a. The integral expression for the change in potential energy of the spring is ΔU = ∫kxdx
b. The change in potential energy of the spring is ΔU = k(x₂² - x₁²)/2
Since we are given the differential elastic potential energy, du, to find the integral expression, we integrate du.
a. The integral expression for the change in potential energy of the springThe integral expression for the change in potential energy of the spring is ΔU = ∫kxdx
Since the infinitesimal elastic potential energy of the spring du = kxdx, integrating both sides of the expression, we have
ΔU = ∫du
ΔU = ∫kxdx
So, the integral expression for the change in potential energy of the spring is ΔU = ∫kxdx
b. The elastic potential energy of the springThe change in potential energy of the spring is ΔU = k(x₂² - x₁²)/2
Performing the integration for the change in potential energy of the spring
ΔU, we have that integrating for change in length from x₁ to x₂
ΔU = ∫kxdx
ΔU = k[x²/2]₁²
ΔU = kx₂²/2 - kx₁²/2
ΔU = k(x₂² - x₁²)/2
So, the change in potential energy of the spring is ΔU = k(x₂² - x₁²)/2
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A 1.2-kg mass is oscillating without friction on a spring whose spring constant is 3400 N/m. When the mass's displacement is 7.2 cm, what is its maximum acceleration
The maximum acceleration of the mass oscillating on the spring whose spring constant is 3400 N/m, is determined as 204 m/s².
Applied force on the springThe force applied on the spring to cause the mass to displace to the given distance is determined by applying Hooke's law;
F = kx
F = (3400 N/m) x (0.072 m)
F = 244.8 N
Maximum accelerationThe maximum acceleration of the mass is determined from Newton's second law of motion as shown below;
F = ma
a = F/m
a = 244.8 / 1.2
a = 204 m/s²
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The mechanical energy of the diver is the same at every height. What is the mechanical energy of the diver
Which two characteristics might a model have if it is a three-dimensional model of magnetic force made by using a magnet and magnetic field lines? A. Some field lines have arrows that point in different directions. B. Arrows on the field lines point from the magnet's north pole to its south pole. C. The field lines are closest together in and near the magnet D. The field lines cross paths as they go from one pole of the magnet to the other.
Answer:
B C I suppose , though A is correct too
Explanation:
The arrows on the magnetic field lines point from the magnet's north pole to its south pole. The field lines are closest together in and near the magnet. Thus, the correct options are B and C.
What is Magnetic force?Magnetic force is the force of the electrically charged particles which are in motion, such as attraction, or repulsion results from their activity. It is the fundamental force behind the phenomena like how electric motors operate and magnets are drawn to metals.
Usually, when we draw magnetic field lines, we start to draw outwardly from the North pole to the South Pole. This same direction is prevalent on the Earth due to the fact that the Earth functions as a giant magnet. Thus, the model describes that the magnetic field lines will spread out of the north end of the magnet to the south end. The magnetic field lines are closest in and near the magnet.
Therefore, the correct options are B and C.
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A 400g mass object at rest is acted on by a 200 N net force for 12 seconds. What is it’s final velocity?
The answer is supposed to be 6000 m/s but I’m not sure how…
Explanation:
do we can say that the first step is finding the acceleration of the object. We do so by saying F = ma
so a = F/m
a = 500 m/s^2
we now have the time, acceleration and initial velocity.
so we can find the final velocity by using one of newtons equations which is: vf = vi + at
so:
vf = 0 + 500 × 12
vf = 6000
note that our initial velocity was zero since the object was initially at rest.
if you still have any doubt dont hesitate to ask for further help.
A scuba diver uses his waterproof flashlight to shine a beam of light so that it strikes the surface of the water at an angle of incidence . Use Snell’s law to find the angle of incidence that would give an angle of refraction for the refracted ray to be directed right along the surface, and show that is the same as the critical angle for total internal reflection.
Answer:
the light speed up and change it directtions
A boy swings a 30 g fishing sinker around his head attached to his fishing line. The radius ofthe circular motion of the sinker is 65 cm. The sinker does 2 revolutions per second.
(a) What is the period of rotation of the sinker?
(b) What is the tangential velocity of the sinker?
(c) Calculate the acceleration of the sinker.
Explanation:
a) Peroid = 1/frequency
F = 2 rev. per second = 2Hz
period = 1/2 = 0.5s
b) Tangential velocity(Vt) = ωr, where ω is thr angular velocity(2 * Pi(3.142) * f(frequency)) and r is the radius
Therefore; Vt = 2 * 3.142 * 2 * 0.65(65/100)
= 8.1692
= 8.2m/s
c) a = (V^2)/r where V is the velocity and r is the radius
a = (8.2^2)/0.65
a = 103m/s^2
What is Newton's Third law of motion? Explain how this roller coaster
demonstrates Newton's Third law of motion.
Answer:
Newton's third law of motion says, "For every action there is an equal and opposite reaction." So that applied to the student's roller coaster, between the marble and the track. When the marble went up and down the hill, it created different forces onto the track.
Explanation:
mark as brainiest
Can someone help me with this please :(
Answer:
it should be iii) Upthrust exerted on P is more than the upthrust exerted on Q
Most stars in the Milky Way's halo are _________. blue or white in color very young very old found inside molecular clouds
Answer:
Most stars in the Milky Way's halo are very old
very oldThere is no recycling of gas in the halo, so halo stars are quite old.
The requried, "Most stars in the Milky Way's halo are very old."
What is milk way's halo?The Milky Way halo is a large, spherical region surrounding the disk of the galaxy, and it is believed to be composed primarily of ancient stars that formed early in the history of the galaxy.
Here,
These stars are typically metal-poor, which means they have lower abundances of elements heavier than hydrogen and helium compared to stars in the disk. They are also old, with estimated ages of several billion years or more.
The halo stars are believed to have formed in small, isolated systems that were later accreted by the Milky Way. They are widely dispersed and do not form dense concentrations like those found in the disk or in globular clusters.
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What do ethical guidelines for research with human subjects mean?
By minimizing harms and risks and maximize benefits , respect human dignity, privacy and autonomy, take special precautions with vulnerable population and strive to distribute the benefits and burdens of research fairly
While on the surface of the earth a student has a weight of 450n if she is moved twice as far from the center of the earth then how does the new weight compare to her old?
Based on the fact that the student is moved twice as far from the center of the earth, her new weight will be 112.5 N.
What is her new weight?When the student was moved by the same distance from the center of the earth, her weight was halved.
When she was then moved twice as far, her weight was halved again.
This means that her new weight is:
= 450 x 1/2 x 1/2
= 450 x 1/4
= 112.5 N.
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When an old information system in shut down and a new system starts up right after the shut down, we call this a __________ inforomation system conversion. phased parallel plunge pilot
Parallel information system is when an old information system in shut down and a new system starts up right after the shut down.
What is an information system?An information system is a system in which information are passed or transmitted from one end to another especially from senders to receivers to achieve a particular goal.
Therefore, Parallel information system is when an old information system in shut down and a new system starts up right after the shut down.
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A tow truck pulls a 3500 kg mazda car out of the mud. The car is moved 20 M in 4 seconds by the truck. What is the work done by the tow truck
Answer:
W = F * S one does not know the work performed because one does not know what force produced the resulting work. Neither can one calculate the power required because P = W / t (work / time)
One only knows the distance and the time but not the force required.
Which nasa spacecraft is studying jupiter and its moons?.
Answer:
Juno
Explanation:
The NASA spacecraft Juno (2016) is the one that was studying Jupiter more in detail.
I hope it helps! Have a great day!
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What type of particle carries an electric current through a wire? Voltage is another name for the __________ difference. What word completes the sentence?
Answer:
electric potentialbrainless plsss
A laser emits a narrow beam of light. The radius of the beam is 1.5 mm, and the power is 1.9 mW. What is the intensity of the laser beam?
Answer: 268.80 W/m^2
Explanation:
Intensity = Power/Area
first convert radius to meters
1.5mm= 1.5x10^-3m
area= pi (1.5x10^-3)^2
= 7.069m^2
convert power to W
1.9mW= 1.9x10^-3W
plug into intensity formula
(1.9x10^-3)/(7.069) = 268.80 W/m^2
A net force of 15N is applied to a cart with a mass of 5kg. What is the
acceleration of the cart?
Answer:
3 m/s^2
Explanation:
Simply F = ma
15 = 5 a
a = 3 m/s^2
The ratio of force and mass is known as
A. Velocity B. Momentum C. Acceleration D. Displacement
Answer:
Acceleration
Explanation:
We know that Force = Mass * Acceleration according to the formula.
Divide both sides by “Mass” which leaves us with Force/Mass = Acceleration, in word, it’s ratio of force and mass equals acceleration.
Most meteors burn up in the
Answer:
the Mesosphere
Most meteors burn up in the mesosphere. Unlike the stratosphere, temperatures once again grow colder as you rise up through the mesosphere.
Explanation:
Have a nice day
Answer:
The Mesosphere
Explanation:
It is the coldest layer.
Which two energy sources can help a star maintain its internal thermal pressure?.
Which statement describes the law of conservation of energy
Answer:
law of action and riactiond
2. Following a strength training plan, someone who increases lean muscle mass by .5 pounds per month will achieve a weight gain of ______
a) 5 pounds in two months.
b) pound in one month.
c) 2 pounds in four months
Answer:
C
Explanation:
.5 lb/month * 4 month = 2 lbs
Distinguish between infrasonic and ultrasonic sound waves.
How we could distinguish them is that the infrasonic sounds are the lower limit of human hearing while ultrasonic sound is above human hearing. The sound of frequency more than 20,000Hz are called ultrasonics while the frequency less than 20Hz are called infrasonics.
Explanation:
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Look at the diagram. Both cars start from the same point. Which describes the motion shown?
A:One car travels south at 4 m/s. The other car travels east at 2 m/s.
B:One car travels north at 4 m/s. The other car travels west at 2 m/s.
C;One car travels north at 2 m/s. The other car travels east at 4 m/s.
D: One car travels south at 4 m/s. The other car travels west at 2 m/s. 7 of 10
The original photo wouldn't load...
Answer: The answer is C.
Explanation: C is the correct answer. The magnitude of the vector increases with the length of the line. Consider a compass when it comes to direction.
The density of water is 1.0 gram per milliliter at 4 degrees Celsius.
Shelby drops a spoonful of sugar into water at this temperature and it
sinks to the bottom of the container. Compare the densities of the sugar
and water and explain how this affects the position of the sugar in the
liquid water.
Sugar molecules present at the bottom of solution due to more mass.
Which is more denser water or sugar?Table sugar is more dense than water due to the presence of more mass of sugar molecule as compared to water. We know that denser objects has more mass so that's why sugar molecules present at the bottom of solution due to more mass.
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A car travels from City A to City B to the north. It takes 4 hours, and the road mileage is 200 miles. The map shows that
the cities are only 80 miles apart (straight-line distance).
Answer:
The average speed would be the 200 miles/4 hours.
The average velocity would be the net displacement to the north at 80 miles/4 hrs = mph
Explanation:
When studying the photoelectric effect, which parameters did scientists think were relevant for electrons to be released or not in both the wave and particle models?
A. intensity only for both models
B. frequency and intensity for the particle model; frequency only for the wave model
C. frequency only for both models
D. frequency and intensity for the wave model; frequency only for the particle model
I marked it as B, but I am not certain.
Answer:
D.
Explanation:
The answer should be D. frequency and intensity for the wave model; frequency only for the particle model.
I hope it helps! Have a great day!
Anygays-
The parameter will be frequency and intensity for the wave model and the frequency only for the particle model.
What is the photoelectric effect?When a medium receives electromagnetic radiation, electrostatically charged particles are emitted from or inside it.
The emission of ions from a steel plate when light falls on it is a common definition of the effect. The substance could be a solid, liquid, or gas; and the released particles could be protons or electrons.
The above effect is the photoelectric effect. Frequency and intensity for the wave model; frequency only for the particle model.
Hence option D is correct.
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A 30kg bullet strikes a tree trunk of diameter 40cm at 200ms and leaves it from the opposite side at 100ms find the kinetic energy of the bullet just before it strikes the tree
Answer:
Before it strikes the tree:
KE = 1/2 m v^2 = 1/2 * 30 kg * (200 m/s)^2
This KE would be 6.0E5 Joules
30 kg would about 66 lbs - obviously too heavy
You might consider 30 mg = .03 kg (still quite heavy)
KE = 1/2 * .03 kg * 40000 m.s^2 = 600 J more realistic
Force f acts between two charges, q1 and q2, separated by a distance d. if q1 is increased to twice its original value and the distance between the charges is also doubled, what is the new force acting between the charges in terms of f? one quarterf one halff f 2f
The new force acting between the charges in terms of f given the data from the question is half f
Coulomb's law equationF = Kq₁q₂ / r²
Where
F is the force of attraction K is the electrical constant q₁ and q₂ are two point charges r is the distance apart How to determine the initial force Charge 1 = q₁Charge 2 = q₂ Electric constant (K) = 9×10⁹ Nm²/C²Distance apart (r) = dInitial force (F₁) = f =?F = Kq₁q₂ / r²
F₁ = f = Kq₁q₂ / d²
How to determine the new force Charge 1 = 2q₁Charge 2 = q₂ Electric constant (K) = 9×10⁹ Nm²/C²Distance apart (r) = 2dNew force (F₂) =?F = Kq₁q₂ / r²
F₂ = K2q₁q₂ / (2d²
F₂ = 2Kq₁q₂ / 4d²
F₂ = Kq₁q₂ / 2d²
F₂ = ½(Kq₁q₂ / d²)
But
f = Kq₁q₂ / d²
Therefore
F₂ = ½f = half f
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Answer:
C or 1/2
Explanation:
Superkid, finally fed up with Superbully's obnoxious behaviour, hurls a 1.35 kg stone at him at 0.501 of the speed of light. How much kinetic energy do Superkid's super arm muscles give the stone
Answer:
See below
Explanation:
A lot !
KE = 1/2 m v^2
= 1/2 * 1.35 * ( .501 * 3 * 10^8)^2 =
1.5248 x 10^16 j
kinetic energy do Superkid's super arm muscles give the stone is 62.6 × 10⁶ J.
What is kinetic energy ?Kinetic energy is the energy associated with a motion of a body. When a body is in motion having mass m then it has kinetic energy. Kinetic energy is denoted by K or T. it is expressed in joules. Kinetic energy is given by,
K = 1/2 mv²
Hence an object having zero mass or zero velocity have zero kinetic energy.
In this problem the stone is moving with velocity which is comparable with the speed of light, hence we have to find relativistic kinetic energy.
The relativistic kinetic energy is given by,
[tex]K = m_{0} c^2(\frac{1}{\sqrt{1-\frac{v^2}{c^2}} } -1)[/tex]
putting all the values in the equation
[tex]K = 1.35*3*10^8(\frac{1}{\sqrt{1-\frac{(0.5c)^2}{c^2} } }-1 )[/tex]
K = 62.6 × 10⁶ J
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