Answer:
a) The velocity when it passes the equilibrium point is [tex]\pm 2.451[/tex] meters per second.
b) The velocity when it is 0.10 meters from equilibrium is [tex]\pm 1.567[/tex] meters per second.
c) The total energy of the system is 1.802 joules.
d) The equation describing the motion of the mass, assuming that initial position is a maximum is [tex]x(t) = 0.13\cdot \sin (18.850\cdot t +0.5\pi)[/tex].
Explanation:
a) If all non-conservative forces can be neglected and spring has no mass, then the mass-spring system exhibits a simple harmonic motion (SHM). The kinematic formula for the position of the system ([tex]x(t)[/tex]), measured in meters, is:
[tex]x(t) = A\cdot \sin(\omega \cdot t +\phi)[/tex] (1)
Where:
[tex]A[/tex] - Amplitude, measured in meters.
[tex]\omega[/tex] - Angular frequency, measured in radians per second.
[tex]t[/tex] - Time, measured in seconds.
[tex]\phi[/tex] - Phase, measured in radians.
The kinematic equation for the velocity formula of the system ([tex]v(t)[/tex]), measured in meters per second, is derived from (1) by deriving it in time:
[tex]v(t) = \omega\cdot A\cdot \cos (\omega\cdot t+\phi)[/tex] (2)
The velocity when it passes the equilibrium point occurs when the cosine function is equal to 1 or -1. Then, that velocity is determined by following formula:
[tex]v = \pm \omega\cdot A[/tex] (3)
The angular frequency is calculated by this expression:
[tex]\omega = 2\pi\cdot f[/tex] (4)
Where [tex]f[/tex] is the frequency, measured in hertz.
If we know that [tex]f = 3\,hz[/tex] and [tex]A = 0.13\,m[/tex], then the velocity when it passes the equilibrium point, which is the maximum and minimum velocities of the mass:
[tex]\omega = 2\pi\cdot (3\,hz)[/tex]
[tex]\omega \approx 18.850\,\frac{rad}{s}[/tex]
[tex]v = \pm \left(18.850\,\frac{rad}{s} \right)\cdot (0.13\,m)[/tex]
[tex]v = \pm 2.451\,\frac{m}{s}[/tex]
The velocity when it passes the equilibrium point is [tex]\pm 2.451[/tex] meters per second.
b) First, we need to determine the spring constant of the system ([tex]k[/tex]), measured in newtons per meter, in terms of the angular frequency ([tex]\omega[/tex]), measured in radians per second, and mass ([tex]m[/tex]), measured in kilograms. That is:
[tex]k = \omega^{2}\cdot m[/tex] (5)
If we know that [tex]\omega \approx 18.850\,\frac{rad}{s}[/tex] and [tex]m = 0.60\,kg[/tex], then the spring constant is:
[tex]k = \left(18.850\,\frac{rad}{s} \right)^{2}\cdot (0.60\,kg)[/tex]
[tex]k = 213.194\,\frac{N}{m}[/tex]
Lastly, we determine the velocity when the mass is 0.10 meters from equilibrium by the Principle of Energy Conservation:
[tex]U_{k} + K = K_{max}[/tex] (6)
[tex]\frac{1}{2}\cdot k\cdot x^{2} + \frac{1}{2}\cdot m\cdot v^{2} = \frac{1}{2}\cdot m\cdot v_{max}^{2}[/tex] (7)
Where:
[tex]U_{k}[/tex] - Current elastic potential energy, measured in joules.
[tex]K[/tex] - Current translational kinetic energy, measured in joules.
[tex]K_{max}[/tex] - Maximum translational kinetic energy, measured in joules.
[tex]v[/tex] - Current velocity of the system, measured in meters per second.
[tex]m[/tex] - Mass, measured in kilograms.
[tex]v_{max}[/tex] - Maximum velocity of the system, measured in meters per second.
If we know that [tex]k = 213.194\,\frac{N}{m}[/tex], [tex]x = 0.10\,m[/tex], [tex]m = 0.60\,kg[/tex] and [tex]v_{max} = \pm 2.451\,\frac{m}{s}[/tex], then the velocity of the mass-spring system is:
[tex]\frac{k}{m} \cdot x^{2} + v^{2} = v_{max}^{2}[/tex]
[tex]v^{2} = v_{max}^{2}-\frac{k}{m}\cdot x^{2}[/tex]
[tex]v = \sqrt{v_{max}^{2}-\frac{k\cdot x^{2}}{m} }[/tex] (8)
[tex]v = \sqrt{\left(\pm 2.451\,\frac{m}{s} \right)^{2}-\frac{\left(213.194\,\frac{N}{m} \right)\cdot (0.10\,m)^{2}}{0.60\,kg} }[/tex]
[tex]v \approx \pm 1.567\,\frac{m}{s}[/tex]
The velocity when it is 0.10 meters from equilibrium is [tex]\pm 1.567[/tex] meters per second.
c) The total energy of the system ([tex]E[/tex]), measured in joules, can be determined by the following expression derived from the Principle of Energy Conservation:
[tex]E = \frac{1}{2}\cdot m\cdot v_{max}^{2}[/tex] (9)
If we know that [tex]m = 0.60\,kg[/tex] and [tex]v_{max} = \pm 2.451\,\frac{m}{s}[/tex], then the total energy of the system is:
[tex]E = \frac{1}{2}\cdot (0.60\,kg)\cdot \left(\pm 2.451\,\frac{m}{s}\right)^{2}[/tex]
[tex]E = 1.802\,J[/tex]
The total energy of the system is 1.802 joules.
d) Given that initial position of the mass-spring system is a maximum, then we conclude that the equation of motion has the following parameters: ([tex]A = 0.13\,m[/tex], [tex]\omega \approx 18.850\,\frac{rad}{s}[/tex] and [tex]\phi = 0.5\pi\,rad[/tex])
From (1) we obtain the resulting formula:
[tex]x(t) = 0.13\cdot \sin (18.850\cdot t +0.5\pi)[/tex] (10)
The equation describing the motion of the mass, assuming that initial position is a maximum is [tex]x(t) = 0.13\cdot \sin (18.850\cdot t +0.5\pi)[/tex].
A block that slides on a rough surface slows down and eventually stops. The reverse process never occurs. That is, a block at rest never begins to move and accelerate on a rough surface without the action of an external agent. The second situation is forbidden because it would violate:_________.
a) conservation of total energy
b) conservation of momentum
c) the first law of thermodynamics
d) the second law of thermodynamics
e) both the first and second law of thermodynamics
Gracias.
Answer:
d) the second law of thermodynamics
Explanation:
Here we take an example
The entropy represents a measurement of the energy dispersal in the system. Also, the campfire would an entropy example. The burning of the solid wood and then it became the ash, smoke and gases this all would be spread the energy to the outward as compared to the solid fuel
Therefore as per the given statement, the correct option is d.
An object whose specific gravity is 0.850 is placed in water. What fraction of the object is below the surface of the water?
Answer:
The fraction of the object that is below the surface of the water is ¹⁷/₂₀
Explanation:
Given;
specific gravity of the object, γ = 0.850
Specific gravity is given as;
[tex]specific \ gravity = \frac{density \ of the \ object}{density \ of \ water}\\\\0.85= \frac{density \ of the \ object}{1000 \ kg/m^3} \\\\density \ of the \ object = 850 \ kg/m^3[/tex]
Fraction of the object's weight below the surface of water is calculated as;
[tex]= \frac{850}{1000} \ \times\ 100\%\\\\= 85 \% \\\\= \frac{17}{20}[/tex]
Therefore, the fraction of the object that is below the surface of the water is ¹⁷/₂₀
Calculate the change in entropy of 0.020 kg of ice when it melts at 0.0°C. The heat of fusion of ice is 3.36 x 10'J/kg.
Answer:
S = 2461.53 [kJ]
Explanation:
The change in entropy in a process such as melting can be calculated by means of the following expression.
[tex]S=\frac{H*m}{T}[/tex]
where:
S = entropy [kJ]
H = fusion heat = 3.36*10¹ [J/kg]
m = mass = 0.02 [kg]
T = temperature in kelvin = 273 [K]
[tex]S = \frac{0.02*3.36*10^{1} }{(273+0)}\\S = 2461.53 [kJ][/tex]
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Research what is known about Earth’s magnetic field. Begin by looking for images and credible sites on the Internet or refer to some books in a library. Answer the following questions:
What is the approximate size of Earth’s magnetic field?
Where are Earth’s magnetic poles?
Where is the magnet that causes Earth’s magnetic field located? What is this magnet made of?
Does Earth’s magnetic field move?
The earth has a magnetic field. It is much like a bar magnet. Imagine a gigantic bar magnet inside the Earth. But there is no giant magnet inside it.
To have a pretty good idea what earth's magnetic field is shaped like we imagine a bar magnet inside the earth.
The magnetic field is made by the motion of molten iron in earth's outer core. The swirling motion of molten iron changes all the time. Therefore, the magnetic fields will also get change. Then, the magnet poles also move.
The North pole and the south pole are two geographic poles of earth. These poles are the places on the earth's surface that earth's imaginary spin axis passes through.
There are two magnetic poles of the earth: North magnetic pole and South magnetic pole.
Earth's magnetic field is tilted a little bit. If we imagine that earth's magnetic field is made by a giant bar magnet. Then, the bar magnet would make an with earth's spin axis.
The geographic poles and the magnetic poles are not in the same place.
If we are standing at one magnetic poles then the magnetic field lines would be straight up and down.
Earth's magnetic field is a complex and dynamic phenomenon that is generated by the motion of molten iron in its outer core. The magnetic field extends far beyond the planet and is responsible for protecting Earth from harmful solar radiation and cosmic rays.
What is the approximate size of Earth's magnetic field?Earth's magnetic field is roughly dipolar in shape, meaning it has two main magnetic poles - north and south - and the field lines emerge from the north and re-enter at the south pole. The magnetic field has a strength of about 25-65 microteslas (μT) at the Earth's surface, and it extends for several tens of thousands of kilometers into space.
2. Where are Earth's magnetic poles?
Earth's magnetic poles are not fixed and are constantly moving due to the complex and dynamic nature of the planet's magnetic field. Currently, the north magnetic pole is located in the Arctic Ocean, close to Canada's Ellesmere Island, and the south magnetic pole is located in the Antarctic Ocean, near the coast of Antarctica.
3. Where is the magnet that causes Earth's magnetic field located? What is this magnet made of?
The magnet that causes Earth's magnetic field is not a physical magnet but rather a result of the motion of molten iron in the Earth's outer core. The outer core is a layer of liquid iron and nickel that surrounds the solid inner core. The motion of this molten iron generates electrical currents, which in turn create a magnetic field.
4. Does Earth's magnetic field move?
Yes, Earth's magnetic field is not static and is constantly changing due to the complex nature of the planet's interior. The magnetic poles are constantly moving and the strength of the magnetic field can vary over time. The magnetic field can also be influenced by external factors such as solar storms and changes in the solar wind. Scientists continue to study Earth's magnetic field to better understand its behavior and how it affects the planet.
Therefore, The magnetic field of the Earth is a complex and dynamic phenomenon caused by the movement of molten iron in its outer core. The magnetic field extends far beyond the planet and is in charge of shielding the planet from harmful solar radiation and cosmic rays.
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Choose all correct sentences Group of answer choices The power is maximum when the value of the impedance is greater than the value of the resistance. Resonance occurs when omega squared space equals 1 divided by space L C At resonance, the power is maximum and the impedance is minimum. At resonance, R squared space equals space (X subscript L minus X subscript c )squared The impedance Z is always larger than the resistance R.
Answer:
True b and c
Explanation:
In an RLC circuit the impedance is
[tex]Z = \sqrt{[R^{2} + ( (wL)^{2} + (\frac{1}{wC})^{2} ] }[/tex]
examine the different phrases..
a) False. The maximum impedance is the value of the resistance
b) True. Resonance occurs when
(wL)² + (1 / wC)² = 0
w² = 1 / LC
c) True. In resonance the impedance is the resistive part and the power is maximum
d) False. In resonance the inductive and capacitive part cancel each other out
e) False. The impedance is always greater outside of resonance, but at the resonance point they are equal
Which has a greater force: a semi-truck at rest or a moving bicycle?
Although the semi truck certainly has a larger mass, it is not in motion and therefore does not have any momentum. The bicycle however has both mass and velocity and therefore has the larger momentum of the pair.
In the Fresnel circular aperture setup, the distances from the aperture to the light source and the reception screen are 1.5 m and 0.6 m, respectively. The wavelength is 630 nm. Suppose that the radius of the aperture can be increased from 0.5 mm, determine: (a) The first two radii when the center intensity at the reception screen is maximum. (b) The first two radii when the center intensity is minimum.
Explanation:
The width of the central maximum is given by
W = 2 λ L / a
where W is the width of the central maximum
λ is the wavelength of the light used.
L is the distance between the aperture and screen
a is the width of the slit or aperture
So we can see that if any one quantity is varied by keeping others constant in the above formula , there would be a change in width of central maximum.
Which of the following examples best represents an object with balanced forces acting upon it?
A - A boat accelerating through the water.
B - A book sitting at rest on a high shelf.
C- A wagon rolling down a steep hill.
D- A baseball thrown into the air.
Answer:the answer is “A book sitting on a high shelf” :)
Explanation:
A 300 g bird flying along at 6.0 m/s sees a 10 g insect heading straight toward it with a speed of 30 m/s. the bird opens its mouth wide and enjoys a nice lunch. What is the bird's speed immediately after swallowing?
Answer:
6.77m/s
Explanation:
Using the law of conservation of momentum
m1u1 + m2u2 = (m1+m2)v
m1 and m2 are the masses of the object
u1 and u2 are the velocities before collision
v is the final collision
Given
m1 = 300g = 0.3kg
u1 = 6.0m/s
m2 = 10g = 0.01kg
u2 = 30m/s
Required
The bird's speed immediately after swallowing v
Substitute the given values into the formula
m1u1 + m2u2 = (m1+m2)v
0.3(6) + 0.01(30) = (0.3+0.01)v
1.8+0.3 = 0.31v
2.1 = 0.31v
v = 2.1/0.31
v = 6.77m/s
Hence the bird's speed immediately after swallowing is 6.77m/s
Sadie rolls a marble down a ramp. When the marble reaches the bottom of the ramp, it then rolls across the floor. After a few seconds, the marble slows down, then stops. What caused the marble to stop? *
A Friction between the marble and the floor.
B Air pressure pushing down on the marble.
C The force of gravity pulling the marble down.
D Magnetic attraction between Earth and the marble.
HELP ASAP!! i’ll mark you the brainliest!!
Answer:
yes
Explanation:
mester Exam 1 11 of 35
A car has an oil drip. As the car moves, it drips oil at a regular rate, leaving a trail of spots on the road. Which diagram shows the spots
of car that is continuously slowing down?
A ray moving in water at 55.5 deg
enters plastic, where it bends to
48.7 deg. What is the index of
refraction for the plastic?
( water n = 1.33, Air n = 1.00 )
Answer:
Refractive index of the plastic = 1.46
Explanation:
By Snell's law,
[tex]\frac{\text{sin}\theta _{2} }{\text{sin}\theta _{1}}=\frac{n_1}{n_2}[/tex]
Here, [tex]\theta _1[/tex] = Angle of incidence in medium 1 (Plastic)
[tex]\theta_2[/tex] = Angle of refraction in medium 2 (Water)
[tex]n_1[/tex] = Refractive index of medium 1 (Plastic)
[tex]n_2[/tex] = Refractive index of medium 2 (Water)
By substituting values in the formula,
[tex]\frac{\text{sin}(48.7)}{\text{sin}(55.5)}=\frac{1.33}{n_2}[/tex]
[tex]n_2=\frac{1.33\times \text{sin}(55.5)}{\text{sin}(48.7)}[/tex]
= 1.46
Therefore, refractive index of the plastic = 1.46
In specific heat capacity experiment, the ammeter in circuit is connected in
Answer:
In series
Explanation:
In such experiment, the ammeter is connected in series with the heater, in order to measure the circulating current.
By the way, ammeters are always connected in series in circuits to measure the running current in it.
A thyristor (SCR) is a
Answer:
A thyristor (/θaɪˈrɪstər/) is a solid-state semiconductor device with four layers of alternating P- and N-type materials. It acts exclusively as a bistable switch, conducting when the gate receives a current trigger, and continuing to conduct until the voltage across the device is reversed biased, or until the voltage is removed (by some other means).
Explanation:
Correct me if im wrong
Use the image below to answer the question.
What does the arrow 'B' represent?
Question 7 options:
wavelength
refraction
frequency
compression
What kind of electricity does turning wheel generates? Please help!
Answer: Kinetic Energy to Electrical.
Explanation: The magnet is rotated as a result of the spinning wheels, and this results in a powerful stream of electrons, therefore converting kinetic to electrical.
Define a rotation of the earth answer fast
Answer:
here u go
Explanation:
Earth's rotation is the rotation of planet Earth around its own axis. Earth rotates eastward, in prograde motion. As viewed from the north pole star Polaris, Earth turns counterclockwise.
Multiply.
(2x + 4)(x - 4)
Answer:
(2x + 4)(x - 4)=2x^2-4x-16
g While hauling a log in the back of a flatbed truck, a driver is pulled over by the state police. Although the log cannot roll sideways, the police claim that the log could have slid out the back of the truck when accelerating from rest. The driver claims that the truck could not possibly accelerate at the level needed to achieve such an effect. Regardless, the police write a ticket, and the drive
Answer:
The minimum coefficient of static friction required, µ = 0.10
Note. The question is incomplete. The complete question is given below:
While hauling a log in the back of a flatbed truck, a driver is pulled over by the state police. Although the log cannot roll sideways, the police claim that the log could have slid out the back of the truck when accelerating from rest. The driver claims that the truck could not possibly accelerate at the level needed to achieve such an effect. Regardless, the police write a ticket anyway and now the driver court date is approaching.
The log has a mass of m = 929 kg; the truck has a mass of M = 8850 kg. According to the truck manufacturer, the truck can accelerate from 0 to 55 mph in 23.0 seconds, but this does not account for the additional mass of the log. Calculate the minimum coefficient of static friction μs needed to keep the log in the back of the truck.
Explanation:
First, velocity in mph is converted to m/s
1 mph = 0.447 m/s
55 mph ≈ 24.6 m/s
The acceleration of the empty truck is a = v/t = 24.6 / 23 = 1.07 m/s²
Force that can be generated by the truck, F = ma
F = 8850kg * 1.07 m/s² = 9469.5 N
However, with the added mass of the log on it, the acceleration of the truck will become;
a = F / m = 9469.5 N / (8550+929)kg = 0.97 m/s²
Frictional force between the log and the truck = 0.97 m/s² * 929 kg = 901.13 N
Normal reaction on the truck due to the weight of the log, R = mg
R = 929 kg * 9.8m/s² = 9104.2 N
Coefficient of static friction, µ = F/R
µ = 901.13/9104.2
µ = 0.098 ≈ 0.10
Therefore, the minimum static friction required is µ = 0.10
What is the volume of a brick that is 30 cm long, 8 cm wide, and 10 cm tall?
How fast, in meters per second, does an observer need to approach a stationary sound source in order to observe a 7.1 % increase in the emitted frequency?
Answer:
v0 = 24.42 m/s (Approx)
Explanation:
Given:
Increase in frequency = 7.1% =
Computation:
Assume n = 100%
n1 = [(v+v0)/(v+v1)]n
[100 + 7.1] = [(344+v0)/(344+0)]100
107.1 = [(344+v0)/(344)]100
v0 = 24.42 m/s (Approx)
what is the difference between alcoholic and Mercury thermometer based on their function?
12 seconds after starting from rest a frewly falling cantaloupe has a speed of
Answer:
The cantaloupe has a speed of 117.6 m/s
Explanation:
Free Fall Motion
It occurs when an object falls under the sole influence of gravity. Any object that is being acted upon solely by the force of gravity is said to be in a state of free fall. Free-falling objects do not face air resistance.
If an object is dropped from rest in a free-falling motion, it falls with a constant acceleration called the acceleration of gravity, which value is [tex]g = 9.8 m/s^2[/tex].
The final velocity of a free-falling object after a time t is given by:
vf=g.t
The cantaloupe has been dropped from rest. We are required to find the speed after t=12 seconds.
Calculate the final speed:
vf=9.8 * 12 = 117.6 m/s
The cantaloupe has a speed of 117.6 m/s
a passenger of mass m on a Ferris wheel moves in a vertical circle of radius r with constant speed v assuming that the seat remains upright during the motion which is true about the force the seat exerts on the passenger at the top of the circle
the upward force is equal in magnitude to the passenger's weight
the upward force is greater in magnitude than the passenger's weight
the upward force is smaller in magnitude than the passenger's weight
the upward force is zero
Answer:
the upward force is equal to the passenger weight
The answer that is the truth about the force that the seat exerts on the passenger is the upward force is equal in magnitude to the passenger's weight.
Why the upward force is equal in magnitude to weight
The acting forces on the body has been said to be vertical. This implies that the upward force and the downward force of gravity are the same.
Using the second law of Isaac Newton, the downward direction of the forces would be ascertained.
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According to The Flash, The heroes top speed is Mach 3.3, or 2,500 miles per hour. How
long would it take for him to run around the planet? (circumference of the earth is
roughly 25,000 miles) *
Answer:
nearly 2 days or less hes fast but not that fast
Explanation:
but maybe he can run it in five minutes
what are the importance of informal education?
Answer:
Informal education is important because it can help individual to learn how to react and control situations.
It help individual to improve on its existing knowledge, new skills or ideas. This kind of education can happen any where and it can add values to the learner.
Explanation:
Informal education is a type of education that is learned from different life experiences, happenings outside a structured curriculum.
Informal education is important because it can help individual to learn how to react and control situations.
It help individual to improve on its existing knowledge, new skills or ideas. This kind of education can happen any where and it can add values to the learner.
2. Using Graph 2, calculate the net force experienced by the particle between 4 and 6 seconds. The
particle has a mass of 0.25 kg.
A +5.0 N
B. +0.5 N
C. -0.5 N
D. -2.0 N
Using Newtons Second Law:
F = m×a
F = (0.25 kg)(-2 m/s²)
F = -0.5 N
The correct option is CWhen 26400j of energy is supplied to a 2.0kg bloom of aluminum it temperature rise from 20oc to 35oc.The block is well so there is no energy lost to sorround determine the specific heat capacity of aluminum
Answer:
880J/kelvin
Explanation:
Q =MC ×change in t
c =C/m
C=Q/change in t
c= Q/ m× change in t
c = 26400 / 2.0 × 15
c = 880 J/kelvin
An object is moving diagonally (down and to the left). You want it to stop moving. In what direction (or
directions) should you exert a force to get the object to stop?
a. Force direction(s):
b. Explain your answer: