conditions
the equation given in the problem is
y = 5.26 sin (1.65 x - 4.64 t + 1.33)
if we compare the terms of the two equations
2π /λ = 1.65
λ = 2π / 1.65
λ = 3.81 m
2π / T = 4.64
T = 2π / 4.64
T = 1.35 s
we seek the speed of the wave
v = 3.81 / 1.35
v = 2.82 m / s
Since this speed is constant, we use the uniformly moving ratios
v = d / t
t = d / v
t = 5 / 2.82
t = 1.77 s
A rectangular neoprene sheet has width W = 1.00 m and length L = 4.00 m. The two shorter edges are affixed to rigid steel bars that are used to stretch the sheet taut and horizontal. The force applied to either end of the sheet is F = 81.0 N. The sheet has a total mass M = 4.00 kg. The left edge of the sheet is wiggled vertically in a uniform sinusoidal motion with amplitude A = 10.0 cm and frequency f = 1.00 Hz. This sends waves spanning the width of the sheet rippling from left to right. The right side of the sheet moves upward and downward freely as these waves complete their traversal.
(A) Derive an expression for the velocity with which the waves move along the sheet. Express your answer in terms of the variables F, L, and M.
(B) What is the value of this speed for the specified choices of these parameters? Express your answer with the appropriate units.
Answer:
(a) [tex]\sqrt{FL/M}[/tex]
(b) [tex]9 ms^{-1}[/tex]
Explanation:
(a)
The speed of the wave depends on the type of the material. Here we have neoprene sheet so the speed of the wave will depend on the linear density of neoprene sheet. Linear Density is defined as Mass per unit length of the material (as materials of same type can have different thickness). The symbol used for the Linear Density is .
μ = Mass of the sheet / Length of the sheet
The speed of the wave in such material can be be found by using the equation:
[tex]\frac{1}{v^{2} } = {\frac{Linear Density}{Force} }[/tex] (where v is speed)
The equation can be rearranged:
v = [tex]\sqrt{Force/Linear Density}[/tex]
so,
v = sqrt(F/μ)
v = sqrt(F/ (M/L))
v = [tex]\sqrt{FL/M}[/tex] (answer)
(b)
Putting the values
F = 81 N
M = 4kg
L = 4m
v = [tex]\sqrt{FL/M}[/tex]
v = 9m/s
In an alcohol-in-glass thermometer, the alcohol column has length 12.66 cm at 0.0 ∘C and length 22.49 cm at 100.0 ∘C. Part A What is the temperature if the column has length 18.77 cm ? Express your answer using four significant figures. T = nothing ∘C Request Answer Part B What is the temperature if the column has length 14.23 cm ? Express your answer using four significant figures.
Answer:
[tex]62.1566632757\ ^{\circ}C[/tex]
[tex]15.9715157681\ ^{\circ}C[/tex]
Explanation:
[tex]\Delta T[/tex] = Change in termperature
[tex]\Delta L[/tex] = Change in length
We have the relation
[tex]\dfrac{\Delta L}{\Delta T}=\dfrac{22.49-12.66}{100-0}=\dfrac{18.77-12.66}{t-0}\\\Rightarrow t=\dfrac{18.77-12.66}{0.0983}\\\Rightarrow t=62.1566632757\ ^{\circ}C[/tex]
The temperature is [tex]62.1566632757\ ^{\circ}C[/tex]
[tex]\dfrac{\Delta L}{\Delta T}=\dfrac{22.49-12.66}{100-0}=\dfrac{14.23-12.66}{t-0}\\\Rightarrow t=\dfrac{14.23-12.66}{0.0983}\\\Rightarrow t=15.9715157681\ ^{\circ}C[/tex]
The temperature is [tex]15.9715157681\ ^{\circ}C[/tex]
(A)
According to the question,
The change in length will be:
= [tex]l_2-l_1[/tex]
= [tex]22.49-12.66[/tex]
= [tex]9.83 \ cm[/tex]
The change per degree will be:
= [tex]\frac{Change \ in \ length}{Temperature}[/tex]
= [tex]\frac{9.83}{100}[/tex]
= [tex]0.0983 \ cm/deg[/tex]
Now,
The change in length,
= [tex]18.77-12.66[/tex]
= [tex]6.11 \ cm[/tex]
hence,
The temperature,
= [tex]\frac{6.11}{0.0983}[/tex]
= [tex]62.2^{\circ} C[/tex]
(B)
The change in length,
= [tex]14.23-12.66[/tex]
= [tex]1.57 \ cm[/tex]
hence,
The temperature will be:
= [tex]\frac{1.57}{0.0983}[/tex]
= [tex]15.98^{\circ} C[/tex]
Thus the above answers are correct.
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A wire 3.22 m long and 7.32 mm in diameter has a resistance of 11.9 mΩ. A potential difference of 33.7 V is applied between the ends. (a) What is the current in amperes in the wire? (b) What is the magnitude of the current density? (c) Calculate the resistivity of the material of which the wire is made.
Answer:
(a) Current is 2831.93 A
(b) [tex]8.40A/m^2[/tex]
(c) [tex]\rho =15.52\times 10^{-9}ohm-m[/tex]
Explanation:
Length of wire l = 3.22 m
Diameter of wire d = 7.32 mm = 0.00732 m
Cross sectional area of wire
[tex]A=\pi r^2=3.14\times 0.00366^2=4.20\times 10^{-5}m^2[/tex]
Resistance [tex]R=11.9mohm=11.9\times 10^{-3}ohm[/tex]
Potential difference V = 33.7 volt
(A) current is equal to
[tex]i=\frac{V}{R}=\frac{33.7}{11.9\times 10^{-3}}=2831.93A[/tex]
(B) Current density is equal to
[tex]J=\frac{i}{A}[/tex]
[tex]J=\frac{2831.93}{4.20\times 10^{-5}}=8.40A/m^2[/tex]
(c) Resistance is equal to
[tex]R=\frac{\rho l}{A}[/tex]
[tex]11.9\times 10^{-3}=\frac{\rho \times 3.22}{4.20\times 10^{-5}}[/tex]
[tex]\rho =15.52\times 10^{-9}ohm-m[/tex]
A simple pendulum is made my attaching a rod of negligible mass to a 2.0 kg pendulum bob at the end. It is observed that on Earth, the period of small-angle oscillations is 1.0 second. It is also observed that on Planet X this same pendulum has a period of 1.8 seconds. How much does the pendulum bob weigh on Planet X
Final answer:
The weight of the pendulum bob on Planet X remains 2.0 kg, the same as on Earth, because the mass of the pendulum bob does not affect the period of a simple pendulum. The difference in periods indicates a change in gravitational strength, not mass.
Explanation:
The question revolves around understanding how the period of oscillation of a simple pendulum changes with gravity on different planets. Since the mass of the pendulum bob does not affect the period of a simple pendulum, which depends only on the length of the pendulum and the gravitational acceleration (g), the weight of the pendulum bob on Planet X would still be 2.0 kg, the same as on Earth. However, the difference in periods between Earth and Planet X indicates a difference in gravitational acceleration, implying that g on Planet X is weaker than on Earth. The formula for the period (T) of a simple pendulum is T = 2π√(l/g), where l is the length of the pendulum and g is the gravitational acceleration. Since the mass of the pendulum bob does not factor into this equation, the weight of the pendulum bob on Planet X remains the same, but its apparent weight will change according to the planet's gravitational pull.
A 2.13-kg object on a frictionless horizontal track is attached to the end of a horizontal spring whose force constant is 5.00 N/m. The object is displaced 3.54 m to the right from its equilibrium position and then released, initiating simple harmonic motion. (a) What is the force (magnitude and direction) acting on the object 3.50 s after it is released
Answer:
17.54N in -x direction.
Explanation:
Amplitude (A) = 3.54m
Force constant (k) = 5N/m
Mass (m) = 2.13kg
Angular frequency ω = √(k/m)
ω = √(5/2.13)
ω = 1.53 rad/s
The force acting on the object F(t) = ?
F(t) = -mAω²cos(ωt)
F(t) = -2.13 * 3.54 * (1.53)² * cos (1.53 * 3.50)
F(t) = -17.65 * cos (5.355)
F(t) = -17.57N
The force is 17.57 in -x direction
The switch in the circuit has been in the left position for a long time. At t=0 it moves to the right position and stays there.a. Write the expression for the capacitor voltage v(t), fort≥0. b. Write the expression for the current through the 2.4kΩ resistor, i(t), fort≥0+.
Answer:
Pls refer to attached file
Explanation:
Magnetic fields and electric fields are identical in that they both-
Answer:
Similarities between magnetic fields and electric fields: Electric fields are produced by two kinds of charges, positive and negative. Magnetic fields are associated with two magnetic poles, north and south, although they are also produced by charges (but moving charges). Like poles repel; unlike poles attract.
they attract each other
Explanation:
Double the resistance of the resistor by changing it from 10 Ω to 20 Ω. What happens to the current flowing through the circuit?
Answer:
2 amps
Explanation:
you just divide
The power liens that run through your neighborhood carry alternating currents that reverse direction 120 times per second. As current changes so does magnetic field. If you put a loop of wire up near the power line to extract power by tapping the magnetic field, sketch how you would orient the coil of wire next to a power line to develop the max emf in the coilo If magnetic flux through a loop changes, induced emf is produced
o If the area of the loop is parallel to the field, the flux through the loop is minimum
• So no emf is produced
o To get the most of the flux through the loop you place it closer to the power lines and in orientations so the plane of the loop also contains power lines
• Flux would be max and result in greater induced emf as field goes from max to zero to max and then in other direction
Answer:
the normal to the area of the loop parallel to the wire to induce the maximum electromotive force
Explanation:
Faraday's law is
ε = - dΦ / dt
where Ф magnetic flow
the flow is
Ф = B. dA = B dA cos θ
therefore, to obtain the maximum energy, the cosine function must be maximum, for this the direction of the fluctuating magnetic field and the normal direction to the area must be parallel.
The magnetic field in a cable through which current flows is circular, so the loop must be perpendicular to the wire, this is the normal to the area of the loop parallel to the wire to induce the maximum electromotive force
an outline is shown in the attachment
the correct answer is b
Which of the following is NOT a cause for the intervention of antitrust authorities?
a.
Companies abuse their market power by acquiring new firms that allow for the increase of prices above a level that would occur in a competitive market.
b.
The merger between two companies allows for several customer options and substantial competition within the industry.
c.
An acquisition that creates too much consolidation and increases the potential for future abuse of market power.
d.
A company cuts prices when a new competitor enters the industry to force the competitor out of business.
e.
Dominant companies use their market power to crush potential competitors.
Answer:
b.
The merger between two companies allows for several customer options and substantial competition within the industry.
Explanation:
Antitrust authorities will only come in if the merger was to remove competition and reduce consumer options.
Final answer:
Antitrust authorities intervene when firms engage in practices that reduce competition. These practices include abusive use of market power, anticompetitive mergers and acquisitions, and restrictive practices. A merger enhancing competition does NOT warrant such intervention. Thus, option B is correct.
Explanation:
The intervention of antitrust authorities is generally warranted when actions are taken by firms that reduce competition and harm the economic ideal of a competitive market. These actions may include abusive use of market power, mergers and acquisitions that significantly increase market concentration and reduce competition, and various restrictive practices that limit competition, such as tie-in sales, bundling, and predatory pricing.
However, not all actions that affect competition trigger antitrust intervention. For example, if the merger between two companies allows for several customer options and substantial competition within the industry, that would not be a cause for concern for antitrust authorities. In this case, the merger does not lead to abusive market power or reduce competition, and therefore, option b 'The merger between two companies allows for several customer options and substantial competition within the industry' would be the correct answer as it is NOT a cause for intervention by antitrust authorities.
A pilot flies in a straight path for 1 hour 30 minutes. She then makes a course correction, heading 45 degrees to the right of her original course, and flies 2 hours 15 minutes in the new direction. If she maintains a constant speed of 345 mi/h, how far is she from her starting position? Give your answer to the nearest mile.
Answer:
1199 miles
Explanation:
1 hour 30 minutes = 1 + 30/60 = 1.5 hours
2 hours 15 minutes = 2 + 15/60 = 2.25 hours
The distance she flew in the 1st segment is:
1.5*345 = 517.5 miles
The distance she flew in the 2nd segment is:
2.25 * 345 = 776.25 miles
Since the 2nd segment is 45 degree with respect to the 1st segment, this means that she has flown
776.25 * cos(45) = 549 miles in-line with the 1st segment and
776.25* sin(45) = 549 miles perpendicular to the 1st segment:
So the distance from the end to her starting position is
[tex]\sqrt{(517.5 + 549)^2 + 549^2} = 1199 miles[/tex]
A standard door into a house rotates about a vertical axis through one side, as defined by the door's hinges. A uniform magnetic field is parallel to the ground and perpendicular to the axis. Through what angle must the door rotate so that the magnetic flux that passes through it decreases from its maximum value to 1/4 of its maximum value?
Answer:
75.5degrees
Explanation:
Magnitude of magnetic flux= BA
If rotated through an angle= BAcos theta
= (0.25)BA=BAcos theta
= costheta= 0.25
= theta= cos^-1 0.25
=75.5degrees
Point charges 1 mC and −2 mC are located at (3, 2, −1) and (−1, −1, 4), respectively. Calculate the electric force on a 10 nC charge located at (0, 3, 1) and the electric field intensity at that point.
Answer:
See attached handwritten document for answer
Explanation:
Answer:
Explanation:
a) You can compute the force by using the expression:
[tex]F=k\frac{q_1q_2}{[(x-x_o)^2+(y-y_o)^2+(z-z_o)^2]^{\frac{1}{2}}}[/tex]
where k=8.98*10^9Nm^2/C^2 and q1, q2 are the charges. By replacing for the forces you obtain:
[tex]F_T=k[\frac{(1*10^{-3}C)(10*10^{-9}C)}{[(3-0)^2+(2-3)^2+(-1-1)^2]}}][(3-0)\hat{i}+(2-3)\hat{j}+(-1-1)\hat{k}]\\\\ \ \ \ \ +k[\frac{(-2*10^{-3}C)(10*10^{-9}C)}{[(-1-0)^2+(-1-3)^2+(4-1)^2]}}][(-1-0)\hat{i}+(-1-3)\hat{j}+(4-1)\hat{k}]\\\\F_T=6.41*10^{-3}N[3i-j-2k]-6.9*10^{-3}N[-1i-4j+3k]\\\\=0.026N\hat{i}-0.034N\hat{j}-0.033\hat{k}[/tex]
b)
[tex]E=k[\frac{1*10^{-3}C}{[(3-0)^2+(2-3)^2+(-1-1)^2]}]+k[\frac{(-2*10^{-3}C)}{[(-1-0)^2+(-1-3)^2+(4-1)^2]}]\\\\E=641428.5N/C+690769.23N/C=1332197.73N/C[/tex]
[tex]E=k[\frac{1*10^{-3}C}{[(3-0)^2+(2-3)^2+(-1-1)^2]}][3i-2j-2k]+\\\\k[\frac{(-2*10^{-3}C)}{[(-1-0)^2+(-1-3)^2+(4-1)^2]}][-1i-4j+3k]\\\\E=641428.5N/C[3i-2j-2k]-690769.23N/C[-1i-4j+3k]=2615054.7i+1480219.92j-4973626.23k\\\\|E|=\sqrt{(E_x)^2+(E_y)^2+(E_z)^2}=5810896.56N/C[/tex]
where we you have used that E=kq/r^2