A simple harmonic oscillation for a spring-mass system is described by x(t)= 3.4cos(8.2t+0.78) in SI units. The mass of the particle m=0.5kg. What is spring constant? a. 33.6 N/m b. 42.7 N/m c. 13.2 N/m d. 4.1 N/m e. none of above is within 5% from the correct answer.
Answers
The spring constant is 13.2 N/m. The correct option is c.
The equation for simple harmonic motion of a spring-mass system is x(t) = A cos(ωt + φ), where A is the amplitude, ω is the angular frequency, and φ is the phase angle.
Comparing this with the given equation, we can see that the amplitude A = 3.4.
The angular frequency can be calculated as ω = 2πf = 8.2 rad/s, where f is the frequency in Hz.
The mass of the particle is given as m = 0.5 kg.
The spring constant k can be calculated using the formula k = mω², where ω is the angular frequency.
Substituting the values, we get k = (0.5 kg) * (8.2 rad/s)² = 13.2 N/m.
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Related Questions
What formula is used for the questions two forces of magnitude 5 Newton and 4 Newton act on a body of mass 4.0 kg at a right angle to each other determine the magnitude of the acceleration of the body
Answers
The magnitude of the acceleration of the body is approximately 1.802 m/s^2 when forces of magnitude 5 Newton and 4 Newton act on a body of mass 4.0 kg at a right angle to each other.
To determine the magnitude of the acceleration of a body when two forces act on it at a right angle, we can use the Pythagorean theorem and Newton's second law of motion.Newton's second law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). In this case, the net force is the vector sum of the two forces acting on the body.Using the Pythagorean theorem, we can find the magnitude of the net force. Let's call the force with magnitude 5 Newton as F1 and the force with magnitude 4 Newton as F2. The net force (Fnet) can be calculated as the square root of the sum of the squares of the individual forces: Fnet = sqrt(F1^2 + F2^2).Now we can substitute the net force into Newton's second law to find the acceleration (a). Rearranging the formula, we have a = Fnet / m.Plugging in the values, Fnet = sqrt(5^2 + 4^2) = sqrt(25 + 16) = sqrt(41) Newtons. The mass (m) is given as 4.0 kg.
Finally, the magnitude of the acceleration of the body is calculated as a = Fnet / m = sqrt(41) / 4.0 ≈ 1.802 m/s^2.
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what are some ways that engineers might be able to use electromagnets?
Answers
Electromagnets are versatile devices that can be used in a variety of engineering applications.
Some ways that engineers might use electromagnets include: Motors and Generators: Electromagnets are used in the construction of electric motors and generators. When a current flows through a wire wound around an iron core, an electromagnetic field is created, which generates a force that can be used to move or generate electrical energy.
Magnetic Levitation: Electromagnets can be used in magnetic levitation systems, where they create a magnetic field that levitates and propels objects, such as high-speed trains or Maglev vehicles.
Magnetic Separation: Electromagnets can be used in the separation of magnetic materials from non-magnetic materials, such as in the recycling industry, where they are used to separate ferrous metals from other waste materials.
MRI Machines: Electromagnets are used in Magnetic Resonance Imaging (MRI) machines, where they create a strong magnetic field that interacts with the body's tissues to produce images. Particle Accelerators: Electromagnets are used in particle accelerators to create magnetic fields that guide and accelerate charged particles, such as electrons or protons, to high speeds.
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explain any two effects of refraction of light experienced by you
Answers
Answer:
1) during monsoon light passing through the water surface refracts causing the formation of rainbow.
2) a swimming pool looks more shallower than it actually is because the light coming from the bottom of the pool bends when it comes out at the surface due to refraction of light.
Answer:
1) during monsoon light passing through the water surface refracts causing the formation of rainbow.
2) a swimming pool looks more shallower than it actually is because the light coming from the bottom of the pool bends when it comes out at the surface due to refraction of light.
Explanation:
Write a 150-200 word response. your class requires you to use a program that you must download on your computer you have waited until day 5 of the week to download the program and you need it for an assignment that is due in 2 days now you are having issues with the program how do you approach solving this problem who would you contact first and why what are the resources available to support you when obstacles arise and why is effective communication important in linking you to these resources
Answers
A person would contact his fellow students and his friends inquiring whether they have encountered the same issue as it is with him.
What is program?The program is a system software which helps students to learn or accomplish any projects.
The class requires a student to use a program that you must download on his computer. He have waited until day 5 of the week to download the program and need it for an assignment that is due in 2 days now. He is having issues with the program.
He must contact his fellow friends and students whether they are facing the same error in starting the program. There are many resources to be used in place of that software. He can also use the internet to find out the troubleshooting methods. He can also contact the software developer and discuss the problems regarding software.
The effective communication can resolve the issues. If no communication is there, no problem is being solved. The person will never understand what other person is facing until and unless he doesn't speak.
Therefore, proper communication and complete details must be shared in order to solve any issue. Any critical problem can be solved even by just discussing.
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Problem #3: a) A circular channel section has diameter of 6m and it is running half. Calculate the discharge through the channel if the bed slope is 1 in 600 and manning's co efficient is equal to 0.014. b) The diameter of a circular channel section which is running full is 8m. Determine the discharge through the channel section if the bed slope is 1 in 600 and the value of the manning's co efficient is 0.013.
Answers
The discharge through the channel if the bed slope is 1 in 600 and manning's coefficient is equal to 0.014 and 0.013 when the diameter of a circular channel section is 6m and 8m respectively are 3.8 m³/s and 16.87 m³/s respectively.
a) Diameter of the circular channel section = 6m Bed slope = 1 in 600 Manning's coefficient = 0.014. The cross-sectional area of the channel is given by; A = π/4 D²A = π/4 (6m)²A = 28.27 m²wetted perimeter = π D
Because the channel is running half full, the hydraulic radius is given by;R = A/P = 28.27/ (π * 6m/2)R = 1.88 m
Using the Manning's equation; Q = 1/n A R²/3/2 S^(1/2)Q = 1/0.014 * 28.27 * (1.88)²/3/2 * 1/600^(1/2)Q = 3.8 m³/s (Answer)
b) Given data: Diameter of the circular channel section = 8mBed slope = 1 in 600 Manning's coefficient = 0.013The cross-sectional area of the channel is given by; A = π/4 D²A = π/4 (8m)²A = 50.27 m² wetted perimeter = π D
Because the channel is running full, the hydraulic radius is given by; R = A/P = 50.27/ (π * 8m/2)R = 2.35 m
Using the Manning's equation; Q = 1/n A R²/3/2 S^(1/2)Q = 1/0.013 * 50.27 * (2.35)²/3/2 * 1/600^(1/2)Q = 16.87 m³/s (Answer)
Hence, the discharge through the channel if the bed slope is 1 in 600 and manning's coefficient is equal to 0.014 and 0.013 when the diameter of a circular channel section is 6m and 8m respectively are 3.8 m³/s and 16.87 m³/s respectively.
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At time t = 0, a static object at position x = 0 starts to move such that its position x(t) satisfies the equation
d^2x/dt^2 + dx/dt = te^-t
Using Laplace Transforms, determine the function x(t)
Answers
Based on the above illustration, the required function is `x(t) = t²e⁻ᵗ / 2`.
Given: The equation is, `d²x/dt² + dx/dt = te⁻ᵗ`.
Required:
Find `x(t)` using Laplace Transforms.
Let us apply the Laplace transform to both sides of the equation.
d²x/dt² → s² X(s) - s x(0) - x'(0)dx/dt → s X(s) - x(0)x(0) is 0 as the object starts from rest.
Putting the given value, `d²x/dt² + dx/dt = te⁻ᵗ` in the Laplace transform of the equation, we get (s² X(s) - s x(0) - x'(0)) + (s X(s) - x(0)) = 1 / (s + 1)²
On solving the above equation for `X(s)`, we get `X(s) = 1 / (s + 1)³`
On taking the inverse Laplace transform, we get, `x(t) = t²e⁻ᵗ / 2`
Hence, the required function is `x(t) = t²e⁻ᵗ / 2`.
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La velocidad de la luz es de 300 000 km/s, convertir a m/s.
ayudenme porfa
Answers
which one of the storage devices that are supported by the linux operating system uses electromechanical devices that use magnetic storage technology to store data, usually in large amounts?
Answers
Hard Disk Drive (HDD) is the storage devices that are supported by the linux operating system uses electromechanical devices that use magnetic storage technology to store data, usually in large amounts.
A hard drive, often known as a hard disk or HDD, houses our computer's operating system, software, and data files, including documents, photos, and music.The remaining parts of your computer cooperate to display the programs and files on your hard disk.A hard disk drive is made consisting of a platter with compartments for data storing (HDD). our operating system, programs, and any files you've made are included in this data. A reader or writer arm that slides over the plate to read or write the desired information is also present. The platter spins while the accuator arm passes over it to speed up this process.To know more about Hard Disk Drive (HDD) visit : https://brainly.com/question/24178832
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I will give Brainliest to WHoever answers truthfully!!!!!T/F net force charge and net electric force are the same thing
Answers
Answer:
it's true I'm pretty sure
Answer:
the answer is true.I'm sure
Examine the Pythagorean theorem below. In this form you can find the length of the hypotenuse c) of a right triangle if you know the lengths of the two short sides (a &). Solve this equation for the short side b. If you need to indicate a square root in your answer, type it like this: root * (e + f) to mean the square root of the sum (e + f) . For example, the equation below can be typed as c = root (a^ ^ 2+b^ ^ 2)
Answers
Answer:
what is the number
Explanation:
Which describes the sum of potential energy and kinetic energy of objects or systems? *
a. nuclear energy and electric energy
b. nuclear and mechanical energy
c. thermal energy and electric energy
d. thermal energy and mechanical energy
Answers
Answer:
The Total Mechanical Energy
The total amount of mechanical energy is merely the sum of the potential energy and the kinetic energy. This sum is simply referred to as the total mechanical energy (abbreviated TME).
Thermal energy and mechanical energy describes the sum of potential energy and kinetic energy of objects or systems. Correct option is D.
Potential Energy: This is the energy that an object possesses due to its position or condition. For example, a book placed on a shelf has potential energy because it can potentially fall down. The higher the object is positioned, the more potential energy it has.
Kinetic Energy: This is the energy of motion. An object that is moving has kinetic energy. The kinetic energy of an object depends on its mass and its velocity (speed).
Thermal Energy: This is the energy associated with the random motion of particles within a substance. It's related to temperature and is a form of kinetic energy at the microscopic level.
Mechanical Energy: This is the sum of potential energy and kinetic energy in a mechanical system. In other words, it accounts for both the energy an object has due to its position and the energy it has due to its motion.
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What is the meaning of “Eg” in physical science
Answers
Answer:
e.g. means "for example" but is physics is also stands for gravitational potential energy
How do I calculate wind chill?
Answers
By multiplying the wind speed by 0.7 and then deducting that number from the air temperature, one may find an accurate approximation of the Wind Chill temperature.
Wind chill is the perceived temperature on exposed skin due to the combined effect of wind and temperature. To calculate wind chill, the following formula is used:
Wind chill temperature (°F) = 35.74 + 0.6215 * T - 35.75 * v^0.16 + 0.4275 * T * v^0.16
Where:
T = air temperature (°F)
v = wind speed (mph)
The wind chill temperature is the temperature equivalent perceived by a person at a given air temperature and wind speed. The formula is only applicable to temperatures below 50°F and wind speeds above 3 mph.
It's important to note that the wind chill temperature is not a measure of the actual temperature of the air, but rather the combined effect of wind and temperature on exposed skin. It helps to provide an estimate of how cold the wind makes it feel and how much danger there is of hypothermia. In other words, wind chill is an index that quantifies the combined effect of temperature and wind on the thermal comfort of a human body.
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Please help!! I'll give brainliest and this is due tomorrow!!
What are two conservation practices that help prevent wind erosion?
plant barriers and plowed ridges in fields
setting up wind generators that absorb high winds
halting agriculture and planting native species
covering fields with tarps and building wind barriers
Answers
Answer:
The answer is building Wind Barriers
The reasoning is because irrigation, if used too much, causes water erosion. Planting crops deeper in the ground would would prevent the plants from being uprooted. Finally, terracing would prevent from run-off eroding the ground away from the plants.
Explanation:
Answer:
plant barriers and plowed ridges in fields
Explanation:
i had this in an exam and it was right!! =]
A force off 700 newtons is applied to a 600 kg bowling ball. What is the acceleration of the bowling ball once the force is applied?
Answers
Answer:
1.17 m/s²Explanation:
The acceleration of an object given it's mass and the force acting on it can be found by using the formula
\(a = \frac{f}{m} \\ \)
f is the force
m is the mass
From the question we have
\(a = \frac{700}{600} = \frac{7}{6} \\ = 1.1666666...\)
We have the final answer as
1.17 m/s²Hope this helps you
If a soil has a bulk density of 1.4Mg/m 3
and a particle density of 2.66Mg/m 3
, what percentage of the soil volume is pore space and what percentage is solid particles?
Answers
Approximately 47.37% of the soil volume is pore space, and approximately 52.63% is solid particles.
To calculate the percentage of pore space and solid particles in the soil volume, we can use the following formula:
Pore space percentage = ((Particle density - Bulk density) / Particle density) x 100
Solid particles percentage = 100 - Pore space percentage
Given:
Bulk density = 1.4 Mg/m³
Particle density = 2.66 Mg/m³
Substituting the values into the formulas:
Pore space percentage = ((2.66 - 1.4) / 2.66) x 100
Solid particles percentage = 100 - Pore space percentage
Calculating the values:
Pore space percentage ≈ 47.37%
Solid particles percentage ≈ 52.63%
Therefore, approximately 47.37% of the soil volume is pore space, and approximately 52.63% is solid particles.
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Which one of the following is an accurate statement about light?
a) When light strikes a surface at Brewster's angle, only the reflected light is 100% polarized.
b) When light strikes a surface at Brewster's angle, the reflected and transmitted light are both 100% polarized.
c) When light strikes a surface at the critical angle, all the light passes through the surface.
d) When light strikes a surface at Brewster's angle, it is completely reflected at the surface.
e) When light strikes a surface at the critical angle, only the reflected light is 100% polarized.
Answers
The accurate statement about light is: a) When light strikes a surface at Brewster's angle, only the reflected light is 100% polarized.
Your question is about which statement about light is accurate, including the terms "accurate", "light", and "Brewster's angle". The correct answer is:
a) When light strikes a surface at Brewster's angle, only the reflected light is 100% polarized.
Brewster's angle is the angle of incidence at which light, when striking a surface, is completely polarized in the reflected light. At this angle, the reflected light is polarized perpendicular to the plane of incidence, while the transmitted light is not polarized. This is because, at Brewster's angle, the reflected light is polarized parallel to the surface, while the transmitted light is not completely polarized.
Therefore, option a) correctly states that only the reflected light is 100% polarized at Brewster's angle.
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If a football player hits the ball with a force of 50 N, determine the reaction force.
Answers
Answer: 60
Explanation: if u hit it it will have impact and the impact added 10n
Need an actual answer, no links.
Answers
Answer:
8.70 s
Explanation:
Given (in the y direction):
v₀ = 2.38 m/s
v = 0 m/s
a = 0.310 sin (-62.0°) m/s²
Find: t
v = at + v₀
0 m/s = (0.310 sin (-62.0°) m/s²) t + (2.38 m/s)
t = 8.70 s
Water flows at a rate of 3.11 kg/s through a hose with a diameter of 3 cm. what is the speed of the water in the hose?
Answers
Water flows at a rate of 3.11 kilograms / seconds through a hose with a diameter of 3 centimetres. then the speed of the water in the hose would be 4.40 meters / second.
What is Velocity?The total displacement covered by any object per unit of time is known as velocity. The velocity of an object depends on the magnitude as well as the direction of the object.
As given in the problem if Water flows at a rate of 3.11 kg/s through a hose with a diameter of 3 cm.
Area of the hose = πD²/4
=3.14*3*3/40000
=7.065×10⁻⁴ meter²
The discharge of the water = 3.11/1000
=3.11×10⁻³ meter³
The discharge of the water = area of hose ×velocity
3.11×10⁻³ meter³ = 7.065×10⁻⁴ meter²×velocity
velocity = 3.11×10⁻³ / 7.065×10⁻⁴
=4.40 metes/ second
Thus,the speed of the water in the hose would be 4.40 metes/ second.
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A group of particles of total mass 49 kg has a total kinetic energy of 321 j. the kinetic energy relative to the center of mass is 88 j. what is the speed of the center of mass?
Answers
The speed of the center of mass is approximately 3.07 m/s. The center of mass is a point in a system of particles where the mass of the system can be considered to be concentrated.
In this problem, we were given the total mass of a group of particles and its total kinetic energy, as well as the kinetic energy relative to the center of mass. Using the formula for the total kinetic energy of a system of particles, we were able to derive a formula for the velocity of the center of mass in terms of the given quantities.
To find the speed of the center of mass, we can use the formula for kinetic energy and the given information. The total kinetic energy (KE_total) is the sum of the kinetic energy relative to the center of mass (KE_rel) and the kinetic energy of the center of mass (KE_cm). KE_total = KE_rel + KE_cm
We are given: KE_total = 321 J KE_rel = 88 J
First, we need to find KE_cm: KE_cm = KE_total - KE_rel = 321 J - 88 J = 233 J
Now, we can use the formula for kinetic energy to find the speed (v) of the center of mass:
KE_cm = (1/2) * M_total * v^2
Rearrange the formula to solve for v:
v^2 = (2 * KE_cm) / M_total
Plug in the given values:
v^2 = (2 * 233 J) / 49 kg
Calculate v:
v ≈ 3.07 m/s
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A piece of iron wire has a resistance of 30. What will be the resistance of aluminum wire of one-fourth the length and one third the diameter of iron wire. It the specific resistance of aluminum is 30 times that of silver. [Ans: 202.5.02]
Answers
Answer
Explanation: R=p l/A , we are given specific resistance of aluminium in terms of silver.
What is the force of gravity on a 80. kg man who is orbiting the Earth at a height 4.0 X 10 ^ 6 m above the surface ?
Answers
Answer:
I hope this might help.
A car tart from ret and travel for 3. 4 with a uniform acceleration for 17. 0 m/. What i the final velocity of the car?
Answers
Final velocity = 57.8m/s
What is acceleration?
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities. The orientation of an object's acceleration is given by the orientation of the net force acting on that object
Acceleration = (Initial velocity - Final velocity) /time
Given,
time = 3.4s
Acceleration = 17 m/s^2
17 = (0-v)/3.4
final velocity = 17 X 3.4 = 57.8 m/s
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137 . a nearsighted man cannot see objects clearly beyond 20 cm from his eyes. how close must he stand to a mirror in order to see what he is doing when he shaves?
Answers
Because the image of the item is created in front of the retina rather than on the retina itself, a nearsighted person cannot see distant objects clearly.
If the human eye can clearly perceive items up close but not far away, how can this be corrected?When light from a faraway object enters the eye lens and converges at a point in front of the retina, it is called myopia, also known as nearsightedness.
Why can't we see anything clearly if it's placed right in front of our eyes?Through the use of ciliary muscles, the lens is able to change its fixed ability to shift the focus length. To adjust the eye's focal length, ciliary muscles cannot be contracted any further than a certain point.
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a ball is dropped from a cliff. what is the velocity after 4 seconds?
Answers
Answer:
\(v = u + gt \\ v = (0) + 9.8(4) \\ v = 39.2 \: m. {s}^{ - 1} \)
When the point of reference (the observer) is in motion, it flips the "rules" of vector addition (you ADD the vectors going in opposite directions, and SUBTRACT vectors going in the same direction).
True
False
Answers
Answer:
the statement is TRUE
Explanation:
When we move in the same direction, the relative speed of the two vehicles is lower, so we must subtract their speeds, if the result is positive the vehicles approach and if it is negative they move away.
v_relative = v₁ - v₂
When the two vehicles go in opposite directions, the speed is much higher, so we must add their speeds
v_relative = v₁ - (-v₂))
v_relative = v₁ + v₂
therefore the statement is TRUE
Choose the law that BEST explains the example:
A driver without a seat belt getting thrown from the car in a collision is an example of Newton’s
Group of answer choices
1st law
2nd law
3rd law
None of these
Answers
Answer:
Newton 3rd law
Explanation:
The driver of the vehicle crashes without a seatbelt will have an opposite reaction than the car that crashed.
Hope this helped
You are pushing a cart of groceries with a force of 368 N. The mass of the cart is 24 kg. What is the cart’s acceleration?
A. 0 m/s2
B. 15.3 m/s2
C. 8.9 x 103 m/s2
D. 0.7 m/s2
Answers
Answer:
B
Explanation:
A car begins from rest and accelerates at a rate of +3.0 m/s2 for 5.0 seconds. what is the car's final speed?
Answers
Answer:
15m/s
Explanation:
we know that
v = u + at
= 0+ 3*5
=15m/s