The maximum internal torque at rated voltage and frequency is 149.8 N-m The slip at maximum torque is 0.0201The internal starting torque at rated voltage and frequency is 0.218 N-m.
Given: Power rating of the motor, P = 15 kW Voltage rating of the motor, V = 230VFrequency, f = 60 Hz Number of poles, n = 4Resistance per phase, R1 = 0.21 ohm Reactance per phase, X1 = X2 = 0.26 ohm Magnetizing reactance, Xm = 10.1 ohm .
We know that, Power developed by a 3 phase induction motor is given by P = 3VIsinφwhere, I = Phase current, and φ = Power factor angle Since core losses are neglected, the power developed by the motor is equal to the output power. Output power, Pout = P = 15 kW Also,Full-load internal torque developed by a 3 phase induction motor is given by,T = Pout/(2πn/60)
Where, n = Synchronous speed of the motor in RPM The synchronous speed of a 3 phase induction motor is given by,n = (120f)/n Poles Here, f = 60 Hz and n = 4 poles So, n = 1800 RPM Now,T = Pout/(2πn/60) = 15×10³/(2×3.14×1800/60)≈ 80.36 N-m
The maximum torque developed by a 3 phase induction motor is given by, Tmax = 3V²/2ωs(R1²+ (X1 + X2 + Xm)²) Where,ωs = Angular synchronous speed of the motor,ωs = 2πn/60Here, n = 1800 RPMSo,ωs = 188.5 rad/s Putting the given values, Tmax = 3V²/2ωs(R1²+ (X1 + X2 + Xm)²)= 3×(230)²/(2×188.5)(0.21²+(0.26+0.26+10.1)²)≈ 149.8 N-m The slip corresponding to maximum torque is given by,smax = (R1/X1 + X2 + Xm) = 0.0201 .
The starting torque developed by a 3 phase induction motor is given by,Tst = 3V²s/(2ωs(X1 + X2 + Xm))
Where, s = SlipHere, s = 1 (At starting, the slip is maximum, and equal to 1)Putting the given values, Tst = 3V²s/(2ωs(X1 + X2 + Xm))= 3×(230)²×1/(2×188.5×(0.26+0.26+10.1))≈ 0.218 N-m . Therefore, The maximum internal torque at rated voltage and frequency is 149.8 N-m The slip at maximum torque is 0.0201The internal starting torque at rated voltage and frequency is 0.218 N-m.
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Details The force on a particle is described by 10x³ - 5 at a point x along the x-axis. Find the work done in moving the particle from the origin to x = 2.
Answer:
To find the work done in moving the particle from the origin to x = 2, we need to integrate the force over the given interval.
The work done (W) is calculated by integrating the force function with respect to displacement (dx) from the initial position (0) to the final position (2):
W = ∫(0 to 2) (10x³ - 5) dx
Integrating the force function, we get:
W = ∫(0 to 2) (10x³ - 5) dx = [2.5x⁴ - 5x] evaluated from 0 to 2
Now, substituting the upper limit (2) and lower limit (0) into the equation:
W = [2.5(2)⁴ - 5(2)] - [2.5(0)⁴ - 5(0)]
= [2.5(16) - 10] - [0 - 0]
= 40 - 10
= 30
Therefore, the work done in moving the particle from the origin to x = 2 is 30 units of work.
Explanation:
if a car travels 270 meters in 30 seconds then what is its average speed
Answer:
the answer is 32,400
Explanation:
I looked it up for you
The average speed denotes the average rate of speed over the extent of a trip. The average speed of a car which travels 270 meters in 30 seconds is 9m/s.
What is average speed?The average speed can be defined as the ratio of the total distance travelled by an object to the total time taken. It is a scalar quantity. It is represented by the magnitude and does not have direction. Its SI unit is m/s.
The average speed of an object help us to calculate the rate of travel time and the distance. The average speed of an object when it covers the same distance at two different speed, X and Y is:
Average speed = 2XY/ X+Y
The equation used here to calculate the average speed is:
Average speed = Total distance / Total time
Average speed = 270 m / 30 s = 9 m/s
Thus the average speed is 9 m/s.
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On February 20, 1962, John Glenn became the first American to orbit Earth.
If John Glenn weighed 640 N on Earth's surface,
a) how much would he
have weighed if his Mercury spacecraft had (hypothetically) remained
at twice the distance from the center of Earth?
b) Why is it said that an
astronaut is never truly "weightless?"
a. John Glenn would have weighed 160 N if his Mercury spacecraft had (hypothetically) remained at twice the distance from the center of Earth
b. An astronaut is never truly weightless because the earth still exerts a gravitational pull on the astronaut since the spaceships are not at an infinite distance from the earth who in space is actually experiencing free fall due to gravity.
From Newton's law of Universal gravitation:
F = Gm₁m₂/d²Where F is the gravitational force acting on two objects of masses m₁ and m₂ respectively.d is the distance of separation between the two objects.G is the Universal gravitational constantFrom the question, the distance between the spacecraft and the center of the earth is twice the distance on the earth's surface.
All other values remained constant, therefore, only the change in distance will affect the force.
Weight or force of gravity on John on the earth's surface is given as:
F = 640 NThe equation for calculating the new force or weight, Fₓ will simply be;
Fₓ = F/d²since d = 2
Fₓ = 640 / 2²
Fₓ = 160 N
Therefore, John Glenn would have weighed 160 N if his Mercury spacecraft had (hypothetically) remained at twice the distance from the center of Earth.
b. The spacecraft carrying astronauts orbit the earth at very high speeds. So astronauts even though experiencing free fall due to the gravitational force of the earth, never really fall onto the earth's surface.
An astronaut is never truly weightless because the earth still exerts a gravitational pull on the astronaut since the spaceships are not at an infinite distance from the earth who in space are actually experiencing free fall due to gravity.
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usually, tall trees collapse in stroms?
Answer:
yes this is true
Explanation:
Identify the following major moons of Jupiter.
A. Europa
B. Ganymede
C. Io
D. Callisto
These are the four largest moons of Jupiter and are collectively known as the Galilean moons. They were discovered by Galileo Galilei in 1610 and are named after characters from Greek mythology. Europa, Ganymede, Io, and Callisto are all fascinating celestial bodies with unique features and scientific significance
Europa is known for its subsurface ocean that may harbour conditions suitable for life, Ganymede is the largest moon in the solar system, Io is the most volcanically active object in the solar system, and Callisto is heavily cratered and geologically diverse. These moons have been studied extensively by spacecraft missions such as NASA's Galileo and Juno missions, providing valuable insights into the nature of Jupiter's moons and their geological processes. The major moons of Jupiter are Europa, Ganymede, Io, and Callisto. The major moons of Jupiter are Europa, Ganymede, Io and Callisto.
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Olivia needs to provide a visual summary of expenses to management. She chooses a system that shows different levels for the expenses based on filled
Olivia can provide a visual summary of expenses to management using a filled bar chart or a stacked bar chart. In this type of chart, each expense category is represented by a separate bar, and the height of each bar corresponds to the total expense amount.
Here's how Olivia can create the visual summary:
Choose a horizontal or vertical bar chart: Olivia can decide whether to use a horizontal or vertical orientation based on the space available and the preference of the management. Define the expense categories: Identify the different expense categories that need to be included in the summary. These could be categories such as salaries, marketing, utilities, supplies, etc. Assign levels of expenses: Assign different levels or sections within each expense category based on the filled portion of the bar. For example, if the bar represents the total budget for a specific expense category, Olivia can divide it into sections to show different levels of expenses. Each section will be filled to represent the portion of the budget spent. Fill the sections: Color or shade the sections within each bar to represent the corresponding level of expenses. For example, if a section represents 50% of the total budget, Olivia can fill it halfway. Label the bars and sections: Clearly label each bar with the expense category it represents. Additionally, label each section within the bar to indicate the specific level of expenses it represents. Add a legend: Include a legend that explains the color or shading used to represent different levels of expenses. This will help management understand the chart at a glance.By using a filled bar chart or stacked bar chart, Olivia can provide a visual representation of the expense levels for each category. This allows management to quickly grasp the distribution and proportion of expenses across different areas.
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If a spacecraft is moving at 20,000 mph (in space), it will continue to move at 20,000 mph when its engines shut off.
Which Law explains this?
Choose matching definition
Newton's first law of motions
All of these
Fruitfulness
scope
testability
Sum to you equal weight
If a spacecraft is moving at 20,000 mph (in space), it will continue to move at 20,000 mph when its engines shut off.
The law that explains this is Newton's first law of motion.
Newton's first law of motion, also known as the law of inertia, states that an object at rest will stay at rest, and an object in motion will continue in motion with the same speed and direction, unless acted upon by an external force.
In the case of the spacecraft moving at 20,000 mph, it will continue to move at that speed when its engines shut off, because there are no external forces acting upon it in the vacuum of space.
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(a) A submersible vehicle is in a lake at a depth of 23.6 m. What is the absolute pressure (in Pa) at this depth? The density of the water in the lake is 1.00 ✕ 103 kg/m3, and the air above is at a pressure of 101.3 kPa.
(b) The submersible vehicle has a circular window with a diameter of 30.0 cm. What force (in N) is exerted by the water on the window of the vehicle at the depth from part (a)? (Enter the magnitude.)
The absolute pressure on the submersible vehicle is 332.5 kPa and the force on the window is 23.4 N.
(a) The submersible vehicle is in the lake at a depth of 23.6m and the density of the water is given to be 1000 kg/m³. The pressure due to air above the water surface is 101.3 kPa.
Now, the absolute pressure at that point in the lake will be,
P = pgh + 101.3kPa.
P = 1000 x 9.8 x 23.6 + 101.3kPa.
P = (231.2 + 101.3)kPa
P = 332.5 kPa.
So, the absolute pressure is 332.5 kPa.
(b) The force on the window will be given as,
Force = Pressure x area
Area = π(D/2)², D is the diameter of the window.
Area = 3.14(0.3/2)²
Area = 0.070 m².
Now, the force = 0.070 x 332.5
The force on the window is 23.4 N.
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a variety of time and temperature combinations can be applied to milk (including banana flavor!) to make it safe to drink. collectively, all of these heat-based approaches are referred to as
A variety of time and temperature combinations can be applied to milk (including banana flavor!) to make it safe to drink. Collectively, all of these heat-based approaches are referred to as pasteurization. Pasteurization is a process that involves heating food to a specific temperature for a specific period of time to destroy potentially harmful pathogens while preserving its flavor and nutritional value.
The method was first used by French chemist and microbiologist Louis Pasteur in the 19th century to keep wine and beer from spoiling.
There are several methods of pasteurization, but the most common involves heating milk to 145°F (63°C) for at least 30 minutes, followed by rapidly cooling it to 39°F (4°C) or lower.
Another method, called high-temperature, short-time (HTST) pasteurization, heats the milk to 161°F (72°C) for 15 seconds, followed by rapid cooling to 39°F (4°C) or lower.
Other heat-based approaches include ultra-pasteurization, which involves heating milk to 280°F (138°C) for two seconds, and flash pasteurization, which heats the milk to 161°F (72°C) for 15 seconds before cooling it quickly.
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What is the mass of an object that is accelerating at a rate of 25 m/s² and is using 15 N of force?
Does the electric potential energy increase, decrease, or stay the same? explain.
Answer:
Yes. To maintain constant total energy, when released from rest the charge loses potential energy as it gains kinetic energy in its "fall" toward the negative plate.
Explanation:
Answer:
Yes. Left. To maintain constant total energy, when released from rest the charge loses potential energy as it gains kinetic energy in its "fall" toward the negative plate.
The work done to compress a gas is. As a result, of heat is given off to the surroundings. Calculate the change in energy of the gas. Be sure your answer has the correct number of significant digits.
The change in the energy of the gas is obtained as 56J.
What is the change in the energy of the gas?We know that the change in the energy of the gas can be obtained by the application of the first la of thermodynamics. From the first of law of thermodynamics, we know that energy can neither be created nor destroyed but can be changed from one form to another.
ΔE = q + w
ΔE = energy change
q = heat absorbed or evolved
w = work done
ΔE = -27 J + 83.0 J
ΔE = 56J
Thus the new energy of the gas is obtained as 56J.
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Missing parts;
The work done to compress a gas is 83.0 J. As a result, 27.0 J of heat is given off to the surroundings. Calculate the change in energy of the gas.
a 3 m long ladder leans against a frictionless wall at an angle of 60 degrees what is the minimum value of the coefficinet of static friction twith the ground that prevents the ladder from slipping
For a 3 m long ladder leaning against a frictionless wall, the minimum value of the coefficient of static friction is mathematically given as
mu=0.2886
What is the minimum value of the coefficient of static friction with the ground that prevents the ladder from slipping?Generally, the equation for the Force is mathematically given as\(-\mu N_{1}+N_{2}=0\)
Therefore
\(\mu=\frac{1}{2}tan\theta\)
\(\mu=\frac{1}{2}tan30^{0}\)
mu=0.2886
In conclusion, the minimum value of the coefficient of static friction
mu=0.2886
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a jet plane travels 1500 km in 2 hours. what is the speed of the jet
Answer:
Speed = distance / time
= 1500 /2
= 750 km/h
Colette launches an air rocket in the upward, positive direction. It launches
with an initial velocity of 25.5 m/s. It accelerates in the downward, negative
direction at a rate of 9.81 m/s2. After 3.5 seconds, what is the magnitude of
the rocket's displacement?
A) 29 meters
B) 31 meters
C) –150 meters
D) 150 meters
Answer:
b
Explanation:
Answer:
The answer is A) 29 meters
Explanation:
I got this question right on the test! :)
Density of oil is less than the density of water. *
true
False
Answer:
false
Explanation:
because oil is thicker than water
Answer:
answer is false
Explanation:
water is more dense than oil so they can't mix . Oil float above the water
complete the following statement: the maximum speed at which a car can safely negotiate a frictionless banked curve depends on all of the following except
The angle of banking does not affect the maximum speed at which a car can safely negotiate a frictionless banked curve.
What is a banked curve?We know that when a car is trying to negotiate a curve, the car is undergoing a circular motion at the bend. The car is tending to move around the bend and then emerge at the other side. Sometimes the bend is made a bit or somewhat steeper at a give angle and this can help the cars to negotiate the ben successfully without skidding off the road.
We know that we can obtain the maximum velocity of the motion of the car as it negotiates the bend using thee formula;
v = √mgr/h
v = velocity
m = mass
g = acceleration due to gravity
r = radius
h = height
It the follows that the maximum speed at which a car can safely negotiate a frictionless banked curve depends on all of the following except the angle of banking.
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Missing parts;
Complete the following statement: The maximum speed at which a car can safely negotiate a frictionless banked curve depends on all of the following except
A. the diameter of the curve.
B. the acceleration due to gravity.
C. the angle of banking.
D. the mass of the car.
E. the radius of the curve.
please help!! ill give brainlist its for my finals!
Give a real-world example of an energy transformation that uses two of the following forms of energy: chemical, mechanical, nuclear, gravitational, radiant, electrical, thermal (heat), and/or sound.
Answer:
candle for chemical energy.
Loudspeakers are the best example of electrical energy to sound energy conversion
Explanation:
If a star was the same size as our Sun, but was 81times more luminous, it must be
A. twice as hot as our Sun.
B. nine times hotter than the Sun.
C. three times hotter than the Sun.
D. 81 times hotter than the Sun.
E. four times hotter than the Sun.
A. If a star is the same size as our Sun, but is 81 times more luminous, it means that it is emitting 81 times more energy than the Sun.
Luminosity is directly related to temperature, and the more luminous a star is, the hotter it must be. However, temperature increases at a slower rate than luminosity, so a star that is 81 times more luminous than the Sun is only twice as hot as our Sun. Therefore, the correct answer is A, twice as hot as our Sun. This demonstrates the importance of understanding the relationship between luminosity and temperature when studying stars.
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b. Which station broadcasts waves with a shorter wavelength
Answer:
blue and purple light
Explanation:
Light waves have very, very short wavelengths. Red light waves have wavelengths around 700 nanometers (nm), while blue and purple light have even shorter waves with wavelengths around 400 or 500 nm.
a ball is dropped from a height of 10 m. what is its velocity upon impact with the ground? a) 14 m/sb) 20 m/sc) 10 m/sd) 8 m/s
A ball is dropped from a height of 10 m. Its velocity upon impact with the ground is (v) = (a) 14 m/s.
What is velocity?Velocity is a term that means that the object has changed its position by making a distance in a given time. That called the velocity of the object. It can be measured in m/s, cm/s.
How can we calculate the velocity?To calculate the velocity we are using the formula,
v²-u²=2gh
As we know the ball start velocity from rest so, u=0
v²=2gh
Or, v=√2gh
Here we are given,
h= the height of the cliff from the ball fell. = 10m.
g= The acceleration due to gravity. = 9.8 m/s².
We have to calculate the velocity of the ball = v m/s.
Now we put the values in above equation, we get
v=√2gh
Or, v= √2*9.8*10
Or, v= 14 m/s.
So from this we can say that, Its velocity upon impact with the ground is (v) = (a) 14 m/s
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"Please include all relevant working out as detailed as possible
and all relevant diagram to find the answer. Much appreciated! I
will upvote! Thank you so much"
Find total response of the system (transient+steady state). Do not solve for coefficients. Determine the frequency of applied force at which resonance will occur? M = 20 kg F, = 90 N Given: -6 rad/s M
Given the following information:Mass of the system, m = 20 kg.Damping coefficient, b = 6 Ns/m.Force, F = 90 N.Frequency of applied force, f = ?Applied force angular frequency, w = 6 rad/s.Forced vibration equation:F(t) = F0 sin(wt)where F0 = 90 N and w = 6 rad/s.Under the action of the force F, the mass m will oscillate.The equation of motion for the mass-spring-damper system is given by:$$\mathrm{m\frac{d^{2}x}{dt^{2}}} + \mathrm{b\frac{dx}{dt}} + \mathrm{kx = F_{0}sin(\omega t)}$$where k is the spring constant.x(0) = 0 and x'(0) = 0.As we have the damping coefficient (b), we can calculate the damping ratio (ζ) and natural frequency (ωn) of the system.Damping ratio:$$\mathrm{\zeta = \frac{b}{2\sqrt{km}}}$$where k is the spring constant and m is the mass of the system.Natural frequency:$$\mathrm{\omega_{n} = \sqrt{\frac{k}{m}}}$$where k is the spring constant and m is the mass of the system.Resonant frequency:$$\mathrm{\omega_{d} = \sqrt{\omega_{n}^{2}-\zeta^{2}\omega_{n}^{2}}}$$At resonance, the amplitude of the system will be maximum when forced by a sinusoidal force of frequency equal to the resonant frequency.Resonant frequency:$$\mathrm{\omega_{d} = \sqrt{\omega_{n}^{2}-\zeta^{2}\omega_{n}^{2}}}$$$$\mathrm{\omega_{d} = \sqrt{(6.57)^{2}-(-2.88)^{2}} = 6.98 rad/s}$$Hence, the frequency of applied force at which resonance will occur is 6.98 rad/s.
The frequency of the applied force at which resonance will occur is ω = 2√5 rad/s.
To determine the frequency of the applied force at which resonance will occur, resonance happens when the frequency of the applied force matches the natural frequency of the system. The natural frequency can be determined using the formula:
ωn = √(K / M),
where ωn is the natural frequency, K is the spring constant, and M is the mass of the system.
Substituting the given values of K = 400 N/m and M = 20 kg into the equation, we can calculate the natural frequency ωn.
ωn = √(400 N/m / 20 kg) = √(20 rad/s²) = 2√5 rad/s.
Therefore, the frequency of the applied force at which resonance will occur is ω = 2√5 rad/s.
The correct question is given as,
M= 20kg
Fo = 90 N
ω = 6 rad/s
K = 400 N/m
C = 125 Ns/m
Determine the frequency of applied force at which resonance will occur?
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a load having a resistance of 67 ω is connected across the output terminals of the filter. what is the corner, or cutoff, frequency of the loaded filter?
The cutoff frequency of the loaded filter with 67 ω resistance load connected to output terminals is unknown.
The cutoff frequency of a filter is the frequency at which the filter's output falls to 70.7% of its maximum value.
However, in this scenario, a load having a resistance of 67 ω is connected across the output terminals of the filter.
Without knowing the values of the filter's components, it is impossible to determine the cutoff frequency of the loaded filter.
The load impedance affects the filter's frequency response, causing a shift in the cutoff frequency.
To calculate the cutoff frequency, we need to know the values of the filter components and how they interact with the load impedance.
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The corner frequency of a loaded filter depends on the value of the load resistance. Without knowing the capacitance value of the filter, we cannot determine the corner frequency with certainty.
We can make some general observations about how changes in load resistance will affect the corner frequency. The corner or cutoff frequency of a loaded filter is dependent on the value of the load resistance. In this case, the load resistance is given as 67 ω. The corner frequency of a filter is the frequency at which the filter starts to attenuate the input signal. It is also known as the -3 dB frequency since it is the frequency at which the output power is reduced to half (-3 dB) of the input power. To calculate the corner frequency of the loaded filter, we need to use the following formula: \(f_{c}\) = 1 / (2πRC) Where f_c is the corner frequency, R is the resistance of the load and C is the capacitance of the filter. Since the capacitance value is not given in the question, we cannot calculate the corner frequency with certainty. However, we can still make some observations. As the load resistance increases, the corner frequency of the filter decreases. This is because a higher load resistance causes a larger voltage drop across the load, reducing the voltage seen by the filter. As a result, the filter starts to attenuate the signal at a lower frequency.
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The Hale Telescope The 200-inch-diameter concave mirror of the Hale telescope on Mount Palomar has a focal length of 16.9 m. An astronomer stands 21.0m in front of this mirror.A)Where is her image located?B) s it in front or behind the mirrorC) is her image real or virtualD) what is the magnification of her image?
A) To find the location of the image, we can use the mirror formula: 1/f = 1/do + 1/di, where f is the focal length (16.9m), do is the object distance (21.0m), and di is the image distance.
1/16.9 = 1/21.0 + 1/di
To solve for di, first calculate the right side of the equation:
1/21.0 = 0.0476
Subtract this from 1/16.9:
1/16.9 - 0.0476 = 0.0124
Now, find the reciprocal of the result to get di:
di = 1/0.0124 = 80.6m
B) The image is located behind the mirror since di > f.
C) The image is virtual because it is formed behind the concave mirror, where light rays do not converge.
D) To find the magnification, use the formula M = -di/do:
M = -80.6/21.0 = -3.84
The magnification of her image is -3.84, which means it is inverted and 3.84 times larger than the object (the astronomer).
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(a) When the mass is removed, the length of the cable is found to be l0=4.76m. After the mass is added, the length is measured and found to be l1=5.49m. Determine Young's Modulus Y in N/m2 for the steel cable if the weight has a mass m=35kg and the cable has a radius r=0.015m.
b) If this cable is pulled down a distance d in m from its equilibrium position it acts like a spring when released. Write an expression determining the spring constant k of this material using the cable-specific variables Y,l0,l1, and r.
To find Young's modulus Y, use \(Y = mg( l1 - l0 ) / ( πr^2l0 )\) with given values. For the spring constant k, use \(k = Yπr^2 / l0, with Y, r,\) and l0 given. (a) Young's modulus Y is a measure .
the stiffness of a material and is calculated using the formula Y = (mg( l1 - l0 )) / ( πr^2l0 ), where g is the acceleration due to gravity. Substituting the given values,\(Y = 2.08 × 10^11 N/m^2.\) This means that the steel cable is relatively stiff and can resist deformation under stress. n(b) The spring constant k of the steel cable indicates its stiffness as a spring, with a higher value indicating a stiffer material that will resist deformation more strongly. In this case, the steel cable has a relatively high spring constant of 9.16 × 10^4 N/m, meaning that it will not stretch much when a force is applied.
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A vector has a magnitude of 82 m
and an angle of 25 degrees. What is
the Y-component of the vector?
[?]m
Enter text here
Enter
The Y-component of the vector is 34.65 m.
What is a vector?Vectors are quantities that have both magnitude and direction.
The Y-component of the vector can be calculated using the formula below.
Formula:
Y = rsin∅............. Equation 1Where:
Y = Y-component of the vectorr = magnitude of the vector∅ = angle of the vector to the horizontal.From the question,
Given:
r = 82 m∅ = 25°Substitute these given values into equation 1
Y = 82(sin25°)Y = 34.65 mHence, The Y-component of the vector is 34.65 m.
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Where is earth's magnetic north pole located?
Answer: it is located over Ellesmere Island, Canada
Explanation
it is now drifting away from North America and toward Siberia.
Answer:ellesmere island, Canada
Electric potential depends on which factors?
O A. Distance and amount of charge
B. Density and amount of charge
OC. Mass and distance
D. Mass and amount of charge
Electric potential is influenced by charge and distance.
What does electric potential mean?The amount of effort required to shift a unit of electric charge from a reference point to a particular place in an electric field is known as the electric potential.
What influences electric potential?Any charge in an electric field has an electric potential that is determined by the type (positive or negative), quantity, and location of the charge inside the electric field.
The potential actually grows as you get farther away from the charge, becoming less negative as you get closer to it and eventually reaching zero. The potential for both positive and negative charges is zero at infinite distances from the charge.
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A car traveling at 52 km/h hits a bridge abutment. A passenger in the car moves forward a distance of 61 cm (with respect to the road) while being brought to rest by an inflated air bag. What magnitude of force (assumed constant) acts on the passenger's upper torso, which has a mass of 37 kg
Therefore, the magnitude of the force acting on the passenger's upper torso is approximately 5320 N. The negative sign indicates that the force acts in the opposite direction of the passenger's motion.
To calculate the magnitude of the force acting on the passenger's upper torso, we can use the equations of motion and the concept of impulse.
Given:
Initial velocity (v₀) of the car = 52 km/h
Distance traveled (s) by the passenger = 61 cm = 0.61 m
Mass of the passenger (m) = 37 kg
Step 1: Convert the initial velocity to m/s:
v₀ = 52 km/h × (1000 m÷3600 s) = 14.44 m/s
Step 2: Calculate the change in velocity:
Change in velocity (Δv) = 0 m/s - v₀ = -v₀
Step 3: Calculate the time interval (Δt) using the equation for uniformly accelerated motion:
s = (v₀ × Δt) + (0.5 × a× Δt²)
0.61 m = (14.44 m/s × Δt) + (0.5 × a × Δt²)
Since the passenger comes to rest, the final velocity is 0 m/s. The initial velocity is v₀. We can solve for the time interval Δt and acceleration a using the above equation.
Step 4: Calculate the time interval Δt and acceleration a:
0.61 m = (14.44 m/s × Δt) + (0.5 × a × Δt²)
0 = (14.44 m/s × Δt) + (0.5 × a ×Δt²)
Solving these equations simultaneously will give us the values of Δt and a.
Step 5: Calculate the impulse (J) experienced by the passenger:
Impulse (J) = m × Δv
Step 6: Calculate the magnitude of the force (F) using the equation:
F = J ÷ Δt
Let's perform the calculations to find the magnitude of the force acting on the passenger's upper torso.
(Note: For simplicity, we will consider the acceleration due to the airbag and other factors as negligible. This assumption allows us to treat the motion as uniform deceleration.)
Solving Steps 3 and 4:
0.61 m = (14.44 m/s × Δt) + (0.5 × a ×Δt²)
0 = (14.44 m/s × Δt) + (0.5 × a ×Δt²)
Solving these equations yields Δt ≈ 0.1004 s and a ≈ -144.1 m/s².
Step 5: Calculate the impulse J:
J = m ×Δv = 37 kg × (-14.44 m/s) = -534.28 N·s
Step 6: Calculate the magnitude of the force F:
F = J ÷ Δt = (-534.28 N·s) ÷ (0.1004 s) ≈ -5320 N
Therefore, the magnitude of the force acting on the passenger's upper torso is approximately 5320 N. The negative sign indicates that the force acts in the opposite direction of the passenger's motion.
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what is a hydraulic system
Explanation:
Hydraulic systems use the pump to push hydraulic fluid through the system to create fluid power. The fluid passes through the valves and flows to the cylinder where the hydraulic energy converts back into mechanical energy. The valves help to direct the flow of the liquid and relieve pressure when needed