Answer:
4 I
Explanation:
The initial resistance of the wire is given by:
[tex]R=\frac{\rho L}{A}[/tex]
where
[tex]\rho[/tex] is the resistivity of the material
L is the length of the wire
A is the cross-sectional area of the wire
Since the resistance is proportional to the length of the wire, when the wire is cut in half, each wire will have half of the initial resistance:
[tex]R' = \frac{\rho \frac{L}{2}}{A}=\frac{R}{2}[/tex]
Later, these two pieces of wire are connected in parallel to the battery (because the right ends of both wires are attached to one terminal, while the left ends are attached to the other terminal, so they are connected in parallel). Therefore, their total resistance will be:
[tex]\frac{1}{R_T} = \frac{1}{R_1}+\frac{1}{R_2}=\frac{1}{R/2}+\frac{1}{R/2}=\frac{2}{R}+\frac{2}{R}=\frac{4}{R}\\R_T = \frac{R}{4}[/tex]
so the total resistance of the circuit will be 1/4 of the initial resistance.
The initial current in the circuit was given by Ohm's law:
[tex]I=\frac{V}{R}[/tex]
Since the voltage V has not changed, the new resistance will be
[tex]I' = \frac{V}{R_T}=\frac{V}{R/4}=4 \frac{V}{R}=4I[/tex]
so, the current will increase by a factor 4.
When the length of the wire is halved and connected in parallel, then the current increases four times the initial current.
What is Ohm's law?Ohm's law states that when there is no physical change in the conductor, the potential difference is directly proportional to the current flowing in it.
V = RI
V be the potential difference
I be the current.
R be the resistance of the circuit.
A resistor is made out of a wire having a length of L.
When the ends of the wire are attached across the terminals of an ideal battery having a constant voltage V₀ across its terminals, a current I flows through the wire.
We know that the resistance is given by
[tex]\rm R = \dfrac{\rho L}{A}[/tex]
where L is the length, A is the area, and ρ is the resistivity of the conductor.
If the wire were cut in half, making two wires of length L/2, and both wires were attached across the terminals of the battery. Then we have
[tex]\rm R '= \dfrac{\rho \frac{L}{2}}{A} = \dfrac{R}{2}[/tex]
These two wires are in parallel. Then we have
[tex]\rm \dfrac{1}{R_{eq}} = \dfrac{1}{R_1}+\dfrac{1}{R_1}\\\\\\\dfrac{1}{R_{eq}} = \dfrac{1}{\frac{R}{2}}+\dfrac{1}{\frac{R}{2}}\\\\\\R_{eq } \ = \dfrac{R}{4}[/tex]
Then the current will be given by Ohm's law
[tex]\rm I' = \dfrac{V}{R_{eq}}\\\\\\I' = \dfrac{V}{\frac{R}{4}} \\\\\\I' = 4 \dfrac{V}{R} \\\\\\ I ' = 4 \ I[/tex]
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The full range of wavelengths of em waves is called the
Answer:
Electromagnetic Spectrum
Explanation:
The is the the distance between two crests or two troughs on a transverse wave. It is also the distance between compressions or the distance between rarefactions on a longitudinal wave.
Answer:
Wavelength
Explanation:
The wavelength of a transverse wave (where the oscillation occurs perpendicular to the direction of propagation of the wave) is defined as the distance between two consecutive crests ot two consecutive troughs.
In a longitudinal wave, where the oscillation occurs parallel to the direction of propagation of the wave, the wavelength is defined as the distance between two consecutive compressions or between two consecutive rarefactions.
Other important definitions for a wave are:
- Frequency: the number of complete cycles per second
- Period: the time needed for one complete cycle to occur
- Amplitude: the distance between the equilibrium position and the maximum displacement of the wave
Answer:
wavelength
Explanation:
The part of the electromagnetic spectrum that has the longest wavelengths is .
Answer:
Radio waves
Explanation:
An electromagnetic spectrum is an arrangement of electromagnetic waves in order of increasing frequency and decreasing wavelengths.The spectrum ranges from gamma rays which have the highest frequency and the shortest wavelength to radio waves which have the longest wavelength and the lowest frequency and energy.Other electromagnetic waves in the spectrum are, microwaves, infrared, Visible light, ultra-violet radiation and X-rays.Answer:
radio waves
Explanation:
PLEASE HELP ASAP! THANKS!
Why is it a rare occasion to see a solar eclipse from your home?
Answer:
It is very rare to see a solar eclipse from your home, because the Earth, Sun, and the moon need to align just right. Not everyone in the world can view a solar eclipse, only some area can. A solar eclipse is where the moon blocks out the sun. If you think about it: Let's say you live in Florida, U.S.A. You may see the moon coming in front of the sun, but if you lived in California or sumthin', the moon and the sun wouldn't be aligned to form a solar eclipse. It all depends on location... so it is rare to see one.
A ray in glass arrives at the glass-water interface at an angle of 48° with the normal. The refracted ray, in water, makes a 72° angle with the normal. The index of refraction of water is 1.33. Then the ray in glass is redirected so its new angle of incidence is 37°. What is the new angle of refraction in the water? Show all work.
Answer:
50.4°
Explanation:
Snell's law states:
n₁ sin θ₁ = n₂ sin θ₂
where n is the index of refraction and θ is the angle of incidence (relative to the normal).
When θ₁ = 48°:
n sin 48° = 1.33 sin 72°
n = 1.702
When θ₁ = 37°:
1.702 sin 37° = 1.33 sin θ
θ = 50.4°
The new angle of refraction in the water is [tex]50.35^{\circ}[/tex].
Given data:
The angle made by ray at glass-water interface is, [tex]\theta _{1} = 48^{\circ}[/tex].
The angle made by the refracted ray with the normal is, [tex]\theta_{2} = 72^{\circ}[/tex].
The index of refraction of water is, [tex]n=1.33[/tex].
The angle of incidence for the redirected glass is, [tex]\theta_{3} = 37^{\circ}[/tex].
The entire problem is based on the concepts of Snell's law, which says that the ratio of sine of angle of incidence to sine of angle of refraction is equal to the ratio of refractive index and incident index.
So on applying the Snell's law as,
[tex]n' \times sin \theta_{1} = n \times sin \theta_{2}[/tex]
Here, n' is the index of refraction of glass.
Solving as,
[tex]n' \times sin 48 = 1.33 \times sin 72\\\\n' = \dfrac{ 1.33 \times sin 72}{sin 48} \\\\n' =1.702[/tex]
For redirected condition, again apply the Snell' law as,
[tex]n' \times sin \theta_{3} = n \times sin \theta_{4}[/tex]
Here, [tex]\theta_{4}[/tex] is the new angle of refraction in the water.
Solving as,
[tex]1.702 \times sin 37 = 1.33 \times sin \theta_{4}\\\\sin \theta_{4} = \dfrac{1.702 \times sin 37}{1.33} \\\\\theta_{4} =sin^{-1}(0.770)\\\\\theta_{4} =50.35^{\circ}[/tex]
Thus, we can conclude that the new angle of refraction in the water is [tex]50.35^{\circ}[/tex].
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The material through which a mechanical wave travels is
The medium is the main factor that differentiates a mechanical wave from an electromagnetic wave, since the first can not propagate without its existence, while the second can propagate regardless of whether the medium exists or not.
In addition, it is the medium that will define, the propagation speed of the wave, according to its specific physical characteristics.
How does the kinetic energy of particles vary as a function of temperature?
Answer:
It is directly proportional
Explanation:
For an ideal gas, the average kinetic energy of the particles and the temperature (in Kelvin) are directly proportional, according to the equation:
[tex]E_K = \frac{n}{2}kT[/tex]
where
Ek is the average kinetic energy
k is the Boltzmann constant
T is the absolute temperature
n is the number of degrees of freedom of the molecules in the gas (n=3 for monoatomic gases, n=5 for di-atomic gases, etc..)
Therefore, as the temperature of a gas increases, the average kinetic energy of the molecules increases proportionaly to it.
The temperature of a substance is proportional to the average kinetic energy of its particles, and as temperature increases, particles move faster, resulting in a wider range of kinetic energies, and the entropy of the substance increases.
Explanation:Understanding Kinetic Energy and Temperature
Kinetic energy is the energy that particles have due to their motion. According to the kinetic-molecular theory, the temperature of a substance is directly proportional to the average kinetic energy of its particles. As the temperature increases, particles move faster, resulting in greater kinetic energy. The Boltzmann distribution illustrates that at higher temperatures, not only is the average kinetic energy higher, but the range of kinetic energies also becomes broader, indicating a larger distribution of speeds among the particles. In other words, there are more particles with energies significantly higher or lower than the average.
At absolute zero, the theoretical temperature where all kinetic motion ceases, particles would have no kinetic energy. However, in reality, substances increase their temperature by absorbing energy, which then increases the motion of their constituent particles. As a result, the energy of the particles in a substance can be simply related to the temperature of the substance using the equation E ≅ kT, where 'E' represents the typical kinetic energy of the particles and 'T' is the temperature in kelvins. The constant 'k' is Boltzmann's constant.
With an increase in temperature, solids will have more extensive vibrations, liquids will have more rapid translations, and gases will have faster-moving particles. This increase in energy transfer among particles results in a greater distribution of kinetic energies and also affects the entropy of the substance, which increases with temperature. A visual representation of the different average kinetic energies for particles at two temperatures can be seen in energy distribution curves where a flatter curve corresponds to a higher temperature.
The material through which a mechanical wave travels is
A mechanical wave is a disturbance in matter that transfers energy through the matter.
Mechanical waves require a medium to travel through, such as a solid, liquid, or gas.
Explanation:Mechanical waves require a medium through which they can travel. The medium can be a solid, liquid, or gas. Examples of mechanical waves include water waves, sound waves, and seismic waves.
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Jackson and Mia want to do an experiment to determine how the temperature of water affects how much salt can be dissolved in it
In what order should they perform the following steps?
Step 1: Bring the water in one of the beakers to the boiling point.
Step 2: Pour equal amounts of water into two identical beakers.
Step 3: Record how many half-teaspoons of salt are completely dissolved in each beaker
Step 4: Gradually put salt into the water of each beaker, a half-teaspoon at a time.
Answer:
First- step 2
Second- step 1
Third- step 4
Fourth- step 3
Explanation:
You need to first make sure you have water or you can’t do any dissolving. Then you need boil it or nothings going to happen to the salt. And then you you can do the fourth step without doing the dissolving first hope this helped :)
An experiment is to determine how the temperature of water affects how much salt can be dissolved in it must be carried out in the correct sequence of steps.
In this experiment, the dependent variable is the amount of salt dissolved in the water, the independent variable is the temperature of the water. The correct sequence of steps in which the experiment should be carried out is;
Step 1: Pour equal amounts of water into two identical beakers. Step 2: Gradually put salt into the water of each beaker, a half-teaspoon at a time.Step 3: Record how many half-teaspoons of salt are completely dissolved in each beaker Step 4: Bring the water in one of the beakers to the boiling point.Above are outlined the correct sequence of steps to carry out the experiment.
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When did robert fulton invent the steamboat
Answer:
1807
Explanation:
Robert Fulton (1765–1815) was an American engineer and inventor who is widely known for developing a commercially successful steamboat called Clermont. In 1807, that steamboat took passengers from New York City to Albany and back again, a round trip of 300 miles, in 62 hours.
Robert Fulton invented the steamboat engine in 1807, significantly improving water transportation with the Clermont on the Hudson River, and facilitating economic growth and western settlement.
Explanation:Robert Fulton invented the steamboat engine which was utilized in his first successful commercial steamboat, the Clermont, in 1807. Operating on the Hudson River, the Clermont was influential in transforming water transportation by allowing more reliable and quicker travel independent of wind. It traveled from New York City to Albany in a mere 32 hours. Fulton's innovation prompted widespread economic development, particularly in the Mississippi River Valley, and revolutionized the settlement of the West. By the 1830s, over a thousand steamboats were in operation. Yet, steamboats were prone to dangers such as boiler explosions, which eventually led to safety regulations.
The force of gravity between two objects: The force of gravity between two objects: depends on the density, not the mass of the bodies. depends on the temperature, density, and size of the bodies. increases with the masses of the bodies, but decreases with their separations. increases with the square of their masses, but decreases with the cube of their periods of orbit about the Sun. increases with the masses of the bodies, but decreases with the square of the distances between them.
According to Newton's law of Gravitation, the force [tex]F[/tex] exerted between two bodies or objects of masses [tex]m1[/tex] and [tex]m2[/tex] and separated by a distance [tex]r[/tex] is equal to the product of their masses divided by the square of the distance:
[tex]F=G\frac{(m1)(m2)}{r^2}[/tex]
Where [tex]G[/tex]is the gravitational constant.
As we can see, this force is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.
This means that the gravity force decreases when the distance between these two bodies increases, and increases when the masses of the bodies increases.
The force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of their separation distance. It is significant with large masses or small separations and is fundamental in celestial mechanics, imparting weight and affecting planetary and satellite motions.
Explanation:The force of gravity between two objects depends on certain factors. Newton's Universal Law of Gravitation states that this force is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Consequently, as the masses of the two objects increase, the gravitational force between them also increases. Conversely, as the distance between the two objects increases, the gravitational force they exert on each other decreases with the square of that separation distance. This is a fundamental principle in understanding celestial mechanics and the behavior of objects under the influence of gravity.
It is also important to note that gravitational force is a relatively weak force compared to other forces in nature, such as electromagnetic forces, and it becomes significant only when involving objects with large masses or when objects are very close to each other. The force of gravity is what imparts weight to objects with mass and it plays a crucial role in the movements of planets, comets, and satellites within our solar system.
Planet with a density so low that it could float on water
Answer:
(Saturn ) is the homogeneous mixture
The amount of force exerted on an object due to gravity. true or false
Answer:
True
Explanation:
Is there ever a situation where an ant will have more momentum than an elephant? Explain why or why not?
Answer:
Yes
Explanation:
The momentum of an object is given by:
[tex]p=mv[/tex]
where
m is the mass of the object
v is the velocity of the object
We know that an elephant has a mass much larger than the mass of an ant. However, we see that the momentum of the animal also depends on its velocity.
If the elephant is at rest, its velocity is zero:
v = 0
so its momentum is also zero:
p = 0
And therefore, an ant which is moving (so, non-zero speed) can have more momentum than an elephant, if the elephant is at rest.
Please help on this one?
Which two processes can generate energy to help a star or gas cloud maintain its internal thermal pressure?
A star is born when the material of a nebula collapses due to the gravitational force of its elements. Converting this later into the nucleus of the new star, composed of hydrogen.
Then, when this nucleus has reached sufficiently high density and temperature, it becomes helium by means of nuclear fusion (union of two light atoms), releasing energy in the process, which is the cause of the great luminosity of the star.
In other words, stars generate their own energy, in a process in which there is a balance between the gravitational pressure that compresses (contracts) matter and raises its temperature sufficiently for nuclear reactions to start, generating pressure in the opposite direction to the gravitational force by the heat produced in the reaction.
So, these nuclear reactions expand the star for most of its life, as long as this equilibrium exists.
A parallel-plate capacitor is formed from two 1.0 cm times 1.0 cm electrodes spaced 2.9 mm apart. The electric field strength inside the capacitor is 1.0 times10^{6} N/C. What is the charge (in nC) on positive electrode?
Answer:
0.89 nC
Explanation:
The strength of the electric field inside a parallel plate capacitor is given by
[tex]E=\frac{Q}{A \epsilon_0}[/tex] (1)
where
Q is the charge stored on one plate
A is the area of one plate
[tex]\epsilon_0[/tex] is the vacuum permittivity
For this problem, we have
[tex]E=1.0\cdot 10^6 N/C[/tex] is the electric field strength
the area of one plate is
[tex]A=1.0 cm\cdot 1.0 cm=(0.01 m)(0.01 m)=1\cdot 10^{-4} m^2[/tex]
Solving the formula (1) for Q, we find the charge on the positive electrode:
[tex]Q=EA\epsilon_0=(1.0\cdot 10^6 N/C)(1\cdot 10^{-4} m^2)(8.85\cdot 10^{-12} F/m)=8.85\cdot 10^{-10}C=0.89 nC[/tex]
Electric field exerts a force on all charged particles. The charge on the positive electrode is 8.854 x 10⁶ C.
What is an electric field?An electric field can be thought to be a physical field that surrounds all the charged particles and exerts a force on all of them.
Given to us
Plate dimensions = 1.0 cm times 1.0 cm
Area of the plate = 0.0001 m²
Distance between the two plates, d = 2.9 mm = 0.0029 m
Electric field strength, [tex]\overrightarrow E[/tex] = 1.0 x 10⁶ N/C
We know that electric field inside a parallel plate capacitor is given as,
[tex]E = \dfrac{Q}{A\epsilon_0}[/tex]
Substitute the value,
[tex]1 \times 10^6 = \dfrac{Q}{0.0001\times 8.854 \times 10^{-12}}\\\\Q = 8.854 \times 10^{-10} \rm\ C[/tex]
Hence, the charge on the positive electrode is 8.854 x 10⁶ C.
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Are light waves longitudinal or transverse
Answer:
Transverse
Explanation:
There are two types of waves, according to the direction of their oscillation:
- Transverse waves: in a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. Examples of transverse waves are electromagnetic waves
- Longitudinal waves: in a longitudinal wave, the direction of the oscillation is parallel to the direction of motion of the wave. Examples of longitudinal waves are sound waves.
Light waves corresponds to the visible part of the electromagnetic spectrum, which includes all the different types of electromagnetic waves (which consist of oscillations of electric and magnetic fields that are perpendicular to the direction of propagation of the wave): therefore, they are transverse waves.
What is the value of x in the equation below 1+2e^x+1=9
Explanation:
We are given this equation and we need to find the value of [tex]x[/tex]:
[tex]1+2e^x+1=9[/tex] (1)
Firstly, we have to clear [tex]x[/tex]:
[tex]2e^x=9-1-1[/tex]
[tex]2e^x=7[/tex]
[tex]e^x=\frac{7}{2}[/tex] (2)
Applying Natural Logarithm on both sides of the equation (2):
[tex]ln(e^x)=ln(\frac{7}{2})[/tex] (3)
[tex]xln(e)=ln(\frac{7}{2})[/tex] (4)
According to the Natural Logarithm rules [tex]xln(e)=x[/tex], so (4) can be written as:
[tex]x=ln(\frac{7}{2})[/tex] (5)
Finally:
[tex]x=1.252[/tex]
How much larger is the earth in diameter than the moon
5,758.5 miles or thr moon is a quarter of the diameter of the earth
The Earth's diameter is 5,758.5 miles larger than the diameter of the moon.
Explanation:The diameter of the Earth is approximately 7,917.5 miles, while the diameter of the moon is about 2,159 miles. Therefore, we can determine how much larger the Earth is in diameter than the moon by subtracting the diameter of the moon from the Earth's diameter.
So, 7,917.5 miles (diameter of Earth) - 2,159 miles (moon’s diameter) = 5,758.5 miles.
Therefore, the Earth's diameter is 5,758.5 miles larger than the diameter of the moon.
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PLEASE HELP SOMEONE!!! An object is located 5.0 cm from a convex lens. The lens focuses light at a distance of 10.0 cm. What is the image distance? Use the equation attached.
A.-10.0 Cm
B.10.0
C.3.33Cm
D.-3.33Cm
Answer:
-10.0 cm
Explanation:
OK so in the equation they're having you use the variables are:
[tex]d_o = 5.0 cm\\\\f = 10.0 cm\\\\d_i = ?[/tex]
So we simply plug in the variables:
[tex]d_i = \frac{d_of}{d_o-f} \\\\d_i = \frac{5.0 * 10.0}{5.0 - 10.0}\\\\d_i = \frac{50}{-5}\\\\d_i = -10.0 cm[/tex]
help fast
at 8:00 am you leave home and walk 0.5 km to a friends house at 11:30 am u return home then travel by car to the mall which is 10km away and arrive at 11:45 am what is the total distance
A)2.8 km/h
B)10km
C)10.5km
D)11km
Answer: 11 Km
Explanation: You walk 0.5 to the friends and 0.5 back. This adds up to 1. Then you drive 10 Km to the mall. When you add 1 and 10 you get 11! Hope this helps!
(PLEASE HELP! Will give Brainliest Answer)
The coaster below starts from rest at point A.
It has a mass of 872 kg. There is no friction or air resistance.
Point A is 50 meters above ground. Point B is 20 meters above ground.
Calculate the speed of the coaster at point B.
A) 24 m/s
B) 50 m/s
C) 20 m/s
Answer:
B
Explanation:
872 / 20 = 43
Two waves meet and interfere
constructively. Which one of the following
factors increases?
a. period
b. amplitude
c. frequency
d. wavelength
Answer:
b. amplitude
Explanation:
There are two types of intereference:
- Constructive interference: it occurs when two waves of same frequency meet at a point in phase - this means , the crest of one wave meets with the crest of the other wave. When this occurs, the resultant wave has an amplitude which is equal to the sum of the amplitudes of the two waves.
- Destructive interference: it occurs when two waves of same frequency meet at a point in opposite phase - this means , the crest of one wave meets with the trough of the other wave. When this occurs, the resultant wave has an amplitude which is equal to the difference between the amplitudes of the two waves.
When interference occurs, the other factors of the waves (period, frequency and wavelength) do not change.
In constructive interference, the factor that increases is the amplitude of the resulting wave. The amplitudes of the individual waves combine to produce a wave with greater amplitude, while the period, frequency, and wavelength remain unchanged.
Explanation:When two waves meet and interfere constructively, the factor that increases is the amplitude of the resulting wave. Constructive interference occurs when waves are in phase and their crests (and troughs) align. The amplitudes of the individual waves add together, resulting in a wave with a greater amplitude. This is shown in various figures such as FIGURE 16.33 and FIGURE 27.11 in your provided references, which illustrate pure constructive interference producing a wave with twice the amplitude, but the same wavelength.
It is important to note that the period, frequency, and wavelength of a wave are not directly affected by interference. The period and frequency are inversely related, so when the period of a wave increases, its frequency decreases. However, this question refers to the effects of interference, not changes in the wave's frequency or period.
The relation between amplitude and frequency of a wave is that they are generally independent of each other; an increase in amplitude does not necessarily cause a change in frequency, and vice versa.
A circuit has a 20-ohm resistor, and a current of 2 amps flows through it. What must be the battery voltage?
The battery voltage in this circuit with a 20-ohm resistor and a current of 2 amps is 40 volts.
Explanation:In order to find the battery voltage, we can use Ohm's Law, which states that voltage (V) is equal to current (I) multiplied by resistance (R). In this case, the resistance is 20 ohms and the current is 2 amps. Using the formula V = IR, we can calculate the battery voltage as follows:
V = 2A * 20Ω = 40V
How do the nuclei of different isotopes of an element vary?
Because isotopes of an element have a different number of neutrons, they also have different mass numbers.
Why is wind energy considered clean energy?
Answer:Wind power is a clean energy source that we can rely on for the long-term future. A wind turbine creates reliable, cost-effective, pollution free energy. ... Because wind is a source of energy which is non-polluting and renewable, the turbines create power without using fossil fuels.
The name for minimum energy expended to keep a resting
i think it's Basel Metabolism
A figure skater rotating at 5.00 rad/s with arms extended has a moment of inertia of 2.25 kg·m2. If the arms are pulled in so the moment of inertia decreases to 1.80 kg·m2
What is:
a) The final angular speed?
b) The initial and final kinetic energy?
a) 6.25 rad/s
The law of conservation of angular momentum states that the angular momentum must be conserved.
The angular momentum is given by:
[tex]L=I\omega[/tex]
where
I is the moment of inertia
[tex]\omega[/tex] is the angular speed
Since the angular momentum must be conserved, we can write
[tex]L_1 = L_2\\I_1 \omega_1 = I_2 \omega_2[/tex]
where we have
[tex]I_1 = 2.25 kg m^2[/tex] is the initial moment of inertia
[tex]\omega_1 = 5.00 rad/s[/tex] is the initial angular speed
[tex]I_2 = 2.25 kg m^2[/tex] is the final moment of inertia
[tex]\omega_2[/tex] is the final angular speed
Solving for [tex]\omega_2[/tex], we find
[tex]\omega_2 = \frac{I_1 \omega_1}{I_2}=\frac{(2.25 kg m^2)(5.00 rad/s)}{1.80 kg m^2}=6.25 rad/s[/tex]
b) 28.1 J and 35.2 J
The rotational kinetic energy is given by
[tex]K=\frac{1}{2}I\omega^2[/tex]
where
I is the moment of inertia
[tex]\omega[/tex] is the angular speed
Applying the formula, we have:
- Initial kinetic energy:
[tex]K=\frac{1}{2}(2.25 kg m^2)(5.00 rad/s)^2=28.1 J[/tex]
- Final kinetic energy:
[tex]K=\frac{1}{2}(1.80 kg m^2)(6.25 rad/s)^2=35.2 J[/tex]
To find the final angular speed, we can apply the conservation of angular momentum. The initial and final kinetic energies can be calculated using a formula involving the moment of inertia and angular velocity.
Explanation:To solve this problem, we can apply the principle of conservation of angular momentum. When the figure skater pulls in her arms, her moment of inertia decreases, causing her angular velocity to increase according to the equation:
Ii * ωi = If * ωf
where Ii and If are the initial and final moments of inertia, and ωi and ωf are the initial and final angular velocities, respectively.
a) Plugging in the given values:
2.25 kg·m2 * 5.00 rad/s = 1.80 kg·m2 * (ωf)
Solving for ωf, we find that the final angular speed is 6.25 rad/s.
b) To calculate the initial and final kinetic energies, we can use the equation:
K.E. = (1/2) * I * ω2
Substituting the values into the equation:
Initial K.E. = (1/2) * 2.25 kg·m2 * (5.00 rad/s)2
Final K.E. = (1/2) * 1.80 kg·m2 * (6.25 rad/s)2
Calculating, we find that the initial kinetic energy is 28.125 J and the final kinetic energy is 42.19 J.
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please help on this one?