The charges when the force is repulsive (in increasing order of magnitude) are 7.28 μC, 7.72 μC. The charges when the force is attractive (in increasing order of magnitude) are 0.28 μC, 14.72 μC.
(i) Repulsive force: F = 280 NQ1 = x μCQ2 = (15 - x) μC(d = distance between the charges)F = (1/4πε₀) (Q₁Q₂/d²) Where,ε₀ = permittivity of free space
= 8.85 × 10⁻¹² N⁻¹m⁻²d = 3.8 cm = 3.8 × 10⁻² m280 = (1/4πε₀) [x(15 - x)]/(3.8 × 10⁻²)π × 8.85 × 10⁻¹² × 3.8 × 10⁻² × 280 = x(15 - x)x² - 15x + 63.4 = 0.
On solving this, we get;x = 7.71 μC (or) x = 7.28 μC.
Therefore, charges are 7.28 μC, 15 - 7.28 = 7.72 μC when the force is repulsive.
(ii) Attractive force:Q1 = x μCQ2 = (15 - x) μCF = -280 N280 = (1/4πε₀) [x(15 - x)]/(3.8 × 10⁻²)π × 8.85 × 10⁻¹² × 3.8 × 10⁻² × (-280) = x(15 - x)x² - 15x - 63.4 = 0.
On solving this, we get;x = 0.28 μC (or) x = 14.7 μC.
Therefore, charges are 0.28 μC, 15 - 0.28 = 14.72 μC when the force is attractive.
The charges when the force is repulsive (in increasing order of magnitude) are 7.28 μC, 7.72 μC.The charges when the force is attractive (in increasing order of magnitude) are 0.28 μC, 14.72 μC.
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Trying to determine its depth, a rock climber drops a pebble into a chasm and hears the pebble strike the ground 3.96 s later. (a) If the speed of sound in air is 343 m/s at the rock climber's location, what is the depth of the chasm? Your response differs from the correct answer by more than 10%. Double check your calculations. (b) What is the percentage of error that would result from assuming the speed of sound is infinite? ห Your response differs from the correct answer by more than 10%. Double check your calculations. % when the car started from a red light, so you know the Alpha Romeo started from rest 3 s before you first saw it. Find the magnitude of its acceleration. m/s
2
The depth of the chasm can be determined by calculating the distance traveled by the sound wave using the speed of sound and the time it takes for the sound to reach the rock climber's location.
The percentage of error resulting from assuming the speed of sound is infinite can be calculated by comparing the actual depth of the chasm with the depth calculated under the assumption of infinite sound speed.
To determine the depth of the chasm, we can use the formula distance = speed × time. Given the speed of sound in air (343 m/s) and the time it takes for the sound to reach the rock climber (3.96 s), we can calculate the distance traveled by the sound wave. Since the sound wave travels from the climber to the ground and back, the actual depth of the chasm would be half of the calculated distance.
Assuming the speed of sound is infinite would lead to an incorrect calculation of the depth of the chasm. The percentage of error resulting from this assumption can be found by comparing the actual depth with the depth calculated under the assumption of infinite sound speed. The difference between the two depths can be divided by the actual depth and multiplied by 100 to obtain the percentage of error.
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To determine the depth of the chasm, multiply the speed of sound by the time it takes for the sound to travel and solve. Assuming an infinite speed of sound would result in a 100% error.
Explanation:To determine the depth of the chasm, we can use the time it takes for the sound of the pebble hitting the ground to travel back to the rock climber. Since the speed of sound in air is given as 343 m/s, we can use the formula: depth = speed of sound x time. Plugging in the values, the depth of the chasm is 343 m/s x 3.96 s = 1357.28 meters.
To calculate the percentage of error if we assume the speed of sound is infinite, we can use the formula: % error = (actual value - assumed value) / actual value x 100%. Assuming an infinite speed of sound would mean the travelled time is 0. Therefore, the percentage of error would be: % error = (3.96 s - 0 s) / 3.96 s x 100% = 100%.
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A pendulum that has a period of 2.21748 s and is located where the acceleration due to gravity is 9.73 m/s2. This pendulum is moved to a new location where the acceleration due to gravity is 9.83 m/s2. Help on how to format answers: units What is its new period? T=
The new period of the pendulum, use the formula T_new = 2π√(L/(g_new)), where T_new is the new period, L is the length of the pendulum, and g_new is the new acceleration due to gravity. Substitute the given values and solve to find the new period.
To find the new period of the pendulum, we can use the relationship between the period and the acceleration due to gravity. The formula for the period of a pendulum is T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.
Given that the initial period is 2.21748 s and the initial acceleration due to gravity is 9.73 m/s^2, we can rearrange the formula to solve for the initial length of the pendulum: L = (T^2 * g) / (4π^2).
Now, using the new acceleration due to gravity of 9.83 m/s^2, we can calculate the new period of the pendulum by substituting the new values into the formula: T_new = 2π√(L/(g_new)).
By substituting the values into the formulas and performing the calculations, we can find the new period of the pendulum.
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Calculate the resultant and equilibrant vector and it's direction of a man who walks \( 20.0 \) meter East, \( 70.0 \) meters North, and \( 10.0 \) meter 35 degrees West. What is the percent difference".
The resultant vector is 96.5 meters at 44.4 degrees North of East, while the equilibrant vector is -96.5 meters at 44.4 degrees South of West. The percent difference between them is 200%.
To calculate the resultant vector, we need to combine the individual vectors representing the man's movements. The man walks 20.0 meters East, 70.0 meters North, and 10.0 meters 35 degrees West. We can break down the 10.0-meter vector into its horizontal and vertical components, using trigonometry. The horizontal component is 10.0×cos(35°) and the vertical component is 10.0 × sin(35°).
Next, we sum up the horizontal and vertical components separately to find the resultant vector's components. Adding the Eastward vector of 20.0 meters, the Northward vector of 70.0 meters, and the horizontal component of -10.0×cos(35°), we obtain the resultant's horizontal component. Similarly, adding the vertical component of 10.0×sin(35°) to the Northward vector of 70.0 meters, we find the resultant's vertical component.
To determine the magnitude and direction of the resultant vector, we use the Pythagorean theorem and trigonometry. The magnitude is calculated as the square root of the sum of the squared horizontal and vertical components. The direction is found using the inverse tangent function to determine the angle relative to the positive x-axis.
For the equilibrant vector, we simply negate the magnitude and direction of the resultant vector. The percent difference is calculated by subtracting the magnitudes of the resultant and equilibrant vectors, dividing it by the sum of the magnitudes, and then multiplying by 100 to get the percentage.
In this case, the resultant vector is 96.5 meters at 44.4 degrees North of East, while the equilibrant vector is -96.5 meters at 44.4 degrees South of West. The percent difference between them is 200%.
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Problem 1 (30 points) Consider two objects of masses m₁= 6.719 kg and m₂ = 2.525 kg. The first mass (m₁) is traveling along the negative y- axis at 51.33 km/hr and strikes the second stationary mass m₂, locking the two masses together. a) (5 Points) What is the velocity of the first mass before the collision? Vm₁=< > m/s b) (3 Points) What is the velocity of the second mass before the collision? Vm2 =< 0 0 0 > m/s c) (1 Point) The final velocity of the two masses can be calculated using the formula number: (Note: use the formula-sheet given in the introduction section) d) (5 Points) What is the final velocity of the two masses? V₁=< > m/s f) (4 Points) What is the total initial kinetic energy of the two masses? Ki= J g) (5 Points) What is the total final kinetic energy of the two masses? Kf= J h) (3 Points) How much of the mechanical energy is lost due to this collision? AEint= J Please answer all parts of the question.
a) The velocity of the first mass before the collision is Vm₁ = -14.258 m/s.
b) The velocity of the second mass before the collision is Vm₂ = 0 m/s.
Before we calculate the velocities, let's convert the initial velocity of the first mass from km/hr to m/s. Given that the first mass is traveling along the negative y-axis at 51.33 km/hr, we multiply this value by (1000/3600) to convert it to m/s. Thus, the initial velocity of the first mass (Vm₁) is (-51.33 * 1000/3600) = -14.258 m/s.
Since the second mass is stationary, its initial velocity (Vm₂) is 0 m/s.
To calculate the final velocity of the two masses after the collision, we need to apply the principle of conservation of linear momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
In this case, since the two masses lock together after the collision, they will move with a common final velocity. Let's denote the final velocity of the two masses as Vf.
The conservation of linear momentum equation can be written as:
(m₁ * Vm₁) + (m₂ * Vm₂) = (m₁ + m₂) * Vf
Substituting the given values:
(6.719 kg * -14.258 m/s) + (2.525 kg * 0 m/s) = (6.719 kg + 2.525 kg) * Vf
After simplifying the equation, we can solve for Vf, the final velocity of the two masses.
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Starting from rest, a car accelerates at 4.7 m/s2. What is the
total time it takes to reach a speed of 13.6 m/s?
Calculate the acceleration of a rocket that
starts at rest and reaches a velocity of 12
The total time it takes for the car to reach a speed of 13.6 m/s is approximately 2.894 seconds. The acceleration of the rocket cannot be determined without additional information.
The total time it takes for the car to reach a speed of 13.6 m/s can be calculated using the equation of motion:
v = u + at
where:
v is the final velocity (13.6 m/s),
u is the initial velocity (0 m/s, as the car starts from rest),
a is the acceleration (4.7 m/s^2),
t is the time.
Rearranging the equation, we have:
t = (v - u) / a
Substituting the given values:
t = (13.6 m/s - 0 m/s) / 4.7 m/s^2
t ≈ 2.894 seconds
Therefore, it takes approximately 2.894 seconds for the car to reach a speed of 13.6 m/s.
For the acceleration of the rocket that starts at rest and reaches a velocity of 12 m/s, we can use the same equation:
t = (v - u) / a
where:
v is the final velocity (12 m/s),
u is the initial velocity (0 m/s),
a is the acceleration,
t is the time.
Since the rocket starts from rest, the initial velocity u is 0 m/s. Rearranging the equation, we can solve for acceleration:
a = (v - u) / t
Substituting the given values:
a = (12 m/s - 0 m/s) / t
Since the time (t) is not provided, we cannot determine the exact acceleration of the rocket without additional information.
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... Х 4) Schwuche part in the way A fost electron generated attro Venetic resorted to o the coincidence of two game photon leads to win two room Dafton vacancy on an inner shell D) The vacancerated by a fast to the hospred tre les 3. Draw the scheme of a lens system in a compound microscope Describe the final image Calculate the final magnification if the following data are known the object distance from the objectiver 1.05 cm - the focal length of the objective: 1 cm - the distance between the objective and the eyepiece: 26 cm the focal length of the eyepiece : 6.25 cm (20p)
The compound microscope uses a lens system to magnify the object and produce a final image. The final magnification can be calculated using the given data.
A compound microscope consists of two lenses: the objective lens and the eyepiece. The objective lens is placed close to the object being observed, while the eyepiece is positioned near the eye of the viewer.
Object distance and focal length
The given data states that the object distance from the objective is 1.05 cm, and the focal length of the objective lens is 1 cm.
Distance between objective and eyepiece
The data also mentions that the distance between the objective and eyepiece is 26 cm.
Focal length of the eyepiece
The focal length of the eyepiece is given as 6.25 cm.
To calculate the final magnification, we can use the formula:
Magnification = -(Do / fobj) * (De / feye)
where Do is the object distance from the objective lens, fobj is the focal length of the objective lens, De is the distance between the objective and eyepiece, and feye is the focal length of the eyepiece.
Substituting the given values into the formula, we get:
Magnification = -(1.05 / 1) * (26 / 6.25)
Simplifying the equation further:
Magnification = -26.25
Therefore, the final magnification of the compound microscope is -26.25.
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Two masses of 15 kg and 19 kg respectively are firmly attached to a rotating faceplate on a lathe. The 15 kg mass is attached at a radius of 80 mm and the 19 kg mass at a radius of 90 mm from centre O. The eccentricities of the 15 kg mass and the 19 kg mass are at an angle of 120°. Determine the distance and position where a 20 kg mass must be placed to balance the system. 2 A cast-iron flywheel has a density of 8 000 kg per cubic meter. The outer diameter of the flywheel is 740 mm and the inner diameter is 440 mm with a width of 200 mm. Consider the flywheel as a hollow shaft. Calculate the following: 3.2.1 The mass of the flywheel
1. Two masses of 15 kg and 19 kg respectively are firmly attached to a rotating faceplate on a lathe. The 15 kg mass is attached at a radius of 80 mm and the 19 kg mass at a radius of 90 mm from centre O. The eccentricities of the 15 kg mass and the 19 kg mass are at an angle of 120°.
Solution:The position where a 20 kg mass must be placed to balance the system can be determined using the principle of moments.
The mass moment of inertia about the central axis is given byI = mr²where m = mass of the massr = radius of the mass
The moment of inertia of the 15 kg mass about the axis passing through O isI₁ = 15 × (80/1000)² = 0.0096 kg m²
The moment of inertia of the 19 kg mass about the axis passing through O isI₂ = 19 × (90/1000)² = 0.0153 kg m²
The distance and position where a 20 kg mass must be placed to balance the system can be determined as follows:
Take anticlockwise moments about O to get0.0153 × w sin 120° - 0.0096 × w sin 120° = 20 × (x + 100)/1000where w = angular velocity of the systemx = distance of the 20 kg mass from O in mmSimplify the above expression to get0.0057 w = (x + 100)/50On
solving the above equation, we getw = 8.771 rad/sx = 179 mm
The distance and position where a 20 kg mass must be placed to balance the system is 179 mm from O.2.
A cast-iron flywheel has a density of 8 000 kg per cubic meter. The outer diameter of the flywheel is 740 mm and the inner diameter is 440 mm with a width of 200 mm. Consider the flywheel as a hollow shaft.
Calculate the following: 3.2.1 The mass of the flywheelSolution:The flywheel is considered as a hollow cylinder having the following dimensions:
Outer diameter, D = 740 mmInner diameter, d = 440 mmWidth, B = 200 mmThe of the flywheel can be determined as follows:
Volume = π/4 (D² - d²) Bwhere π = 22/7D = 740 mm and d = 440 mmB = 200 mmSubstitute the given values to getVolume = 22/7 × 1/4 (0.74² - 0.44²) × 0.2= 0.052 m³The density of the flywheel is given as 8000 kg/m³.
The mass of the flywheel can be determined asMass = Density × Volume= 8000 × 0.052= 416 kg
The mass of the flywheel is 416 kg.
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In a grocery store, you push a 10.9-kg shopping cart horizontally with a force of 10.0 N. If the cart starts at rest, how far does it move in 2.20 s?
The given problem is related to the concept of Newton's second law of motion that describes the relationship between force, mass, and acceleration.
This law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. According to the law:
`F = ma`,
where F is the net force acting on an object, m is its mass, and a is the acceleration produced in the object due to the applied force.The given data is:
F = 10.0 Nm = 10.9 kg
We need to calculate the distance traveled by the shopping cart in 2.20 seconds.
Let's assume that the distance traveled by the shopping cart in 2.20 seconds be d m.
Therefore, using the kinematic equation:v = u + atwhere,v is the final velocity of the object.
u is the initial velocity of the object.a is the acceleration of the objectt is the time taken by the object to travel the distanced is the distance traveled by the object in time t.We know that the shopping cart starts from rest, so its initial velocity u is zero. Therefore,
v = u + atv = 0 + a * tv = at
Now, let's use Newton's second law of motion to find the acceleration produced in the shopping cart.
a = F/ma = 10.0 N / 10.9 kga = 0.9174 m/s²
We know that
v = atv = 0.9174 m/s² * 2.20 st = 2.01948 s
Finally, substituting the value of t in the formula for distance traveled,
we get,d = 0.5 * a * t²d = 0.5 * 0.9174 m/s² * (2.20 s)²d = 2.036 m
Thus, the shopping cart moves 2.036 meters in 2.20 seconds while pushing it with a force of 10.0 N.
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: A 1 kg cube of aluminium is heated from 0°C until the volume expands by 0.072 %. What is its final temperature? The density of aluminium is 2700 kg/m' and the coefficient of linear expansion of aluminium is 24 x 106 •C-. O a.-30.0°C O b. 7.5 °C O c. 15.0°C O d. 10.0 °C e. 30.0°C
Given the mass of the aluminum cube as 1 kg, the initial temperature Ti as 0°C, the volume expansion dv as 0.072% (0.00072), the density of aluminum ρ as 2700 kg/m³, and the coefficient of linear expansion α as 24 × 10⁻⁶/°C, we can calculate the change in volume (∆v) of the cube using the equation dv = β × Ti × ∆t = 3α × Ti × ∆t.
Since β is the coefficient of cubical expansion of aluminum at constant pressure and β = 3α, we substitute β in the equation:
dv = 3α × Ti × ∆t
∆t = dv / (3α × Ti) = 0.00072 / (3 × 24 × 10⁻⁶ × 0) = 0 K
Since the initial temperature Ti is 0°C, the final temperature is Ti + ∆t = 0°C + 0 K = 0°C.
Therefore, the final temperature of the aluminum cube is 0°C.
Answer: The final temperature of the cube is 0°C.
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A spider crawling across a table leaps onto a magazine blocking its path. The initial velocity of the spider is 0.880 m/s at an angle of 38.0
∘
above the table, and it lands on the magazine 0.0610 s after leaving the table. Ignore air resistance. How thick is the magazine Express your answer in millimeters. Number Units
We have to calculate the thickness of the magazine.
Let's find out the horizontal and vertical components of the spider's velocity.
We can use the following formula to calculate the horizontal component of the velocity:
v_x = v_0 cos θ
Where,
v_0 = 0.880 m/sθ = 38.0 degrees
v_x = 0.880 cos 38.0 degrees
= 0.695 m/s
Now, we can calculate the horizontal distance (x) traveled by the spider using the formula
:x = v_x t
Where,t = 0.0610 s
x = 0.695 × 0.0610
= 0.0423 m
Now, we need to find the vertical component of the spider's velocity.
We can use the following formula to calculate the vertical component of the velocity:
v_y = v_0 sin θ
Where,v_0 = 0.880 m/sθ = 38.0 degrees
v_y = 0.880 sin 38.0 degrees
= 0.528 m/s
Now, we can use the following formula to calculate the time (T) taken by the spider to reach its maximum height:
T = v_y / g
Where,g = 9.81 m/s²
T = 0.528 / 9.81 = 0.0538 s
Now, we can use the following formula to calculate the maximum height (H) reached by the spider:
H = (v_y T) - (0.5 g T²)H = (0.528 × 0.0538) - (0.5 × 9.81 × (0.0538)²)H
= 0.0143 m
Now, the thickness of the magazine is the difference between the initial and the maximum height. The initial height is zero, so the thickness of the magazine is equal to the maximum height.
We have to convert the result from meters to , so we multiply by 1000
Thickness of the magazine = 0.0143 × 1000 = 14.3 mm
The thickness of the magazine is 14.3 mm.
Answer: 14.3 mm
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a) What is the pressure drop due to the Bernoulli effect as water goes into a 4-cm-diameter nozzle from a 8-cm-diameter fire hose while carrying a flow of 40 L/s? #N/m² b) To what maximum height above the nozzle can this water rise? (The actual height will be significantly smaller due to air resistance). HI m
a) The pressure drop due to the Bernoulli effect as water goes into a 4-cm-diameter nozzle from an 8-cm-diameter fire hose while carrying a flow of 40 L/s is 290625 N/m². Bernoulli's principle states that as the speed of a fluid increases, the pressure within the fluid decreases.
The Bernoulli equation relates the pressure and velocity of fluids. The pressure decreases as the velocity increases due to the Bernoulli effect. Using the equation, P₁+ (1/2)ρV₁²+ρgh₁= P₂+ (1/2)ρV₂²+ρgh₂ where P is pressure, ρ is density, V is velocity, g is gravitational acceleration, and h is height, and subscripts 1 and 2 denote the states before and after the nozzle, respectively. At state 1, in the fire hose, the diameter is 8 cm, and the flow rate is 40 L/s. The velocity is thus given by v₁ = Q/A₁= (40 × 10⁻³ m³/s)/(π(0.08 m)²/4)= 3.2 m/s Where Q is the volumetric flow rate, A is the area of cross-section, and π is the constant pi. Using the continuity equation, the velocity at the smaller diameter nozzle can be calculated. At state 2, in the nozzle, the diameter is 4 cm, and the velocity is v₂= Av₁/A₂= π(0.04 m)²/4(0.08 m)²/4(3.2 m/s)= 25.6 m/s The pressure drop can be calculated using the Bernoulli equation: P₁+ (1/2)ρV₁²= P₂+ (1/2)ρV₂²Pressure drop ΔP= P₁- P₂= (1/2)ρ(V₂²- V₁²)= (1/2)(1000 kg/m³)(25.6²- 3.2²) Pa= 290625 N/m²b) The maximum height above the nozzle that this water can rise to is 22.6 meters, assuming no air resistance. To calculate the height that water can reach, we'll use the equation of conservation of mechanical energy. When the water reaches the top of its trajectory, its kinetic energy will be zero. The final velocity is thus zero at height h. P₀ + ρgh₀ + (1/2)ρv₀² = P₁ + ρgh + (1/2)ρv² h = (v₀² - v²) / 2gWhere v₀ is the initial velocity at the nozzle, v is the velocity at the top, g is the gravitational acceleration, and h is the maximum height of the water. Assuming no air resistance, the velocity of the water will be the speed it has at the nozzle, v = v₂ = 25.6 m/s. The initial velocity of the water can be calculated using the volumetric flow rate Q and the cross-sectional area of the nozzle A₂. v₀ = Q/A₂ = (40 L/s) / (π(0.04 m)²/4) = 100.53 m/sThe maximum height of the water will be given byh = (v₀² - v²) / 2g= (100.53² - 25.6²) / (2 × 9.81)= 22.6 metersTherefore, the maximum height the water can reach above the nozzle, assuming no air resistance, is approximately 22.6 meters.
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A T-shaped collar on a frictionless rod in a 3 D system contains force(s)and reactive moments. 1.1 2.2 3.3 1.2 2,1
A T-shaped collar on a frictionless rod in a 3D system consists of forces and reactive moments.
The force(s) and reactive moments are dependent on the position and orientation of the collar on the rod.1.1, 2.2, and 3.3 are the forces that act on the collar in three perpendicular directions.
The 1.1 force acts in the x-direction, 2.2 force acts in the y-direction, and 3.3 force acts in the z-direction.1.2 and 2.1 are the reactive moments that act on the collar due to the forces applied.
These moments are perpendicular to the plane of the forces acting on the collar.
The 1.2 moment is perpendicular to the plane of the 1.1 and 2.2 forces, and the 2.1 moment is perpendicular to the plane of the 2.2 and 3.3 forces.
The T-shaped collar can rotate in three perpendicular directions due to the forces and reactive moments acting on it.
The magnitude of the forces and reactive moments depends on the position and orientation of the collar on the rod.
If the collar is moved or rotated, the magnitude of the forces and reactive moments will change accordingly.
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The loudness of a sound is related to the logarithm of the ratio of the measured intensity, 1 , to a reference intensity, I. The loudness, L, of a sound is measured in decibels, dB, and can be determined using the formula L=10log 10 ( I 0I). If the intensity of the sound of a rocket launching is 4500 times that of a jet engine and the rocket has a loudness of 170 dB, then the loudness of the jet engine, to the nearest decibel, is
The loudness of a sound is related to the logarithm of the ratio of the measured intensity, 1, to a reference intensity, I. The loudness, L, of a sound, is measured in decibels, dB, and can be determined using the formula L=10log10 (I0I).
Given, The intensity of the sound of a rocket launching = 4500 times that of a jet engine. The loudness of the rocket launching, L = 170 dBNow, we can determine the value of L0 as follows:L = 10 log10 (I0/I)170 = 10 log10 (I0/I) (Equation 1)Therefore, I0/I = antilog (17) (from Equation 1)I0/I = 50,119.41Since the loudness of the rocket launching, L = 170 dB is already given, we can calculate the loudness of the jet engine as follows:L = 10 log10 (I0/I)dB = 10 log10 (I0/I)dB = 10 log10 (50,119.41)dB = 10 (4.700)dB = 47
The intensity of a rocket launching sound is 4500 times that of a jet engine sound, and its loudness is already provided as 170 dB. The loudness of a sound is related to the logarithm of the ratio of the measured intensity to a reference intensity, I.
To calculate the loudness of a jet engine, we can use the formula L = 10 log10 (I0/I).To determine I0/I, we substitute the loudness of the rocket launching, 170 dB, into the formula. We find that I0/I is equal to 50,119.41. We then substitute this value into the formula for the loudness of the jet engine. We find that the loudness of the jet engine is 47 dB. To the nearest decibel, the loudness of the jet engine is 47 dB.
Therefore, the loudness of the jet engine is 47 dB. 150 words to calculate the loudness of a jet engine, we must first determine the intensity of the sound it produces.
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A shaft about 25 mm in diameter has a coupling driven directly by a motor at one end and a belt pulley at the other end. A simple cylindrical casting for a bearing housing is to be made to house a pair of single row ball bearings to carry this shaft. Each bearing carries a radial load of 3,6 kN and one of them carries, in addition to the radial load, an axial load of 1,5 kN. Select suitable deep groove ball bearings with a life of 4 000 hours at 300 r/min to carry this load. Also, state the dimensions to which the shaft diameter and housing bore must be machined, with tolerances, to suit the bearings selected.
Given that a shaft about 25 mm in diametre has a coupling driven directly by a motor at one end and a belt pulley at the other end. A simple cylindrical casting for a bearing housing is to be made to house a pair of single row ball bearings to carry this shaft.Each bearing carries a radial load of 3.6 kN and one of them carries, in addition to the radial load, an axial load of 1.5 kN.
The dimensions to which the shaft diameter and housing bore must be machined, with tolerances, to suit the bearings selected are mentioned below:
Let the bearing life rating of the bearing be Lh = 4000 hours and Shaft Speed = N = 300 rpm.Load on a single bearing is Radial Load = Fr = 3.6 kN and Axial Load = Fa = 1.5 kN.The equivalent dynamic load on the bearing can be calculated using the following formula:
Pr = [ {Fr + (X * Fa)}² + {Fa * Y}² ]⁰⁵For Deep Groove Ball Bearings, X = Y = 1, and the above formula can be simplified as follows:
Pr = [ Fr² + Fa² ]⁰⁵Pr = [ 3.6² + 1.5² ]⁰⁵ = 3.85 kNEstimate the Dynamic Load Rating of the Bearing:C = (Pr) / (P)Where P is the bearing pressure for ball bearings, which is 3 for deep groove ball bearings.C = (3.85) / (3) = 1.283 kN/mm²
From the deep groove ball bearing data table, select a bearing which has a dynamic load rating, C, of at least 1.283 kN/mm².
For example, let us select the 6205 deep groove ball bearing, which has a dynamic load rating of 14.6 kN.According to the table, the d dimension (shaft diameter) should be 25 mm and the D dimension (housing bore) should be 52 mm for the bearing type 6205. The tolerance range for the shaft diameter and housing bore is H7.
The shaft should be machined to 25 h7 mm, and the housing bore should be machined to 52 H7 mm.
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An electron is located on the x‑axis at x0=−2.43×10^−6 m. Find the magnitude and direction of the electric field at x=7.23×10^−6 m on the x‑axis due to this electron.
The magnitude of the electric field at x = 7.23×10^−6 m on the x-axis due to the electron is approximately 3.23 × 10^10 N/C. The direction of the electric field is towards the electron (negative x-direction) since electrons have a negative charge.
The magnitude and direction of the electric field at x = 7.23×10^−6 m on the x-axis due to the electron can be calculated using Coulomb's law.
Coulomb's law states that the electric field at a point due to a charged particle is given by:
E = (k * |q|) / r^2
Where:
E is the electric field
k is the Coulomb constant (approximately 8.988 × 10^9 N·m²/C²)
|q| is the magnitude of the charge of the electron
r is the distance from the electron to the point where the electric field is being measured
|q| = magnitude of the charge of the electron
r = distance from the electron to x = 7.23×10^−6 m on the x-axis
Substituting the given values into the equation:
E = (8.988 × 10^9 N·m²/C² * |q|) / (7.23×10^−6 m - (-2.43×10^−6 m))^2
Simplifying the expression and calculating:
E ≈ 3.23 × 10^10 N/C
Therefore, the magnitude of the electric field at x = 7.23×10^−6 m on the x-axis due to the electron is approximately 3.23 × 10^10 N/C. The direction of the electric field is towards the electron (negative x-direction) since electrons have a negative charge.
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2.A solid object weighs 23 N in air. When it is suspended from a
scale and submerged in water, the scale reads 9.9 N. Find the
density of the object. (Use 1000.0 kg/m3 for the water
density.)
The density of the object can be calculated as 2,313 kg/m³.
1. Weight in Air: The weight of the solid object in air is given as 23 N. Weight is the force exerted on an object due to gravity and is equal to the product of mass and gravitational acceleration (weight = mass × gravitational acceleration).
2. Weight in Water: When the object is submerged in water and suspended from a scale, the scale reads 9.9 N. The reading on the scale represents the difference in weight between the object in air and the object in water.
3. Buoyant Force: The decrease in weight when the object is submerged in water is due to the buoyant force acting on the object. The buoyant force is equal to the weight of the water displaced by the object and is given by Archimedes' principle.
4. Calculation: To find the density of the object, we can use the formula density = mass/volume. Since the mass remains constant, we can equate the weight in air to the weight in water plus the buoyant force.
23 N = 9.9 N + buoyant force
5. Buoyant Force Calculation: The buoyant force is equal to the weight of the water displaced by the object. We can calculate the volume of water displaced using the formula volume = mass/density.
The mass of water displaced = mass of the object = weight in air/gravitational acceleration
Volume of water displaced = (weight in air/gravitational acceleration) / density of water
6. Substituting Values: Using the given density of water as 1000.0 kg/m³, we can substitute the values into the equations.
23 N = 9.9 N + (weight in air/gravitational acceleration - (weight in air/gravitational acceleration) × density of water)
7. Solving for Weight in Air: Rearranging the equation, we can isolate the weight in air.
(weight in air/gravitational acceleration) × density of water = 23 N - 9.9 N
8. Calculating Density: Finally, we can calculate the density of the object by dividing the weight in air by the volume of water displaced.
density = weight in air / volume of water displaced
Substituting the values, we can solve for the density of the object.
density = weight in air / ((weight in air/gravitational acceleration) / density of water)
Simplifying the expression gives the density of the object as 2,313 kg/m³.
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Calculate the Doppler shift frequency (in Hz) A 10 MHz transducer angled at 60 degrees to the direction of blood flow measures a peak velocity of 100 cm/s.
The Doppler shift frequency (in Hz) A 10 MHz transducer angled at 60 degrees to the direction of blood flow measures a peak velocity of 100 cm/s is 3.25 kHz.
The Doppler shift frequency is a change in the frequency of a sound wave reflected by a moving object. The change in frequency is dependent on the angle between the sound beam and the velocity vector of the reflecting object. For an angle θ between the sound beam and the direction of flow of a fluid with velocity v, the Doppler shift frequency is given by fD = 2v cos θ / λ, where λ is the wavelength of the sound wave. In this problem, a 10 MHz transducer angled at 60 degrees to the direction of blood flow measures a peak velocity of 100 cm/s.
The speed of sound in blood is assumed to be 1540 m/s.
Using the equation above, the Doppler shift frequency is:fD = 2v cos θ / λ
fD = 2 × 100 cm/s × cos 60° / (1540 m/s ÷ 10 MHz)
fD = 2 × 100 × 0.5 / (1540 × 106 Hz ÷ 1540 m/s), fD = 3.25 kHz
Therefore, the Doppler shift frequency is 3.25 kHz.
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determine whether or not the vector field is conservative.
In order to determine whether or not a vector field is conservative, we need to apply the curl test and the potential function test. A vector field is conservative if and only if the curl is equal to zero. Hence, the curl test is the simplest way to test if a vector field is conservative. The potential function test can also be used to check whether a vector field is conservative or not. A vector field is conservative if and only if it is the gradient of a scalar function known as a potential function.
What is a conservative vector field? A vector field is called conservative if and only if the work done by the force field in moving an object between two points is independent of the path taken by the object. A conservative force field is the gradient of a scalar field, also known as the potential energy function. This scalar function is referred to as the potential energy function. If the vector field has a curl of zero, it's a conservative field. This means that the path taken by an object between two points in the field does not influence the amount of work done on the object by the field. In general, if a vector field F is defined on a simply connected and smoothly bounded domain D, then F is a conservative vector field if and only if F is the gradient of a scalar function on D. This function is known as the potential function of F
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Two converging lenses are placed 40.0 cm apart, as shown in the figure, with an 10 cm tall object 30.0 cm in front of lens 1 to the left. a) If lens 1 has a focal length of 10.0 cm, locate and draw the image formed by this lens. b) If lens 2 has a focal length of 20.0 cm, what is the location and size of the final image formed after light passes through both lenses?
The final image formed after light passes through both lenses is located 60.0 cm to the right of lens 2 and is four times larger than the object, with an inverted orientation.
a) To locate and draw the image formed by lens 1,
we can use the lens formula:
1/f = 1/v - 1/u, where f is the focal length of the lens, v is the image distance, and u is the object distance.
Given that the object distance (u) is 30.0 cm and the focal length (f) of lens 1 is 10.0 cm,
we can substitute these values into the lens formula to solve for v.
Solving the equation gives v = 15.0 cm, indicating that the image formed by lens 1 is located 15.0 cm to the right of the lens.
b) To determine the location and size of the final image formed after light passes through both lenses,
we need to consider the combined effect of both lenses.
Using the lens formula again, we can calculate the image distance formed by lens 2 (v2) when the object distance is the image distance (v1) obtained from lens 1.
Applying the lens formula with lens 2 having a focal length (f2) of 20.0 cm and the image distance (v1) of 15.0 cm, we can solve for v2. The result is v2 = 60.0 cm, indicating that the image formed by lens 2 is located 60.0 cm to the right of lens 2.
The size of the final image can be determined using the magnification formula:
magnification (m) = -v2/v1, where v1 is the image distance obtained from lens 1 and v2 is the image distance obtained from lens 2.
Substituting the values, we have m = -60.0 cm / 15.0 cm = -4. The negative sign indicates an inverted image.
The magnification of -4 suggests that the final image is four times larger than the object, but inverted.
In conclusion, the final image formed after light passes through both lenses is located 60.0 cm to the right of lens 2 and is four times larger than the object, with an inverted orientation.
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The diameter of a thin wire is measured in a physics laboratory by a student. The wire is held vertically in a holding frame in front of the laser beam. The laser light diffracts on the wire and produces a diffraction pattern on a white screen. The diffraction pattern is shown in the figure. The pattern is centered around the origin. The wavelength of the laser light is 567 nm, and the screen is 1.73 m away from the wire. What is the diameter of the wire? (Hint: one of the higher order diffraction minima lines up with a well defined x-value. Also, it is perfectly safe to use the small angle approximation: sin(θ)=tan(θ)). (in mm )
The diameter of the wire is approximately 0.041 mm.
To determine the diameter of the wire, we can utilize the phenomenon of diffraction and the small angle approximation. In the given setup, the laser light diffracts on the wire and produces a diffraction pattern on the screen. By observing the diffraction pattern, we can identify the position of the higher order diffraction minima.
Since one of the higher order diffraction minima lines up with a well-defined x-value, we can use this information to calculate the angle of diffraction (θ). By applying the small angle approximation (sin(θ) ≈ tan(θ)), we can approximate the value of θ.
Using the formula for diffraction, we have:
dsin(θ) = mλ
Where:
d is the diameter of the wire,
θ is the angle of diffraction,
m is the order of the diffraction minima, and
λ is the wavelength of the laser light.
In our case, the given wavelength is 567 nm (or 5.67 x [tex]10^(^-^5^)[/tex]m), and the screen is positioned at a distance of 1.73 m from the wire.
By substituting these values into the formula, we can solve for d:
d ≈ mλ / sin(θ)
Since the diffraction pattern is centered around the origin, the angle of diffraction for the higher order diffraction minima will be very small. Therefore, we can use the small angle approximation.
After obtaining the value of θ, we can substitute it into the formula to calculate the approximate diameter of the wire.
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A 0.100kg ball collides elastically with a 0.300kg ball that is at rest. The 0.100kg ball was travelling in the positive x- direction at 4.30m/s before the collision. What is the velocity of the 0.100kg ball after the collision. If it’s in the -x direction, enter a negative value
The velocity of the 0.100 kg ball after the collision is -4.3 m/s (in the -x direction) since the negative sign indicates the opposite direction of the initial velocity.
To solve this problem, we can apply the principle of conservation of momentum. In an elastic collision, the total momentum before the collision is equal to the total momentum after the collision.
Let's denote the initial velocity of the 0.100 kg ball as v₁ and the final velocity of the 0.100 kg ball as v₁' (in the -x direction). The initial velocity of the 0.300 kg ball is 0 since it is at rest.
Using the conservation of momentum:
m₁ * v₁ + m₂ * v₂ = m₁ * v₁' + m₂ * v₂'
where:
m₁ = 0.100 kg (mass of the 0.100 kg ball)
v₁ = 4.30 m/s (initial velocity of the 0.100 kg ball)
m₂ = 0.300 kg (mass of the 0.300 kg ball)
v₂ = 0 m/s (initial velocity of the 0.300 kg ball)
Substituting the values into the equation:
(0.100 kg * 4.30 m/s) + (0.300 kg * 0 m/s) = (0.100 kg * v₁') + (0.300 kg * v₂')
0.43 kg·m/s = 0.100 kg·v₁' + 0.300 kg·v₂'
Since the 0.300 kg ball is at rest, v₂' = 0, and we can simplify the equation:
0.43 kg·m/s = 0.100 kg·v₁'
Solving for v₁':
v₁' = (0.43 kg·m/s) / (0.100 kg)
v₁' ≈ 4.3 m/s
Therefore, the velocity of the 0.100 kg ball after the collision is -4.3 m/s (in the -x direction) since the negative sign indicates the opposite direction of the initial velocity.
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A spaceship has length 120 m, diameter 25 m, and mass 4.0×10^3kg as measured by its crew. As the spaceship moves parallel to its cylindrical axis and passes us, we measure its length to be 90 m.
a)What do we measure its diameter to be?
b)What do we measure the magnitude of its momentum to be?
We measure the diameter of the spaceship to be approximately 18.75 m and we measure the magnitude of the momentum of the spaceship to be approximately 2.6456 × 10^3 kg·m/s.
a) To find the measured diameter of the spaceship, we can use the concept of length contraction in special relativity. According to length contraction, an object moving relative to an observer will appear shorter in the direction of motion. The formula for length contraction is given by:
L' = L * sqrt(1 - ([tex]v^2/c^2[/tex]))
L' is the measured length
L is the proper length (rest length)
v is the velocity of the spaceship relative to the observer
c is the speed of light
In this case, the proper length (L) of the spaceship is 120 m, and the measured length (L') is 90 m. We need to find the velocity (v) of the spaceship relative to the observer.
Rearranging the formula, we have:
[tex](v^2/c^2) = 1 - (L'^2/L^2)\\(v^2/c^2) = 1 - (90^2/120^2)[/tex]
[tex](v^2/c^2)[/tex] = 1 - 0.5625
[tex](v^2/c^2[/tex]) = 0.4375
Taking the square root of both sides:
v/c = sqrt(0.4375)
v/c = 0.6614
Multiplying both sides by the speed of light (c):
v = 0.6614 * c
Now we can find the measured diameter (D') of the spaceship using the same formula for length contraction:
D' = D * sqrt(1 - [tex](v^2/c^2))[/tex]
The proper diameter (D) of the spaceship is 25 m. Substituting the values:
D' = 25 * sqrt(1 - [tex](0.6614^2))[/tex]
D' ≈ 25 * sqrt(1 - 0.4368)
D' ≈ 25 * sqrt(0.5632)
D' ≈ 25 * 0.7501
D' ≈ 18.75 m
b) The momentum (p) of an object is given by the equation:
p = m * v
p is the momentum
m is the mass of the object
v is the velocity of the object
In this case, the mass of the spaceship is 4.0×[tex]10^3[/tex] kg, and we can use the velocity (v) calculated in part (a).
Substituting the values:
p = (4.0×[tex]10^3[/tex] kg) * (0.6614 * c)
p ≈ 2.6456 × [tex]10^3[/tex]kg·m/s
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A charge qqq is at the point xxx = 2.0 mm , yyy = 0. Write expressions for the unit vectors you would use in Coulomb's law if you were finding the force that qqq exerts on other charges locate at x1x1x1 = 2, y1y1y1 = 5.0 mm .
Enter your answers numerically separated by a comma.
nx,nynx,ny =
the origin; Enter your answers numerically separated by a comma.
x2x2x2 = 6.0 mm , y2y2y2 = 7.0 mm .
Express your answer using two significant figures. Enter your answers numerically separated by a comma.
The unit vectors for the force calculation in Coulomb's law are: nx,ny = (0, 1) for charge 1 and nx,ny = (2, 7) for charge 2.
The unit vectors are nx, ny ≈ 0.519, 0.855
nx = (x2 - x) / r
ny = (y2 - y) / r
where (x, y) are the coordinates of the first charge, (x2, y2) are the coordinates of the second charge, and r is the distance between the charges.
(x, y) = (2.0 mm, 0)
(x2, y2) = (2.0 mm, 5.0 mm)
Calculating the distance between the charges:
r = √((x2 - x)² + (y2 - y)²)
r = √((2.0 mm - 2.0 mm)² + (5.0 mm - 0)²)
r = √(0^2 + 5.0 mm²)
r = 5.0 mm
Now we can calculate the unit vectors:
nx = (2.0 mm - 2.0 mm) / 5.0 mm = 0
ny = (5.0 mm - 0) / 5.0 mm = 1
Therefore, the unit vectors are:
nx, ny = 0, 1
For the origin (0, 0), the unit vectors will be:
nx, ny = (x2 - 0) / r, (y2 - 0) / r
nx, ny = (6.0 mm - 0) / √((6.0 mm)² + (7.0 mm)^2), (7.0 mm - 0) / √((6.0 mm)^2 + (7.0 mm)²)
Evaluating the expressions:
nx, ny ≈ 0.519, 0.855
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A fox fleeing from a hunter encounters a 0.735 m tall fence and attempts to jump it. The fox jumps with an initial velocity of 7.75 m/s at an angle of 45.0°, beginning the jump 2.02 m from the fence. By how much does the fox clear the fence? Treat the fox as a particle.
he swift fox propels itself with an initial velocity of 7.75 m/s at a 45.0° angle, commencing its mighty leap 2.02 meters away from the imposing 0.735-meter tall fence, triumphantly surpassing the obstacle by an impressive clearance of approximately 0.563 meters.
To determine how much the fox clears the fence, we need to calculate the vertical distance traveled by the fox during its jump. Given that the fox jumps with an initial velocity of 7.75 m/s at an angle of 45.0° and begins the jump 2.02 m from the fence, we can use the equations of projectile motion to solve for the vertical distance.
First, we need to find the time it takes for the fox to reach the fence. We can use the horizontal component of the velocity and the horizontal distance to calculate the time:
Horizontal distance (x) = initial velocity (V₀) * cos(angle) * time (t)
2.02 m = 7.75 m/s * cos(45°) * t
t ≈ 0.397 s
Next, we can calculate the vertical distance using the time calculated above:
Vertical distance (y) = initial velocity (V₀) * sin(angle) * time (t) - (1/2) * acceleration (g) * time²
y = 7.75 m/s * sin(45°) * 0.397 s - (1/2) * 9.8 m/s² * (0.397 s)²
y ≈ 0.279 m
Therefore, the fox clears the fence by approximately 0.279 m.
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Two 2.0−cm-diameter insulating spheres have a 6.20 cm space between them. One sphere is charged to +52.0nC, the other to −15.0nC. What is the electric field strength at the midpoint between the two spheres? Express your answer with the appropriate units.
The electric field strength at the midpoint between the two spheres is 36,754 N/C.
To calculate the electric field strength at the midpoint between the two spheres, we can use the formula for the electric field of a point charge. The electric field due to each sphere can be calculated separately and then summed up to find the net electric field at the midpoint.
First, we calculate the electric field due to the positively charged sphere. Since the spheres are insulating, we can treat them as point charges. The electric field due to a point charge is given by E = k * (Q / r^2), where k is the electrostatic constant, Q is the charge, and r is the distance from the charge. Substituting the values, we get E1 = (9 * 10^9 N m^2/C^2) * (52.0 * 10^-9 C) / (0.031 m)^2.
Next, we calculate the electric field due to the negatively charged sphere. Following the same formula, we get E2 = (9 * 10^9 N m^2/C^2) * (-15.0 * 10^-9 C) / (0.031 m)^2.
Since the electric fields due to the two spheres are in opposite directions, we subtract E2 from E1 to get the net electric field at the midpoint: E_net = E1 - E2.
Plugging in the values and performing the calculation, we find that the electric field strength at the midpoint between the two spheres is 36,754 N/C.
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temperature is a measure of the average energy of particles in a substance.
a. true
b. false
Temperature is a measure of the average energy of particles in a substance is true.
Temperature is indeed a measure of the average energy of particles in a substance. Temperature reflects the kinetic energy of the particles, which is related to their random motion. In a substance, the particles are in constant motion, and their individual energies contribute to the overall temperature of the substance. A higher temperature indicates that, on average, the particles possess greater energy and are moving more vigorously. Conversely, a lower temperature signifies lower average energy and slower particle motion. Temperature is typically measured using various scales, such as Celsius, Fahrenheit, or Kelvin, and it serves as a fundamental parameter in thermodynamics and many other scientific disciplines.
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Derive the mathematical model of a blushless DC motor with three-phase of stator and two-pole permanent magnet of rotor. Transform it to conventional DC-motor model for parametric identification.
A brushless DC motor is a permanent magnet synchronous motor, meaning it is synchronous with the stator’s rotating magnetic field.
The rotor of this motor is made up of permanent magnets that create a magnetic field around the motor,
which interacts with the stator’s rotating magnetic field.
The motor consists of a rotor, stator, and bearings.
The stator has three phases of windings, with each phase connected to a switch to direct the current in the desired direction.
The rotor is made of two poles and contains a permanent magnet.
The motor’s speed is determined by the frequency of the current supplied to the stator, which is controlled by the voltage applied to the motor.
The mathematical model of a brushless DC motor with three phases of stator and two-pole permanent magnet of rotor can be represented as follows:
ϕ = L*I
where L is the inductance and I is the current.
In the case of a brushless DC motor, the current can be described as follows:
I = K1*V - K2*ω
where V is the voltage applied to the motor, ω is the motor’s angular velocity, and K1 and K2 are constants.
ϕ = L*(K1*V - K2*ω)To transform the brushless DC motor model to a conventional DC-motor model for parametric identification, the following steps can be followed:
First, the flux ϕ can be expressed as follows:
The parameters of the model can be determined experimentally and used to predict the motor’s behavior under different operating conditions.
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the work function of a metal is 1.96 ev. find the kinetic energy of the photoelectrons emitted when light of 320 nm falls on the metal. a. 5.83 ev c. 1.96 ev b. 1.91 ev d. 3.87 ev
The kinetic energy of the photoelectrons emitted when light of 320 nm falls on the metal is approximately 1.91 eV.
Hence, the correct option is B.
To calculate the kinetic energy of the photoelectrons emitted when light of a specific wavelength falls on a metal, we can use the equation:
Kinetic energy of photoelectrons = Energy of incident photons - Work function of the metal
First, we need to convert the given wavelength from nanometers (nm) to electron volts (eV) using the relationship:
Energy (in eV) = 1240 / Wavelength (in nm)
Given that the wavelength of the light is 320 nm, we can calculate the energy of the incident photons as follows:
Energy of incident photons = 1240 / 320
= 3.875 eV
Next, we can subtract the work function of the metal (1.96 eV) from the energy of the incident photons to find the kinetic energy of the photoelectrons:
Kinetic energy of photoelectrons = 3.875 eV - 1.96 eV
= 1.91 eV
Therefore, the kinetic energy of the photoelectrons emitted when light of 320 nm falls on the metal is approximately 1.91 eV.
Hence, the correct option is B.
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(8%) Problem 6: Two large speakers at a concert are separated by a distance of 12.0 m. You stand 5.0 m in front of the midpoint between the speakers (equidistant from the speakers) and observe a sound level of 90.0 dB. What sound level will you observe if you walk to a point directly in front of one of the speakers (a distance 5.0 m in front of it)? B = dB
To determine the sound level observed when walking to a point directly in front of one of the speakers, we can use the inverse square law for sound intensity:
B2 - B1 = 20 * log10(r1/r2)
Where B1 is the initial sound level, B2 is the final sound level, r1 is the initial distance, and r2 is the final distance.
Given that the speakers are separated by 12.0 m and you stand 5.0 m in front of the midpoint between the speakers, the initial distance from each speaker is 7.0 m (half of the speaker separation).
Let's assume B1 is the observed sound level of 90.0 dB. We can calculate the final sound level, B2, when you walk to a point directly in front of one of the speakers (5.0 m in front of it).
B2 - 90.0 dB = 20 * log10(7.0 m / 5.0 m)
Simplifying the equation:
B2 - 90.0 dB = 20 * log10(1.4)
Using logarithmic properties:
B2 - 90.0 dB = 20 * 0.1461
B2 - 90.0 dB = 2.922
B2 ≈ 92.922 dB
Therefore, when you walk to a point directly in front of one of the speakers, you will observe a sound level of approximately 92.922 dB.
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A battery with an emf of 16 V delivers a constant current of 4.9 mA to a device. How much work does the battery do in 5 minutes? Express your answer in J, to at least one digit after the decimal point.
The battery does approximately 23.52 Joules of work in 5 minutes.
To calculate the work done by the battery, we can use the formula:
Work = Power x Time
The power delivered by the battery can be calculated using the formula:
Power = Voltage x Current
Given:
Emf (E) = 16 V
Current (I) = 4.9 mA = 4.9 x 10^(-3) A
Time (t) = 5 minutes = 5 x 60 = 300 seconds
First, let's convert the current to Amperes:
Current (I) = 4.9 mA = 4.9 x 10^(-3) A
Now, let's calculate the power delivered by the battery:
Power = Voltage x Current = 16 V x 4.9 x 10^(-3) A
Next, we can calculate the work done by the battery:
Work = Power x Time = (16 V x 4.9 x 10^(-3) A) x 300 s
Calculating this expression will give us the work done by the battery in Joules (J).
Certainly! Let's calculate the numerical answers for the given problem.
Given:
Emf (E) = 16 V
Current (I) = 4.9 mA = 4.9 x 10^(-3) A
Time (t) = 5 minutes = 5 x 60 = 300 seconds
1. Power = Voltage x Current
Power = 16 V x 4.9 x 10^(-3) A
Calculating the power gives:
Power ≈ 0.0784 W
2. Work = Power x Time
Work = (0.0784 W) x (300 s)
Calculating the work done by the battery gives:
Work ≈ 23.52 J
Therefore, the battery does approximately 23.52 Joules of work in 5 minutes.
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