Answer:
C) equal to zero
Explanation:
Electric potential is calculated by multiplying constant and charge, then dividing it by distance. The location that we want to measure is equidistant from two particles, mean that the distance from both particles is the same(r2=r1). The charges of the particle have equal strength of magnitude but the opposite sign(q2=-q1). The resultant will be:V = kq/r
ΔV= V1 + V2= kq1/r1 + kq2/r2
ΔV= V1 + V2= kq1/r1 + k(-q1)/(r)1
ΔV= kq1/r1 - kq1/r1
ΔV=0
The electric potential equal to zero
Two radio antennas A and B radiate in phase. Antenna B is a distance of 120 m to the right of antenna A. Consider point Q along the extension of the line connecting the antennas, a horizontal distance of 40.0 m to the right of antenna B. The frequency, and hence the wavelength, of the emitted waves can be varied. What is the longest wavelength for which there will be destructive interference at point Q?
Answer:
240 m
120 m
Explanation:
d = Path difference = 120 m
For destructive interference
Path difference
[tex]d=\dfrac{\lambda}{2}\\\Rightarrow \lambda=2d\\\Rightarrow \lambda=2\times 120\\\Rightarrow \lambda=240\ m[/tex]
The longest wavelength is 240 m
For constructive interference
[tex]d=\lambda\\\Rightarrow 120\ m=\lambda[/tex]
The longest wavelength is 120 m
Final answer:
The longest wavelength for destructive interference at point Q, where the path difference is 120 m, is 240 m.
Explanation:
The longest wavelength for which there will be destructive interference at point Q can be found by considering the path difference between the waves from the two antennas at point Q. The waves must differ by an odd multiple of ½ wavelengths for destructive interference to occur. The distance from antenna A to point Q is 120 m + 40 m = 160 m, and the distance from antenna B to point Q is 40 m. Therefore, the path difference is 120 m.
For the first occurrence of destructive interference, the path difference should be ½ wavelength, so we calculate the longest wavelength (λ) as:
½ λ = 120 m
λ = 240 m
This is the longest wavelength that causes destructive interference at point Q.
As your skateboard coasts uphill, your speed changes from 3 m/s to 1 m/s in
3 seconds. What is your deceleration?
Answer:
[tex]a=-0.33\ m/s^2[/tex]
Explanation:
Accelerated Motion
The acceleration of a moving body is defined as the relation of change of speed (or velocity in vector form) with the time taken. The formula is given by
[tex]\displaystyle a=\frac{\Delta v}{t}[/tex]
Or, equivalently
[tex]\displaystyle a=\frac{v_f-v_o}{t}[/tex]
Where vf and vo are the final and initial speeds respectively. The problem gives us these values: v0 = 3 m/s, vf = 1 m/s, t = 3 seconds. Computing a
[tex]\displaystyle a=\frac{1-3}{3}=-0.33\ m/s^2[/tex]
The negative sing of a indicates there is deceleration or decreasing speed
Final answer:
The skateboard's deceleration as it coasts uphill, changing speed from 3 m/s to 1 m/s in 3 seconds, is calculated as -0.67 m/s². This indicates a decrease in speed and is consistent with deceleration.
Explanation:
If a skateboard coasts uphill and experiences a change in speed from 3 m/s to 1 m/s in 3 seconds, to find the deceleration, we use the formula for acceleration, which is the change in velocity divided by the time taken for the change. Deceleration is simply acceleration in the opposite direction to the motion (negative acceleration).
The change in velocity ({\Delta v}) is 1 m/s - 3 m/s, which equals -2 m/s (the negative sign indicates a decrease in speed). The time ({t}) is 3 seconds. Thus, the deceleration is {\Delta v / t} which is (-2 m/s) / (3 s) = -0.67 m/s². This negative sign signifies that it is indeed a deceleration.
A bar magnet is held above the center of a conducting ring in the horizontal plane. The magnet is dropped so it falls lengthwise toward the center of the ring. Will the falling magnet be attracted toward the ring or be repelled by the ring due to the magnetic interaction of the magnet and the ring?
Explanation:
Since, it is given that the magnet drops and falls lengthwise towards the canter of the ring. As a result, change in magnetic flux will occur which tends to induce an electric current in the ring.
Therefore, a magnetic field is also produced by the ring itself which will actually oppose or repel the magnet.
Thus, we can conclude that the falling magnet be repelled by the ring due to the magnetic interaction of the magnet and the ring.
Two plates with area A are held a distance d apart and have a net charge +Q, and -Q, respectively. Assume that all the charge is uniformly distributed on the inner surfaces of the plates.
The left plate has charge -Q, the right plate has charge +Q, separated by distance d.
1) Find the charge density on the plates.
2) Find the electric potential difference between the plates.
3) Show that the capacitance of the enlarged plates in this case is the same as the capacitance in a case where
Answer:
Explanation:
1 )
Charge density of left plate
= - Q / A
Charge density of right plate
= + Q / A
2 )
capacitance c = ε₀ A / d
potential difference = charge / capacitance
= Q / [ ε₀ A / d ]
= Q d / ε₀ A
Final answer:
The charge density on each plate is ±Q/A, the electric potential difference between the plates is calculated using the electric field and the separation distance, and the capacitance C=ε₀A/d demonstrates that the size of the plates does not affect their capacitance as long as their proportion remains constant.
Explanation:
When considering two parallel plates each with area A and charges of +Q and -Q respectively, separated by a distance d, we can address the posed questions systematically.
Finding the Charge Density on the Plates
The surface charge density σ is defined as charge per unit area. Given the total charge +Q or -Q and the area A of each plate, the charge density on each plate is σ = ±Q/A. This is a direct result of the uniform distribution assumption of the charges across the plates.
Finding the Electric Potential Difference Between the Plates
The electric field E created between the plates by the charge distribution is uniform and can be represented as E = σ/ε₀, where σ is the surface charge density and ε₀ is the vacuum permittivity. Consequently, the electric potential difference V between the plates can be derived from the relation V = Ed, linking the electric field and the separation of the plates.
Demonstrating the Capacitance of Enlarged Plates Remains Constant
The capacitance C of a parallel-plate capacitor is given by C = ε₀A/d, which is independent of the charge on the plates. This formula illustrates that the capacitance is solely dependent on the physical characteristics of the capacitor (i.e., the area of the plates A, the distance between them d, and the permittivity of free space ε₀), and does not change with the amount of charge nor with the size of the plates as long as their proportional relationship remains constant.
Problem 7: In a mass spectrometer, a specific velocity can be selected from a distribution by injecting charged particles between a set of plates with a constant electric field between them and a magnetic field across them (perpendicular to the direction of particle travel). If the fields are tuned exactly right, only particles of a specific velocity will pass through this region undeflected. Consider such a velocity selector in a mass spectrometer with a 0.095 T magnetic field.
Answer:
Complete question
In a mass spectrometer, a specific velocity can be selected from a distribution by injecting charged particles between a set of plates with a constant electric field between them and a magnetic field across them (perpendicular to the direction of particle travel). If the fields are tuned exactly right, only particles of a specific velocity will pass through this region undeflected. Consider such a velocity selector in a mass spectrometer with a 0.095 T magnetic field.
a. What electric field strength, in volts per mater, is needed to select a speed of 4.2 x 10^6 m/s?
b. What is the voltage, in kilovolts, between the plates if they are separated by 0.95 cm?
Explanation:
Given that,
magnetic field B = 0.095T
Speed of particle v = 4.2 ×10^6m/s
Separation between plate d = 0.95cm
d = 0.95/100 = 0.0095m
a. Using the mass spectrometer velocity selector relationship between the electric field and magnetic field.
v = E/B
Where
v is the speed selector
B is magnetic field
E is electric field
Therefore, E = vB
E = 4.2 × 10^6 × 0.095
E = 0.399× 10^6
E = 3.99 × 10^5 V/m
b. Voltage?
The relationship between electric field and potential difference between the two plates is given as
V = Ed
V = 3.99 × 10^5 × 0.0095
V = 3790.5 V
To kV, 1kV = 1000V
Then, V = 3.7905kV
V ≈ 3.791 kV
The electric field strength needed in a mass spectrometer to select a velocity of 4.00 × 106 m/s with a 0.100-T magnetic field is 400,000 N/C. The voltage required across plates separated by 1.00 cm is 4,000 V.
Explanation:In a velocity selector within a mass spectrometer, a charged particle remains undeflected when the electric force equals the magnetic force. This condition is given by qE = qvB, where q is the charge, E is the electric field strength, v is the velocity of the particle, and B is the magnetic field strength. The question asks for the electric field strength needed to select particles with a velocity of 4.00 × 106 m/s when subjected to a 0.100-T magnetic field. Using the condition for balance, E = vB, we can substitute the given values to find E = 4.00 × 106 m/s × 0.100 T = 400,000 N/C. For part (b), voltage (V) can be determined by the relation V = Ed, where d is the separation between the plates. For a plate separation of 1.00 cm, or 0.01 m, the voltage is V = 400,000 N/C × 0.01 m = 4,000 V.
In a high-performance computing system 100 CPU chips, each dissipating 25 W, are attached to one surface of a 200 mm by 200 mm copper heat spreader. The copper plate is cooled on its opposite surface by water, which is tripped at the leading edge of the copper so that the boundary layer is turbulent throughout. The plate may be assumed to be isothermal due to the high thermal conductivity of the copper. The water velocity and temperature are 2 m/s and 17˚C. What is the temperature of the copper plate?
Given Information:
Velocity of water flow = 2 m/s
Temperature of water = 17° C
Heat dissipation = 2500 W
Area of copper plate = 0.04 m²
Required Information:
Temperature of copper plate = ?
Answer:
[tex]T_{p} = 27[/tex]° [tex]C[/tex]
Explanation:
Each chip dissipates 25 W so 100 chips will dissipate 25*100 = 2500 W
Area of copper plate = 0.2*0.2 = 0.04 m²
According to the convection rate equation
[tex]T_{p}= T_{w} + \frac{q}{hA}[/tex]
Where Tp is the temperature of copper plate, Tw is the temperature of water, q is the the heat dissipation of chips, A is the area of copper plate and h is the convection coefficient
The convection coefficient is given by turbulent flow correlation
[tex]h = Nu_{L}(k/L) =0.037Re_{L}^{4/5}P_{r}^{1/3}(k/L)[/tex]
Where Nu is Nusselt number, Re is Reynolds number, Pr = 5.2 is Prandtl number and k = 0.620 W/m.K
[tex]Re_{L}= uL/v[/tex]
Where u = 2 m/s and L = 0.2 m and v = 0.96x10⁻⁶m² /s
[tex]Re_{L}= 2*0.2/0.96x10^{-6}[/tex]
[tex]Re_{L}= 416666.66[/tex]
[tex]h = 0.037(416666.66)^{4/5}(5.2)^{1/3}(0.620/0.2)[/tex]
[tex]h = 6223.89[/tex] [tex]W/m^{2}K[/tex]
[tex]T_{p}= 17 + \frac{2500}{(6223.89)0.04}[/tex]
[tex]T_{p} = 27[/tex]° [tex]C[/tex]
Therefore, the temperature of the copper plate is 27° C
The transverse standing wave on a string fixed at both ends is vibrating at its fundamental frequency of 250 Hz. What would be the fundamental frequency on a piece of the same string that is twice as long and has four times the tension
The fundamental frequency of the string will remain at 250 Hz, even when the string is doubled in length and the tension is quadrupled, due to the relationship between string length, tension, and frequency.
Explanation:When a transverse standing wave on a string is vibrating at its fundamental frequency, the length of the string and the tension within it play crucial roles in determining that frequency. The fundamental frequency (f) is given by f = (1/2L) * sqrt(T/μ), where L is the length of the string, T is the tension, and μ is the linear mass density of the string.
In the original scenario, the string vibrates at a fundamental frequency of 250 Hz. If the same piece of string is made twice as long and the tension is increased fourfold, the new fundamental frequency F' can be found using the formula mentioned above.
Considering the string is now twice as long (L' = 2L), and the tension is four times greater (T' = 4T), we can substitute these into the original equation for fundamental frequency: f' = (1/2L') * sqrt(T'/μ). By inserting these new values, we can determine that the new fundamental frequency f' will be the same as the original frequency f, because the doubling of the string length and the quadrupling of the tension will have cancelling effects.
Final answer:
The fundamental frequency of a string that is twice as long and with four times the tension would be half the original frequency; therefore, the new fundamental frequency would be 125 Hz.
Explanation:
The student is asking about how the fundamental frequency of a string changes when its length is doubled and the tension is increased by four times. The fundamental frequency f of a string fixed at both ends can be described by the equation f = √(T/μ)/(2L), where T is the tension, μ (mu) is the mass per unit length, and L is the length of the string. When we double the length of the string, the new length is 2L. When we quadruple the tension, the new tension is 4T. Substituting these values into the equation, the new frequency f' becomes f' = √(4T/μ)/(2 × 2L) = √(T/μ)/2L = f/2.
Therefore, the new fundamental frequency of the longer string with four times the tension is half the original frequency, which is 125 Hz in this case.
Ocean waves are traveling to the east at 4.9 m/s with a distance of 23 m between crests. (b) With what frequency do the waves hit the front of a boat when the boat is moving westward at 1.1 m/s
Answer:
0.26086 Hz
Explanation:
solution:
The relative speed of the wave is:
v = 4.9+1.1 = 6 m/s
the frequency is:
f = v/λ
= 6/23
= 0.26086 Hz
The height (in meters) of a projectile shot vertically upward from a point 2 m above ground level with an initial velocity of 23.5 m/s is h = 2 + 23.5t − 4.9t2 after t seconds. (Round your answers to two decimal places.) (a) Find the velocity after 2 s and after 4 s. v(2) = m/s v(4) = m/s
Answer:
a) [tex]v(2) = 3.9\,\frac{m}{s}[/tex], b) [tex]v(4) = -15.7\,\frac{m}{s}[/tex]
Explanation:
a) The equation for vertical velocity is obtained by deriving the function with respect to time:
[tex]v(t) = 23.5 -9.8\cdot t[/tex]
The velocities at given instants are, respectivelly:
[tex]v(2) = 3.9\,\frac{m}{s}[/tex]
[tex]v(4) = -15.7\,\frac{m}{s}[/tex]
Two point charges Q1 = +4.10 nC and Q2 = −2.40 nC are separated by 55.0 cm.(a) What is the electric potential at a point midway between the charges? 212.7 Incorrect: Your answer is incorrect. Use the expression for the electric potential from each point charge to find the electric potential at the midpoint between the two charges. V(b) What is the potential energy of the pair of charges? 3.22E-7 Incorrect?
Answer:
a. 55.6v
b. [tex]1.61*10^{-7}J[/tex]
Explanation:
Data given
charge 1=+4.10nC
charge 2 =-2.40nC
distance, r= 55cm =0.55m
a. the electric potential at the mid point is the sum of the potential due to individual charge.
The electric potential is expressed as
[tex]V=\frac{kq}{r}\\[/tex]
since we are interested in the electric potential at the mid point, we have
[tex]V=\frac{kq_1}{r/2}-\frac{kq_2}{r/2}\\ V=\frac{2k}{r}(q_1-q_2)\\ V=\frac{2*9*10^9}{0.55}(4.1-2.4)*10^{-9}\\ V=55.6v[/tex]
Hence the electric potential at the mid-point is 55.6v
b. to calculate the potential energy, we use the formula below
[tex]U=\frac{kq_1q_2}{r} \\U=\frac{9*10^9 *4.10*10^{-9}*2.4*10^{-9}}{0.55}\\ U=1.61*10^{-7}J[/tex]
Suppose two children push horizontally, but in exactly opposite directions, on a third child in a wagon. The first child exerts a force of 75.0 N, the second a force of 95.0 N, friction is 12.0 N, and the mass of the third child plus wagon is 21.0 kg.
(c) Calculate the acceleration.
m/s2
(d) What would the acceleration be if friction is 20.0 N?
Final answer:
The acceleration of the child in the wagon can be calculated using Newton's Second Law of Motion. The sum of the forces acting on the system is calculated by adding the forces exerted by the children and subtracting the force of friction. Using the given values, the acceleration can be determined by dividing the sum of the forces by the mass of the system. If the force of friction is increased to 20.0 N, the acceleration can be recalculated using the new value.
Explanation:
To calculate the acceleration of the child in the wagon, we can use Newton's Second Law of Motion:
ΣF = ma
Where ΣF is the sum of all the forces acting on the system, m is the mass of the system, and a is the acceleration.
In this case, the forces acting on the system are the forces exerted by the two children and the force of friction.
Using the given values:
Force1 = 75.0 N
Force2 = 95.0 N
Friction = 12.0 N
Mass = 21.0 kg
The sum of the forces acting on the system is:
ΣF = Force1 + Force2 - Friction
Substituting the values:
ΣF = 75.0 N + 95.0 N - 12.0 N
ΣF = 158.0 N
Now we can calculate the acceleration:
a = ΣF / m
Substituting the values:
a = 158.0 N / 21.0 kg
a = 7.52 m/s²
Therefore, the acceleration of the child in the wagon is 7.52 m/s².
(d) If friction is 20.0 N, we can recalculate the acceleration using the new value:
ΣF = 75.0 N + 95.0 N - 20.0 N
ΣF = 150.0 N
a = ΣF / m
a = 150.0 N / 21.0 kg
a = 7.14 m/s²
Therefore, if friction is 20.0 N, the acceleration of the child in the wagon would be 7.14 m/s².
"Comparing microwaves and visible light, which of the following is true? 1. Microwaves have higher frequency, same speed, and longer wavelength than visible light. 2. Microwaves have lower frequency, same speed, and longer wavelength than visible light. 3. Microwaves have lower frequency, slower speed, and longer wavelength than visible light. 4. Microwaves have lower frequency, faster speed, and shorter wavelength than visible light."
Answer:
2. Microwaves have lower frequency, same speed, and longer wavelength than visible light.
Explanation:
Microwaves are a form of electromagnetic radiation. Most people are familiar with this type of waves because they are used in microwave ovens. When compared to visible light, microwaves have lower frequency, same speed and longer wavelength than visible light. The prefix "micro" is used to indicate that microwaves are smaller (shorter wavelengths) than radio waves.
"The correct option is 2. Microwaves have lower frequency, same speed, and longer wavelength than visible light.
To understand why this option is correct, let's consider the relationship between frequency, wavelength, and speed for electromagnetic waves, which is given by the equation:
[tex]\[ c = f \times \lambda \][/tex]
1. Speed of light (in a vacuum) is constant for all electromagnetic waves, including microwaves and visible light. Therefore, the speed of microwaves and visible light is the same.
2. Microwaves have a lower frequency than visible light. The frequency of microwaves typically ranges from 300 MHz to 300 GHz, while the frequency of visible light ranges from approximately 430 THz to 750 THz. Since microwaves have a lower frequency, they also have a longer wavelength according to the equation [tex]\( c = f \times \lambda \)[/tex].
3. Since the speed of all electromagnetic waves is the same in a vacuum, and microwaves have a lower frequency, they must have a longer wavelength to maintain the constant speed. This is consistent with the relationship , where a lower frequency requires a longer wavelength to keep the speed constant.
In summary, microwaves have a lower frequency and longer wavelength than visible light, but they travel at the same speed. This makes option 2 the correct choice."
You have a battery marked " 6.00 V ." When you draw a current of 0.361 A from it, the potential difference between its terminals is 5.07 V . What is the potential difference when you draw 0.591 A
Answer:
Explanation:
Battery voltage is 6V
A current of 0.361A is draw the voltage reduces to, 5.07V
This shows that the appliances resistance that draws the currents is
Using KVL
The battery has an internal resistance r
V=Vr+Va
Vr is internal resistance voltage
Va is appliance voltage
6=5.07+Va
Va=6-5.07
Va=0.93
Using ohms law to the resistance of the appliance
Va=iR
R=Va/i
R=0.93/0.361
R=2.58ohms
Then if the circuit draws a current of 0.591A
Then the voltage across the load is
V=iR
Va=0.591×2.58
Va=1.52V
Then the voltage drop at the internal resistance is
V=Vr+Va
Vr=V-Va
Vr=6-1.52
Vr=4.48V
Answer:
V = 4.48 V
Explanation:
• As the potential difference between the battery terminals, is less than the rated value of the battery, this means that there is some loss in the internal resistance of the battery.
• We can calculate this loss, applying Ohm's law to the internal resistance, as follows:
[tex]V_{rint} = I* r_{int}[/tex]
• The value of the potential difference between the terminals of the battery, is just the voltage of the battery, minus the loss in the internal resistance, as follows:
[tex]V = V_{b} - V_{rint} = 5.07 V = 6.00 V - 0.361 A * r_{int}[/tex]
• We can solve for rint, as follows:
[tex]r_{int} =\frac{V_{b}- V_{rint} }{I} = \frac{6.00 V - 5.07 V}{0.361A} = 2.58 \Omega[/tex]
• When the circuit draws from battery a current I of 0.591A, we can find the potential difference between the terminals of the battery, as follows:
[tex]V = V_{b} - V_{rint} = 6.00 V - 0.591 A * 2.58 \Omega = 4.48 V[/tex]
• As the current draw is larger, the loss in the internal resistance will be larger too, so the potential difference between the terminals of the battery will be lower.
Light of wavelength 550 nm comes into a thin slit and produces a diffraction pattern on a board 8.0 m away. The first minimum dark fringe appears 3 mm from the central maximum. What is the width of the slit?
Answer:
Width of the slit will be equal to 1.47 mm
Explanation:
We have given wavelength of the light [tex]\lambda =550nm=550\times 10^{-9}m[/tex]
Distance D = 8 m
Distance between first minimum dark fringe and the central maximum is 2 mm
So [tex]x=3\times 10^{-3}m[/tex]
We have to find the width of the slit
For the first order wavelength is equal to [tex]\lambda =\frac{x}{D}\times a[/tex], here a width of slit
So [tex]a=\frac{\lambda D}{x}=\frac{550\times 10^{-9}\times 8}{3\times 10^{-3}}=1466.666\times 10^{-6}=1.47mm[/tex]
So width of the slit will be equal to 1.47 mm
Laminar flow of oil in a 2-in Schedule 40 steel pipe has an average velocity of 10.72 ft/s. Find the velocity at (a) the center of the pipe, (b) at the wall of the pipe, and (c) at a distance of 0.6 inches from the centerline.
Answer:
(a) 21.44 ft/s
(b) 0 ft/s
(c) 19.51 ft/s
Explanation:
2 in = 2/12 ft = 0.167 ft
For steady laminar flow, the function of the fluid velocity in term of distance from center is modeled as the following equation:
[tex]v(r) = v_c\left[1 - \frac{r^2}{R^2}\right][/tex]
where R = 0.167 ft is the pipe radius and [tex]v_c[/tex] is the constant fluid velocity at the center of the pipe.
We can integrate this over the cross-section area of the in order to find the volume flow
[tex]\dot{V} = \int\limits {v(r)} \, dA \\= \int\limits^R_0 {v_c\left[1 - \frac{r^2}{R^2}\right]2\pi r} \, dr\\ = 2\pi v_c\int\limits^R_0 {r - \frac{r^3}{R^2}} \, dr\\ = 2\pi v_c \left[\frac{r^2}{2} - \frac{r^4}{4R^2}\right]^R_0\\= 2\pi v_c \left(\frac{R^2}{2} - \frac{R^4}{4R^2}\right)\\= 2\pi v_c \left(\frac{R^2}{2} - \frac{R^2}{4}\right)\\= 2\pi v_c R^2/4\\=\pi v_c R^2/2\\A = \pi R^2\\\dot{V} = Av_c/2\\[/tex]
So the average velocity
[tex]v = \dot{V} / A = v_c/2 = 10.72[/tex]
[tex]v_c = 10.72*2 = 21.44 ft/s[/tex]
b) At the wall of the pipe, r = R so [tex]v(R) = v_c(1 - 1) = 0 ft/s[/tex]
c) At a distance of 0.6 in = 0.6/12 = 0.05 ft
[tex]v(0.05) = v_c(1 - 0.05^2/0.167^2) = 0.91v_c = 0.91*21.44 = 19.51 ft/s[/tex]
Answer:
The answers to the questions are;
(a) The velocity at the center of the pipe is 21.44 ft/s
(b) The velocity at the wall of the pipe is 0 ft/s
(c) The velocity at a distance of 0.6 inches from the center-line is 19.63 ft/s.
Explanation:
To solve the question, we note that
The velocity profile in the cross section of a circular pipe with laminar flow is given by
U = 2×v×[1 - (r/r₀)²]
Where
U = The sought velocity at a point
r = Pipe radius where velocity is sought
r₀ = Internal radius of pipe = for 2-in Schedule 40 steel pipe = 2.067 in 52.6 mm
v = Average velocity of flow = 10.72 ft/s = 3.2675 m/s
Therefore we have
(a) The velocity at the center of the pipe
At the center r = 0 so we have
U = 2×v×[1 - (r/r₀)²]
At center U = 2×10.72 ft/s×[1 - (0/2.067 in)²] = 2×10.72 ft/s = 21.44 ft/s
(b) The velocity at the wall of the pipe is given by
r = r₀ ⇒ U = 2×v×[1 - (r/r₀)²] ⇒ U = 2×v×[1 - (r₀/r₀)²]
= U = 2×v×[1 - (1)²] = 2×v×0 = 0
The velocity at the wall of the pipe is 0 ft/s
(c) The velocity at a distance of 0.6 inches from the center-line is given by
U = 2×v×[1 - (r/r₀)²] = 2×10.72 ft/s×[1 - (0.6/2.067)²] = 19.63 ft/s.
A long solenoid that has 1,140 turns uniformly distributed over a length of 0.415 m produces a magnetic field of magnitude 1.00 10-4 T at its center. What current is required in the windings for that to occur?
Answer:
Therefore,
Current required is , I
[tex]I = 0.0289\ Ampere[/tex]
Explanation:
Given:
Turns = N = 1140
length of solenoid = l = 0.415 m
Magnetic Field,
[tex]B = 1.00\times 10^{-4}\ T[/tex]
To Find:
Current , I = ?
Solution:
If N is the number of turns in the length, the total current through the rectangle is NI. Therefore, Ampere’s law applied to this path gives
[tex]\int {B} \, ds= Bl=\mu_{0}NI[/tex]
Where,
B = Strength of magnetic field
l = Length of solenoid
N = Number of turns
I = Current
[tex]\mu_{0}=Permeability\ in\ free\ space=4\pi\times 10^{-7}\ Tm/A[/tex]
Therefore,
[tex]I =\dfrac{Bl}{\mu_{0}N}[/tex]
Substituting the values we get
[tex]I =\dfrac{1.00\times 10^{-4}\times 0.415}{4\times 3.14\times 10^{-7}\times 1140}=0.0289\ Ampere[/tex]
Therefore,
Current required is , I
[tex]I = 0.0289\ Ampere[/tex]
A block of mass 3.5 kg, sliding on a horizontal plane, is released with a velocity of 1.6 m/s. The block slides and stops at a distance of 1.6 m beyond the point where it was released. How far would the block have slid if its initial velocity were increased by a factor of 3.5
Answer:
19.6 m
Explanation:
The work-energy theorem applies here,
The theorem states that the change in momentum of a particle between two points is equal to the work done in moving the force between the two distance.
ΔK.E = W
ΔK.E = (final kinetic energy) - (initial kinetic energy)
Kinetic energy = (1/2)(m)(v²)
m = 3.5 kg, v = 1.6 m/s
Final kinetic energy = 0 J, since the block of mass comes to rest.
Initial kinetic energy = (1/2)(3.5)(1.6²) = 4.48 J
ΔK.E = - 4.48 J
The workdone on the block of mass is done by the frictional force, F, which acts opposite to the direction of the displacement.
W = - Fd = - 1.6 F
ΔK.E = W
- 4.48 = - 1.6 F
F = 2.8 N
when the initial velocity is increased by a factor 3.5,
v = 1.6×3.5 = 5.6 m/s
Final kinetic energy = 0 J, since the block of mass comes to rest.
Initial kinetic energy = (1/2)(3.5)(5.6²) = 4.48 J
ΔK.E = - 54.88 J
The workdone on the block of mass is done by the frictional force, F, which acts opposite to the direction of the displacement. The frictional force is the same as above.
W = - Fd = - (2.8) d
ΔK.E = W
- 54.88 = - 2.8 d
d = 19.6 m
Compared to 1.6 m, 19.6 m is an increase by a factor 12.25.
A circular coil has a 18.0 cm radius and consists of 25.0 closely wound turns of wire. An externally produced magnetic field of magnitude 3.00 mT is perpendicular to the coil. (a) If no current is in the coil, what magnetic flux links its turns?
Answer:
The magnetic flux links to its turns = [tex]7.6 \times10^{-3}[/tex] Wb.
Explanation:
Given :
Radius of circular coil = [tex]18 \times 10^{-2}[/tex] m
Number of turns = 25
Magnetic field = [tex]3 \times10^{-3}[/tex] T
Magnetic flux (Φ) is a measure of the magnetic field lines passes through a given area. The unit of magnetic flux is weber (Wb).
We know that,
⇒ Φ = [tex]BA[/tex]
Where [tex]B =[/tex] ext. magnetic field, [tex]A =[/tex] area of loop or coil.
But here given in question, we have turns of wire so our above eq. modified as follows.
⇒ Φ = [tex]NBA[/tex]
Where [tex]N =[/tex] no. of turns.
∴ Φ = [tex]25 \times 3 \times 10^{-3} \pi (18 \times10^{-2} )^{2}[/tex]
Φ = [tex]7.6 \times 10^{-3} Wb[/tex]
Thus, the magnetic flux links to its turns = [tex]7.6 \times 10^{-3} Wb[/tex]
Calculate the noise voltage spectrum Su(f) on a paraller RC circuit with R=1 kOhm and C=1 nF. (Don't forget to provide the unit!) (3 points) - How much it is at 1 Hz ?
Answer: 10^-3 V^2/Hz
Explanation:
1 Hz:
Su(f) = No * |H(f)|^2
= 10^-3 * 1/(1+(2*pi*f*R*C)^2)
= 10^-3 V^2/Hz
If i = 1.70 A of current flows through the loop and the loop experiences a torque of magnitude 0.0760 N ⋅ m , what are the lengths of the sides s of the square loop, in centimeters?
Answer:
Length of the sides of the square loop is given by
s = √[(τ)/(NIB sin θ)]
Explanation:
The torque, τ, experienced by a square loop of area, A, with N number of turns around the loop and current of I flowing in the wire, with a magnetic field presence, B, and the plane of the loop tilted at angle θ to the x-axis, is given by
τ = (N)(I)(A)(B) sin θ
If everything else is given, the length of a side of the square loop, s, can be obtained from its Area, A.
A = s²
τ = (N)(I)(A)(B) sin θ
A = (τ)/(NIB sin θ)
s² = (τ)/(NIB sin θ)
s = √[(τ)/(NIB sin θ)]
In this question, τ = 0.076 N.m, I = 1.70 A
But we still need the following to obtain a numerical value for the length of a side of the square loop.
N = number of turnsof wire around the loop
B = magnetic field strength
θ = angle to which the plane of the loop is tilted, measured with respect to the x-axis.
The question is incomplete! The complete question along with answer and explanation is provided below
Question:
A wire loop with 40 turns is formed into a square with sides of length s. The loop is in the presence of a 2.0 T uniform magnetic field B that points in the negative y direction. The plane of the loop is tilted off the x-axis by 15°. If 1.70 A of current flows through the loop and the loop experiences a torque of magnitude 0.0760 N.m, what are the lengths of the sides s of the square loop, in centimeters?
Given Information:
Number of turns = N = 40 turns
Torque = τ = 0.0760 N.m
Current = I = 1.70 A
Magnetic field = B = 2 T
θ = 15°
Required Information:
Length of the sides of square loop = s = ?
Answer:
s = 4.64 cm
Explanation:
τ = NIABsin(θ)
Where N is the number of turns, I is the current flowing through the square loop, A is the area of square loop, B is the magnetic field, and θ is the angle between square loop and magnetic field strength with respect to the x-axis.
Re-arranging the equation to find out A
A = τ/ NIBsin(θ)
A = 0.0760/40*1.70*2*sin(15)
A = 0.00215 m²
We know that area of a square is
A = s²
Taking square root on both sides yields
s = √A
s = √0.00215 = 0.0464 m
in centimeters
s = 4.64 cm
If you wish to take a picture of a bullet traveling at 500 m/s, then a very brief flash of light produced by an RC discharge through a flash tube can limit blurring. Assuming 1.00 mm of motion during one RC constant is acceptable, and given that the flash is driven by a 600-μF capacitor, what is the resistance in the flash tube?
Explanation:
The given data is as follows.
Speed of the bullet (v) = 500 m/s
Distance during one RC time constant (d) = 1 mm = [tex]1 \times 10^{-3} m[/tex]
Capacitance (C) = 600 [tex]\mu F[/tex] = [tex]600 \times 10^{-6} F[/tex]
Hence, formula for speed of the bullet is as follows.
v = [tex]\frac{d}{t}[/tex]
or, t = [tex]\frac{d}{v}[/tex]
Time constant for RC circuit is as follows.
t = RC
R = [tex]\frac{t}{C}[/tex]
= [tex]\frac{d}{vC}[/tex]
= [tex]\frac{1 \times 10^{-3}}{500 \times 600 \times 10^{-6}}[/tex]
= [tex]3.33 \times 10^{-3} ohm[/tex]
Thus, we can conclude that resistance in the flash tube is [tex]3.33 \times 10^{-3} ohm[/tex].
During a long jump, an Olympic champion's center of mass rose about 1.2 m from the launch point to the top of the arc. 1) What minimum speed did he need at launch if he was traveling at 6.7 m/s at the top of the arc
Answer:
1) [tex]v_{A} \approx 8.272\,\frac{m}{s}[/tex]
Explanation:
1) Let assume that the campion begins running at a height of zero. The movement of the Olympic champion is modelled after the Principle of Energy Conservation:
[tex]K_{A} = K_{B} + U_{g,B}[/tex]
[tex]\frac{1}{2}\cdot m \cdot v_{A}^{2} = \frac{1}{2}\cdot m \cdot v_{B}^{2} + m \cdot g \cdot h_{B}[/tex]
[tex]\frac{1}{2} \cdot v_{A}^{2} = \frac{1}{2} \cdot v_{B}^{2} + g \cdot h_{B}[/tex]
The minimum speed is obtained herein:
[tex]v_{A}=\sqrt{v_{B}^{2} + 2 \cdot g \cdot h}[/tex]
[tex]v_{A} = \sqrt{(6.7\,\frac{m}{s} )^{2}+2\cdot (9.807\,\frac{m}{s^{2}} )\cdot (1.2\,m)}[/tex]
[tex]v_{A} \approx 8.272\,\frac{m}{s}[/tex]
The minimum speed he need at launch point is [tex]8.27m/s[/tex]
Energy conservation :Energy is neither be created nor be destroyed just change into one form to another form.
[tex]\frac{1}{2}mv^{2} =\frac{1}{2}mv_{a}^{2} +mgh\\ \\v=\sqrt{v_{a}^{2}+2gh }[/tex]
Where,
[tex]v[/tex] is velocity at launch.[tex]v_{a}[/tex] is velocity at the top of the arc[tex]g[/tex] is gravitational acceleration, [tex]g=9.8m/s^{2}[/tex][tex]h[/tex] is height of center of mass.Given that, [tex]v_{a}=6.7m/s,h=1.2m,g=9.8m/s^{2}[/tex]
Substitute all values in above relation.
[tex]v=\sqrt{(6.7)^{2}+2*9.8*1.2 } \\\\v=\sqrt{68.41}=8.27m/s[/tex]
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A 30-km, 34.5-kV, 60-Hz, three-phase line has a positive-sequence series impedance z 5 0.19 1 j0.34 V/km. The load at the receiving end absorbs 10 MVA at 33 kV. Assuming a short line, calculate: (a) the ABCD parameters, (b) the sending-end voltage for a load power factor of 0.9 lagging, and (c) the sending-end voltage for a load power factor of 0.9 leading.
Answer:
(a) With a short line, the A,B,C,D parameters are:
A = 1pu B = 1.685∠60.8°Ω C = 0 S D = 1 pu
(b) The sending-end voltage for 0.9 lagging power factor is 35.96 [tex]KV_{LL}[/tex]
(c) The sending-end voltage for 0.9 leading power factor is 33.40 [tex]KV_{LL}[/tex]
Explanation:
(a)
Considering the short transition line diagram.
Apply kirchoff's voltage law to the short transmission line.
Write the equation showing the relations between the sending end and the receiving end quantities.
Compare the line equations with the A,B,C,D parameter equations.
(b)
Determine the receiving-end current for 0.9 lagging power factor.
Determine the line-to-neutral receiving end voltage.
Determine the sending end voltage of the short transition line.
Determine the line-to-line sending end voltage which is the sending end voltage.
(c)
Determine the receiving-end current for 0.9 leading power factor.
Determine the sending-end voltage of the short transition line.
Determine the line-to-line sending end voltage which is the sending end voltage.
A block is placed on an inclined plane with an angle of inclination θ (in degrees) with respect to horizontal. The coefficient of static friction between the block and the inclined plane is 0.4. For what maximum value of θ will the block remain stationary on the inclined surface?
Final answer:
The maximum angle of inclination θ for which a block will remain stationary on an inclined plane, given a coefficient of static friction of 0.4, can be found using the arctangent function resulting in approximately 21.8 degrees.
Explanation:
To find the maximum angle of inclination θ at which a block will remain stationary on an inclined surface, we can relate the coefficient of static friction (0.4 in this case) to the angle using the tangent function. When static friction has reached its maximum value, the block is on the verge of sliding, and the maximum force of static friction is equal to the component of the block's weight parallel to the incline. This force can be described by the equation μsN = mg sin(θ), where μs is the static friction coefficient, N is the normal force, m is the mass of the block, g is the acceleration due to gravity, and θ is the angle of inclination. Since the normal force is equal to mg cos(θ), substituting this into the equation and solving for θ gives us θ = tan-1(μs). Plugging in the given coefficient of static friction, the maximum angle θ can be found.
Using the given coefficient of 0.4, we can calculate the angle: θ = tan-1(0.4). Therefore, the maximum angle θ, for the block to remain stationary, is approximately 21.8 degrees.
Final answer:
The maximum angle of inclination θ at which a block will remain stationary on an inclined plane with a coefficient of static friction of 0.4 is approximately 21.8 degrees.
Explanation:
The maximum angle of inclination θ at which a block will remain stationary on an inclined plane with a coefficient of static friction of 0.4 is determined by using the relationship between the angle of inclination and the coefficient of static friction. This relationship is given by the equation tan(θ) = μ, where μ is the coefficient of static friction. To find the angle where the block starts to slide, we take the inverse tangent (arctan or tan-1) of the coefficient of static friction. Therefore, the maximum angle θ is tan-1(0.4).
Calculating this, we get θ = tan-1(0.4) ≈ 21.8°. Hence, for angles of inclination less than or equal to 21.8 degrees, the block will not slide down the incline due to static friction.
g A particle starts moving from the origin of the coordinate system with the initial velocity v(0)=<0,0,2> and acceleration at time t given by a(t)=<1,2,0> find the moment of time t=T when the particle hits the plane 2x+y-z=4
Answer:
2s
Explanation:
The position function of the motion can be expressed as:
[tex]s = s_0 + v_0t + at^2/2[/tex]
where [tex]s_0 = <0,0,0>[/tex] is the origin where the particle starts off, [tex]v_0 = <0,0,2> m/s[/tex] and a = <1,2,0> m/s2. In the 3-coordinate system it can be written as
[tex]s = <0 + 0t+ t^2/2, 0 + 0t + 2t^2/2, 0 + 2t + 0t^2/2> = <t^2/2, t^2, 2t>[/tex]
For the particle to hit the 2x+y-z=4 plane then its coordinates must meet that criteria
[tex]2t^2/2 +t^2-2t = 4[/tex]
[tex]2t^2 - 2t -4 = 0[/tex]
[tex]t^2 - t - 2 = 0[/tex]
[tex]t= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
[tex]t= \frac{1\pm \sqrt{(-1)^2 - 4*(1)*(-2)}}{2*(1)}[/tex]
[tex]t= \frac{1\pm3}{2}[/tex]
t = 2 or t = -1
Since t can only be positive we will pick t = 2s
Why isn’t a bird sitting on a high-voltage power line electrocuted? Contrast this with the situation in which a large bird hits two wires simultaneously with its wings
Answer:
The reason the bird is not electrocuted is due to some facts about circuit:
1. Completeness of circuit- This circuit needs to be
complete in order for current to flow. The bird standing on only one wire has not completed the circuit.
2. A potential difference: Another factor deciding
the direction of flow of current is (electric)
potential. Current always flows from a higher
potential to a lower potential. In other words it
can be said that electrons flow from lower
potential to higher one. (the direction of electric
current is opposite to that of the electrons). So
we need the potential difference for current to
flow. The bird standing on only one wire has no potential difference.
3. Path of least Resistance- Factor that decides
the path a current will flow in case of parallel
paths is the (electric) resistance offered by the
path. Current will always flow in the path that
offers least resistance. The leg of a bird has high resistance.
Explanation:
It has no potential difference as both the legs of bird are touching the same wire at same constant potential. ... If the bird would touch the ground while sitting on the wire or flap its wings and touch another electric wire with a different voltage, then it would get shocked and likely die by electrocution.
while in the other hand, the Bird that touches two wires with it wings at the same time will get electrocuted because it has completed a circuit and the its feathers created a potential difference .
A bird is not electrocuted on a high-voltage power line because it's not completing a circuit. By contrast, if a large bird touches two wires simultaneously, it creates a closed circuit, allowing electricity to flow through its body, leading to electrocution. Circuit breakers serve to prevent excess current flow.
Explanation:A bird sitting on a high-voltage power line does not get electrocuted because it is not completing a circuit. The bird is not touching the ground or another line, so the electricity stays within the conducting wire and doesn't pass through the bird. The bird is safe as long as it touches only one wire.
However, in contrasting scenarios, a larger bird could span the distance between two wires with its wings. If this happens, the bird would close the circuit, allowing the electricity to pass through its body, which would lead to electrocution. This is due to the significance of voltage difference between two given points to create an electric shock, as there is a potential difference between the two wires.
Also, the role of circuit breakers is important in the context of high voltage power supply. Circuit breakers prevent excess current flow and accidental contact with the line. They interrupt the electricity flow anytime there's a fault, safeguarding anyone who may come in contact with the cable.
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A sports car moves around a banked curve at just the right constant speed v so that no friction is needed to make the turn. During the turn, the driver (mass m) feels as though she weighs x times her actual weight. Find the magnitude of the net force on the driver during the turn in terms of m, g, and x.
The magnitude of the net force on the driver during a turn on a banked curve, when no friction is required, is equal to the driver's mass multiplied by gravity and the factor x, which represents the perceived increase in weight. Therefore, the magnitude of the net force is m × g × x.
Explanation:If a sports car moves around a banked curve at a constant speed such that no friction is needed, this means that the net force is providing the necessary centripetal force for the turn. According to the problem, the driver feels as though she weighs x times her actual weight. This perception of increased weight is due to the normal force provided by the banked road, which has both vertical and horizontal components.
Using Newton's second law, the net force on the driver can be expressed as net force = mass × acceleration. In this case, the centripetal acceleration is due to the net horizontal force, which is the horizontal component of the normal force.
The vertical component of the normal force is balancing the driver's actual weight, and the horizontal component of the normal force equals the centripetal force necessary for circular motion. Therefore, the normal force experienced by the driver (which is responsible for the feeling of increased weight) is FN = m × g × x. Since this is the net force and it is providing the centripetal force, the magnitude of the net force on the driver is also FN = m × g × x.
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A proton is circling the Earth above the magnetic equator, where Earth’s magnetic field is directed horizontally north and has a magnitude of 4.00 × 10–8 T. If the proton is moving at a speed of 2.7 × 107 m/s, how far above the surface of the Earth is the proton
Answer:
[tex]6.65\times 10^5 m[/tex]
Explanation:
We are given that
Magnetic field=B=[tex]4\times 10^{-8} T[/tex]
[tex]v=2.7\times 10^7 m/s[/tex]
We have to find the height of proton from the surface of the Earth.
Mass of proton,[tex]m_p=1.67\times 10^{-27} kg[/tex]
Charge on proton,[tex]q=1.6\times 10^{-19} C[/tex]
Radius of Earth, r=[tex]6.38\times 10^6 m[/tex]
Centripetal force due to rotation of proton=[tex]\frac{mv^2}{r+h}[/tex]
Magnetic force,F=[tex]qvB[/tex]
[tex]\frac{mv^2}{r+h}=qvB[/tex]
[tex]\frac{mv}{r+h}=qB[/tex]
Substitute the values
[tex]\frac{1.67\times 10^{-27}\times (2.7\times 10^7)}{6.38\times 10^6+h}=1.6\times 10^{-19}\times 4\times 10^{-8}[/tex]
[tex]6.38\times10^6+h=\frac{1.67\times 10^{-27}\times 2.7\times 10^7}{1.6\times 10^{-19}\times 4\times 10^{-8}}[/tex]
[tex]6.38\times10^6+h=7.045\times 10^6[/tex]
[tex]h=7.045\times 10^6-6.38\times 10^6[/tex]
[tex]h=0.665\times 10^6=6.65\times 10^5 m[/tex]
A fixed-geometry supersonic inlet starts at a Mach number of 3. After starting, the cruise Mach number is 2, and the operating shock is positioned at a location where the area is 10% larger than the throat. a) Assuming the flow is ideal except for shock losses, find the inlet stagnation b) During cruise, the Mach number at the exit of the diffuser M2 is required to be 0.3. Determine the ratio of the areas at the diffuser exit to that at the inlet (find AJA, and the static pressure ratio p./p. A,JA), and the static pressure ratio p./p
Answer:
Explanation: see attachment below
Problem 8: Consider an experimental setup where charged particles (electrons or protons) are first accelerated by an electric field and then injected into a region of constant magnetic field with a field strength of 0.65 T.
What is the potential difference in volts required in the first part of the experiment to accelerate electrons to a speed of 6 1 × 107 m/s?
Answer:
10581.59 V
Explanation:
We are given that
Magnetic field=B=0.65 T
Speed of electron=[tex]v=6.1\times 10^7m/s[/tex]
Charge on electron, [tex]q=e=1.6\times 10^{-19} C[/tex]
Mass of electron,[tex]m_e=9.1\times 10^{-31} kg[/tex]
We have to find the potential difference in volts required in the first part of the experiment to accelerate electrons.
[tex]V=\frac{v^2m_e}{2e}[/tex]
Where V=Potential difference
[tex]m_e=[/tex]Mass of electron
v=Velocity of electron
Using the formula
[tex]V=\frac{(6.1\times 10^7)^2\times 9.1\times 10^{-31}}{2\times 1.6\times 10^{-19}}[/tex]
[tex]V=10581.59 V[/tex]
Hence, the potential difference=10581.59 V
Final answer:
To accelerate electrons to a speed of 6.1 × 10^7 m/s in a constant magnetic field with a strength of 0.65 T, the potential difference required in the first part of the experiment is approximately 88.6 volts.
Explanation:
To accelerate electrons to a speed of 6.1 × 10^7 m/s in a constant magnetic field with a strength of 0.65 T, we need to calculate the potential difference required in the first part of the experiment. The formula for the potential difference is given by:
V = (1/2)m*(v^2)/(q * B)
Where V is the potential difference, m is the mass of the electron (9.11 × 10^-31 kg), v is the velocity of the electron (6.1 × 10^7 m/s), q is the charge of the electron (-1.6 × 10^-19 C), and B is the magnetic field strength (0.65 T).
Plugging in the values into the formula, we get:
V = (1/2)(9.11 × 10^-31 kg)(6.1 × 10^7 m/s)^2/(-1.6 × 10^-19 C)(0.65 T)
Simplifying the expression, we find that the potential difference required is approximately 88.6 volts.