Final answer:
The velocity at which the softball must be moving to equal the momentum of the baseball is 12.30 m/s.
Explanation:
To find the velocity at which the 0.53 kg softball must be moving to equal the momentum of the 0.31 kg baseball, we can use the equation for momentum:
Momentum = mass × velocity
First, let's find the momentum of the baseball:
Momentum of baseball = 0.31 kg × 21 m/s = 6.51 kg·m/s
Now, we can set the momentum of the softball equal to the momentum of the baseball and solve for its velocity:
Momentum of softball = 6.51 kg·m/s
0.53 kg × velocity = 6.51 kg·m/s
velocity = 6.51 kg·m/s / 0.53 kg = 12.30 m/s
Therefore, the softball must be moving at a velocity of 12.30 m/s to equal the momentum of the baseball.
1)
Car A has a mass of 1,000 kg and is traveling 60 km/hr. Car B has a mass of 2,000 kg and is traveling 30 km/hr. Compare the kinetic energy of car A with that of car B?
A) equal
B) half as much
C) twice as much
D) four times as much
Answer: C
Explanation:
Calculate EkA -kinetic energy of car A
m=1000kg
Va=16.66 m/s
EkA=m*Va²/2
Eka=(1000kg*277.556m²/s²)/2
Eka=138 777.8 J
Calculate kinetic energy of CarB:
m=2000 kg
Vb=8.33 m/s
Ekb=(m*Vb²)/2
Ekb=(2000kg*69.39m²/s²)/2
Ekb=69 388.9 J
compare Eka with EkB
Eka/Ekb=138 777.8 J/69 388.9
Eka/Ekb=2
The kinetic energy of car A is twice as much as that of car B. This is calculated using the formula for kinetic energy, which is 1/2 * mass * (velocity)^2.
Explanation:To compare the kinetic energy of car A with that of car B, we first need to understand the mathematical formula for kinetic energy, which is 1/2 * mass * (velocity)^2.
Let's calculate for each car:
For car A: kinetic energy = 1/2 * 1000 kg * (60 km/hr)^2 = 1800000 Joules For car B: kinetic energy = 1/2 * 2000 kg * (30 km/hr)^2 = 900000 Joules
Therefore, car A has twice as much kinetic energy as car B.
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Which type of solar radiation is the most powerful?
radio waves
microwaves
gamma rays
X-rays
Answer: Gamma rays
Explanation:
Answer:
Gamma rays are the most powerful
Gamma rays are not necessarily harmful to the planet Earth, but to all the living organisms that inhabit it, as Gamma is a powerful form of radiation.Gamma-rays are produced primarily by four different nuclear reactions: fusion, fission, alpha decay and gamma decayGAMMA RAYS
Gamma-rays are a form of electromagnetic radiation, as are radio waves, infrared radiation, ultraviolet radiation, X-rays and microwaves. Gamma-rays can be used to treat cancer, and gamma-ray bursts are studied by astronomers.
Electromagnetic (EM) radiation is transmitted in waves or particles at different wavelengths and frequencies. This broad range of wavelengths is known as the electromagnetic spectrum. The spectrum is generally divided into seven regions in order of decreasing wavelength and increasing energy and frequency. The common designations are radio waves, microwaves, infrared (IR), visible light, ultraviolet (UV), X-rays and gamma-rays.
Gamma-rays fall in the range of the EM spectrum above soft X-rays. Gamma-rays have frequencies greater than about 1,018 cycles per second, or hertz (Hz), and wavelengths of less than 100 picometers (pm), or 4 x 10^9 inches. (A picometer is one-trillionth of a meter.)
Gamma-rays and hard X-rays overlap in the EM spectrum, which can make it hard to differentiate them. In some fields, such as astrophysics, an arbitrary line is drawn in the spectrum where rays above a certain wavelength are classified as X-rays and rays with shorter wavelengths are classified as gamma-rays. Both gamma-rays and X-rays have enough energy to cause damage to living tissue, but almost all cosmic gamma-rays are blocked by Earth's atmosphere.
What happens to a falling object when the force of air resistance equals the force of gravity?
Answer:
A falling object will continue to accelerate to higher speeds until they encounter an amount of air resistance that is equal to their weight.
Explanation:
Answer:
so its basically termonal velocity
Explanation:
Layers of Earth's Atmosphere
First place the names of the atmospheric layers in their correct positions, then add the other labels in the appropriate layer.
Choices
Almost no molecules
Exosphere
Tropsphere
Contains Life Forms
Mesosphere
very low temps
contains ozone layer
stratosphere
where asteroids burn up
contains weather
themosphere
widely varying temps
Answer:
going to work my way down
Troposphere
contains weather
contains life forms
stratosphere
contains ozone layer
mesosphere
where asteroids burn up
very low temps
thermosphere
widely varying temps
exosphere
almost no molecules
Explanation:
Answer:
Hope this helps!!
Which of the following has the lowest density ? A.mineral water b. Water c. Oxygen d. Salt water
Answer:
c
Explanation:
Mineral water, water, and salt water are all liquid solutions, while oxygen is a gas. Gases are less dense than liquids.
Both images were taken by a space telescope orbiting Earth. What do these images indicate?
A.
Ultraviolet light is more important than visible light in providing all information about the universe.
B.
Visible light is more important than ultraviolet light when attempting to detect changes in hotter stars.
C.
Different kinds of electromagnetic radiation can be used to detect various types of stars.
D.
Different kinds of electromagnetic radiation reach different parts of the Earth.
These images indicate that different kinds of electromagnetic radiation can be used to detect various types of stars. (C)
Choices 'A' and 'B' are absurd. "Important" is a wishy-washy, rubber word. It means different things to different people, and it can even mean different things to the same astronomer at different times, depending on what he's trying to see at that moment.
Consider the roller coaster on the track. If you want to increase the kinetic energy of the roller coaster as it proceeds through the course, what is the FIRST thing you should do?
A) Increase the height at point A.
B) Decrease the height at point A.
C) Increase the height at point B.
D) Decrease the height at point B.
Answer:
The answer is A and D but if you want one anwer i think the anwer is A
Explanation:
Increase the height at point A will increase the kinetic energy of the roller coaster. Option A is correct.
What is kinetic energy?The energy of the body by the virtue of its motion is known as the kinetic energy of the body. It is defined as the product of half of mass and square of the velocity.
According to the law of conservation of energy, the total energy is defined as the sum of kinetic energy and potential energy.
Total energy = kinetic energy+energy+potential energy
Also, the energy can not be created nor be destroyed can be transferred from one form to another form.
Work = Force × distance
Kinetic energy = work = weight × height traveled
Increase the height at point A will increase the kinetic energy of the roller coaster.
Hence, option A is correct.
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A child pushes a toy car down a hill. The child has a mass of 20 kg. The car has a mass of 1.6 kg and a speed of 7.4 m/s2. When the car has a gravitational potential energy of 30 J, what is the mechanical energy of the car?
Answer:
The answer is 73.8 J
Explanation:
6. What are 3 different evidences of evolution? How is each form used to provide evidence of evolution?
Answer:
Divergent - This type of evolution often occurs when closely related species diversify to new habitats. On a large scale, divergent evolution is responsible for the creation of the current diversity of life on earth from the first living cells. On a smaller scale, it is responsible for the evolution of humans and apes from a common primate ancestor.
Convergent - Convergent evolution causes difficulties in fields of study such as comparative anatomy. Convergent evolution takes place when species of different ancestry begin to share analogous traits because of a shared environment or other selection pressure. For example, whales and fish have some similar characteristics since both had to evolve methods of moving through the same medium: water.
Parallel evolution - Parallel evolution occurs when two species evolve independently of each other, maintaining the same level of similarity. Parallel evolution usually occurs between unrelated species that do not occupy the same or similar niches in a given habitat.
Final answer:
Evidence of biological evolution includes fossil evidence which shows changes in species over time, molecular evidence demonstrating evolutionary relationships through DNA comparisons, and homologous and vestigial structures that indicate common ancestry and the modification of species.
Explanation:
There are multiple lines of evidence that help support the theory of biological evolution. Here are three distinct forms of evidence:
Fossil Evidence: Fossils offer direct evidence of past life forms and their evolution over time. Through the study of fossils, scientists can trace the development of species, observing gradual changes in the morphology of organisms over geological time scales. This is seen in the fossil record of the horse, which shows a series of species each with slight modifications leading to the modern horse.Molecular Evidence: The comparison of DNA and protein sequences among different organisms reveals similarities and differences that reflect their evolutionary relationships. These molecular similarities can be used to construct phylogenetic trees that demonstrate how species are related through common ancestry.Homologous and Vestigial Structures: Homologous structures are body parts in different species that share a common ancestral origin, whereas vestigial structures are body parts that have lost their original function through evolution. These structures provide evidence for common ancestry and evolutionary change.Each form of evidence is used in conjunction with others to paint a comprehensive picture of life's history on Earth, and how organisms have changed and diversified over time
The force of gravity on Mars is 0.38 times the gravity on Earth. The mass of an
object on Earth is 71 kg.
What are the mass and weight of that object on Mars?
A. mass: 71 kg, weight: 710 N
B. mass: 71 kg, weight: 270 N
C. mass: 27 kg, weight: 270 N
D. mass: 27 kg, weight: 103 N
Answer:
the answer is B
Explanation:
because the mass of any object is constant anywhere so the mass of the object on earth =the mass of the object on mars or any other planet=71kgwhile the weight=massxgravity since the gravity on earth=10m/s^2 and the gravity on mars =0.38x10=3.8m/s^2then the weight =71x3.8=269.8"approximately270N"The mass and weight of that object on Mars is .The correct option is
B.
What is force of gravity?The object experiencing an attraction force towards the another body when placed still on any planet.
The mass of an object is constant on any planet.
Mass of the object on earth = mass of the object on mars = 71kg
The weight is the product of the mass and its acceleration due to gravity.
W=m x g
The acceleration due to gravity on Earth is 10m/s², then the acceleration due to gravity on Mars is
0.38 x 10 = 3.8m/s²
The weight of that object on Mars is
W =71 x 3.8
W = 269.8 Newtons
The weight is approximately 270 N.
Thus, The mass and weight of that object on Mars is 71 kg and 270 N. The correct option is B.
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What did Thomson’s model of the atom include that Dalton’s model did not have?
a nucleus
energy levels
electron clouds
smaller particles
Answer: Option (d) is the correct answer.
Explanation:
Dalton's model of atom states that every matter is made up of atoms and these atoms are indivisible in nature.
On the other hand, Thomson's model of atom states that there are small particles present in an atom that has positive or negative charges.
Thomson's model of atom is also known as plum pudding model where negatively charged particles are represented by plum and positively charged particles are represented by pudding.
Thus, we can conclude that Thomson’s model of the atom include smaller particles that Dalton’s model did not have.
Answer:
smaller particles....(D)
Explanation:
hope this helps
A ray diagram is shown.
Which letter represents the location of the image produced by the lens?
W
X
Y
Z
Answer:
Z
Explanation:
The figure represented the ray diagrams produced by a convex (converging lens). The image will appear at the point where the purple ray and the orange ray meet, so at point Z.
As we see from the picture, the image will be:
- Real (because it is behind the lens, and it can be projected on a screen)
- Inverted (the image is upside down)
- Larger than the object (we can see it by noticing that the distance between the point of intersection purple-orange ray and the axis is larger than the size of the object)
Answer:
Its X
Explanation:
Speed that does not change is referred to as ____________________ speed.
Answer:
Constant speed.
Explanation:
Because when the speed of an object remains the same - it does not increase or decrease - we say it is moving at a constant speed.
Hope I helped :)
Final answer:
Speed that does not change is referred to as constant speed or uniform speed. It is a scalar quantity, indicating magnitude only, and uniform motion involves maintaining the same velocity, including both speed and direction.
Explanation:
Speed that does not change is referred to as constant speed or uniform speed. When an object is moving at constant speed, it covers equal distances in equal intervals of time regardless of the direction of motion. Speed, being a scalar quantity, is only concerned with magnitude, not the direction of the travel.
Motion at a constant velocity, or uniform motion, means that the position of the object is changing at the same rate over time, and this typically indicates that there are no changes in speed and direction – the velocity is consistent. However, when referring specifically to speed without direction, constant or uniform speed can occur even if the direction changes.
The presence of which element would indicate that a star is going through a high-mass star life cycle as opposed to a low-mass star life cycle? hydrogen carbon helium iron
Answer:
Iron
Explanation:
In a high mass star life cycle, there are 5 stages;
Stage 1: hydrogen nuclei combines to form helium
Stage 2: Helium combines to form carbon
Stage 3: carbon used to form heavy metals such as Iron
Stage 4: Supernova explosion
Stage 5: Core of the star collapses
In light mass star life cycle, the core of the star collapses after all the helium combines to form carbon.
Answer:
D. iron
Explanation:
Find the equivalent resistance and the current in each resistor
Answer:
Equivalence resistance: 3 Ω.
Current:
12.0 A in the 1.00 Ω and the 3.00 Ω resistor;4.00 A in the 7.00 Ω and the 5.00 Ω resistor.Explanation:
Equivalent ResistanceThe 1.00 Ω resistor and the 3.00 resistor are in series. Add their resistance up to find the equivalent resistance of the upper branch:
[tex]1.00\;\Omega + 3.00 \;\Omega = 4.00\;\Omega[/tex].
Try the same steps for the lower branch. The equivalent resistance of the 7.00 Ω resistor and the 5.00 Ω resistor in series is 12.00 Ω.
The upper and lower branch are in parallel. Take the reciprocal of the resistance of each branch. Add the two reciprocals to each other. The equivalent resistance of the two branches will be the reciprocal of the sum. In other words, the equivalent resistance of resistors [tex]R_1[/tex] and [tex]R_2[/tex] in parallel will be:
[tex]\dfrac{1}{\dfrac{1}{R_1}+\dfrac{1}{R_2}}[/tex].
For the upper and lower branches in this question, the equivalent resistance will be
[tex]\dfrac{1}{\dfrac{1}{4.00}+\dfrac{1}{12.00}} = 3.00\;\Omega[/tex].
Current in each ResistorThe internal resistance of the power supply is 0. As a result, the voltage across the two parallel branches is 48.0 V, the same as the EMF. Since the two branches are connected in parallel, the voltage across both branch will be 48.0 V.
The two resistors in each branch are in series. The current that flows into each branch is the same as the charge that flows out. As a result, the current through the each resistor in a branch will be the same as the current through the entire branch. In other words,
Current in the 1.00 Ω Resistor
= Current in the 3.00 Ω Resistor
= Current in the upper branch
= [tex]\displaystyle \frac{V}{R} = \frac{48.0}{4.00} = 12.0\;\text{A}[/tex].
Try these steps to find the current in the two resistors in the lower branch:
[tex]\displaystyle I_\text{lower}=\frac{V}{R} = \frac{48.0}{12.00} = 4.00\;\text{A}[/tex].
When calculating the net electrostatic force, a negative value indicates that the two charged objects involved __________.
A. have like charges
B. have unlike charges
C. have the exact same value
D. both experience a force to the left
Answer:
B
Explanation:
The correct answer is B) have unlike charges. Since they are attracted to each other they have to be unlike
Final answer:
A negative value for net electrostatic force signifies that the two charged objects have unlike charges, which attract each other. So the correct option is B.
Explanation:
When calculating the net electrostatic force, a negative value indicates that the two charged objects involved have unlike charges. This is because Coulomb's Law states that the force exerted on one charged particle by another is directed away from the other particle if both have the same kind of charge, resulting in a positive value for the force, signifying repulsion. However, if the value of the force is negative, it implies attraction, as the force is directed toward the other particle; this occurs only when the charges are unlike (one positive and the other negative).
Using the reference information provided, it's clear that unlike charges exhibit an attractive force toward each other which would result in a negative value when calculated, as the direction of the force is opposite to that of repulsive force between like charges.
light takes 8 minutes 30 seconds to travel from sun to the earth the velocity of light with 3 million kilometres square. find the distance of Sun from the Earth
Answer:
1.53 billion kilometers
Explanation:
t = 8 min 30 s = 8×60 + 30 s = 510 s
v = 3×10⁶ km/s
d = vt
d = (3×10⁶ km/s) (510 s)
d = 1.53×10⁹ km
The distance between the surface of the sun and the surface of the earth is 1.53 billion kilometers.
A clear reflection of Mount Hood can be seen in Mirror Lake. Surfaces, such as this one, allow for specular reflection. Light can be thought of as a bundle of individual light rays which are traveling parallel to each other. Each individual light ray follows the law of reflection. If the bundle of light rays is incident upon a smooth surface, like Mirror Lake,
Answer:
All the light rays are reflected into the same direction
Explanation:
Reflection occurs when a light ray hits a surface and bounces back at a certain angle.
The law of reflection states that:
- The angle of incidence, the angle of reflection and the normal to the surface all lie in the same plane
- The angle of reflection is equal to the angle of incidence
(where the angle of incidence is the angle between the incident ray and the normal to the surface, while the angle of reflection is the angle between the reflected ray and the normal to the surface)
We have two cases:
- if the surface is completely smooth (such as the Mirror lake), then all the light rays coming from same direction have same angle of incidence, so they are reflected into the same direction, allowing to see a clear image of the object above --> in this case we talk about specular reflection
- if the surface is not 100% smooth, then the light rays coming from same direction do not hit the surface at same angle of incidence, therefore they are reflected into different directions, and it is not possible to observe a clear image of the object above --> in this case we talk about diffuse reflection
is hydrogen a gas or metal? or both?
Hydrogen is a nonmetal.
At normal room temperature, hydrogen is a gas.
Hope this helps have a noice day
MAY GOD BLESS YOU!!!
Answer:
[tex]\large \boxed{\mathrm{gas}}[/tex]
Explanation:
Hydrogen is a gas at room temperature. Hydrogen has a molecular formula of [tex]\sf H_2[/tex].
Cooper metal has a specific heat of 390 j/kg C. Calculate the amount of heat required to raise the temperature of 22.8 g of copper to 875 C
Answer:
= 7,600 Joules
Explanation:
Heat required to raise the temperature of a material is given by the formula;
Heat = mass × specific heat capacity × change in temperature.
In this case;
mass =22.8 g or 0.0228 kg
specific heat capacity = 390 J/kg°C
Temperature change = 875°C - 20°C = 855 °C
Therefore;
Heat = 0.0228 kg × 390 ×855
= 7,602.66 Joules
= 7,600 Joules
If the given wave has a frequency of 100 Hz, what frequency will the sixth harmonic have?
Answer:
600Hz
Explanation:
In electrical systems of alternating current, the harmonics are, as in acoustics, frequencies multiples of the fundamental working frequency of the system and whose amplitude decreases as the multiple increases. For example, if we have systems fed by the 50 Hz network, harmonics of 100, 150, 200, etc. may appear.
In our case having a fundamental wave of 100Hz, I can have harmonics of 200,300,400, ..., 600Hz
a waves amplitude is 0.5 meters. If the amplitude is increased to 1 metro, how does its energy change
Answer:
The energy becomes 4 times greater.
Explanation:
We know that the energy of a wave is proportional to the square of its amplitude
E ∝ Amplitude^2
Since the original amplitude = 0.5 m
and the new amplitude becomes = 1 m
We are doubling the amplitude. This means that the new energy will be affected by a factor of 4
E_new ∝ (2*Amplitude)^2 =
E_new ∝ 4*(Amplitude)^2
E_new = 4*E
True or false a magnet is never found in nature
Answer:
False.
Explanation:
Isolated magnetic poles or magnetic monopoles cannot be found in nature.
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What is magnetism please define it
Hello There!
It's a Property of matter where atoms in an object are aligned into domains
tyhe mass of an object is 117 g adding 1200j of heat will raise the temperture of the object by 12 celsius what is the specifc heat of the object A 0.35 j/g *k B 6.8 j/g *k C 0.85 j/g*k D 42 j/g*k
Answer:
C 0.85 j/g*k
Explanation:
The specific heat capacity of a material is given by:
[tex]C_s = \frac{Q}{m \Delta T}[/tex]
where
Q is the amount of heat supplied to the object
m is the mass of the object
[tex]\Delta T[/tex] is the increase in temperature of the object
For the object in this problem, we have
m = 117 g is the mass
Q = 1200 J is the heat supplied
[tex]\Delta T=12^{\circ}[/tex] is the increase in temperature
Substituting into the formula, we find the specific heat:
[tex]C_s = \frac{1200 J}{(117 g)(12^{\circ})}=0.85 J/gC[/tex]
What does stat mean
Answer:immediately
Explanation:
I think its like four words put together
what is shown in the diagram?
A: a generator
B: an electromagnet
C: A turbine
D: A motor
B i think because it makes more sense and theirs magnets i made a mistake
Answer:
Its B, and Electro Magnet
Explanation:
You can tell because there is the N and S symbols, meaning north and south on a magnet.
How much heat in kilojoules has to be removed from 225g of water to lower its temperature from 25.0oC to 10.0oC?
Answer:
14108 J
Explanation:
The heat that has to be removed from the water is given by
[tex]Q=m C_s \Delta T[/tex]
where
m = 225 g is the water mass
[tex]C_s = 4.18 J/gC[/tex] is the specific heat capacity of the water
[tex]\Delta T=10.0 C-25.0 C=-15.0 C[/tex] is the charge in temperature of the water
Substituting into the equation, we find
[tex]Q=(225 g) (4.18 J/gC) (-15.0 C)=-14,108 J[/tex]
and the negative sign means the heat is removed from the system.
assuming the earth to be uniform sphere of radius 6400km .calculate the Total energy need to raise a satellite of mass 2000kg to a height of 800km above the surface of the earth and to set it into circular orbit at that their altitude.
Answer:
6.922 × 10¹⁰ J.
Explanation:
The satellite is much smaller than the earth and can be treated as a point mass.
GPE of the SatelliteConsider the equation for the gravitational potential energy of a point mass at a certain distance away from the center of a spherical mass:
[tex]\displaystyle \text{GPE} = -\frac{G \cdot M \cdot m}{r}[/tex],
where
The gravitational constant [tex]G \approx 6.67\times 10^{-11}\;\textbf{m}^{3}\cdot \textbf{kg}^{-1}\cdot \text{s}^{-2}[/tex],[tex]M[/tex] the mass of the sphere (the earth in this case,) [tex]m[/tex] the mass of the satellite, and [tex]r[/tex] is the separation between the point mass and the center of the sphere.As a side note, the GPE here is the same as the work that an external force will do when it brings the point mass from infinitely far away to the current point in space. Gravity pulls the object inwards; the external force acts against gravity in the opposite direction of travel. Energy will be released. The work of the external force will be negative. Hence, the value of GPE shall be either zero (at infinitely far away) or negative.
Convert all values to SI units:
Mass of the earth: [tex]M = 5.972\times 10^{24}\;\textbf{kg}[/tex];Mass of the satellite: [tex]m = 2.000\times 10^{3}\;\textbf{kg}[/tex];Initial separation: [tex]r_{\text{Initial}} = 6400 \;\text{km} = 6.400\times 10^{6}\;\textbf{m}[/tex]; Final separation: [tex]r_{\text{Final}} = 6400 \;\text{km} + 800\;\text{km} = 7200\;\text{km} = 7.200\times 10^{6}\;\textbf{m}[/tex]. Note the the radius of the orbit is the the distance between the satellite and the ground plus the radius of the planet.Initial GPE of the satellite:
[tex]\displaystyle \begin{aligned}\text{GPE(Initial)} &= -\frac{G \cdot M \cdot m}{r_{\text{Initial}}}\\ &=-\frac{(6.67\times 10^{-11})\times (5.972\times 10^{24})\times (2.000\times 10^{3})}{6.400\times 10^{6}} \\ &= -1.245\times 10^{11}\;\text{J}\end{aligned}[/tex].
Final GPE of the satellite:
[tex]\displaystyle \begin{aligned}\text{GPE(Final)} &= -\frac{G \cdot M \cdot m}{r_{\text{Final}}}\\ &=-\frac{(6.67\times 10^{-11})\times (5.972\times 10^{24})\times (2.000\times 10^{3})}{7.200\times 10^{6}} \\ &= -1.106\times 10^{11}\;\text{J}\end{aligned}[/tex].
KE of the SatelliteGravity is the only force that act on the satellite. The velocity [tex]v[/tex] of the satellite in this orbit depends on the size of the net force on the satellite, which is the same as gravity on the satellite. In other words,
[tex]\displaystyle \frac{m\cdot v^{2}}{r} = \Sigma F = W = \frac{G\cdot M\cdot m}{r^{2}}[/tex],
where again, [tex]r = 6400 + 800 = 7200\;\text{km} = 7.200\times 10^{6}\;\text{m}[/tex].
Rearranging gives:
[tex]\displaystyle v^{2} = \frac{G\cdot M}{r}[/tex],
[tex]\displaystyle \begin{aligned} v &= \sqrt{\frac{G\cdot M}{r}} \\ &= \sqrt{\frac{(6.67\times 10^{-11})\times (5.972\times 10^{24})}{7.200 \times 10^{6}}} \\ &= 7.438\times 10^{3}\;\text{m}\cdot \text{s}^{-1}\end{aligned}[/tex].
As a result,
[tex]\displaystyle \text{KE} = \frac{1}{2}\; m \cdot v^{2} = \frac{1}{2} \times (2.000\times 10^{3}) \times (7.438\times 10^{3}) = 5.532\times 10^{10} \;\text{J}[/tex].
Energy requiredAssume no energy loss while lifting the satellite into the space. The energy required will be the same as the change in GPE plus the change in KE (Final minus Initial, keep any negative sign.)
[tex]\begin{aligned} \text{Energy Required} &= (\text{Final GPE} - \text{Initial GPE}) + (\text{Final KE} - \text{Initial KE})\\ &=((-1.106\times 10^{11}) - (-1.245\times 10^{11})) + ((5.532\times 10^{10} \;\text{J})) \\&=6.922 \times 10^{10}\;\text{J}\end{aligned}[/tex].
Two charge spears are 20 cm apart and extract an attractive force of 8x10^-9 N on each other. Which will be the force of attraction when the Spheres are moved to 10 cm apart ?
Answer:
3.2 × 10⁻⁸ N.
Explanation:
By Coulomb's Law, the magnitude of the electromagnetic force between two point charges is inversely proportional to the square of their separation, [tex]r[/tex]. In other words,
[tex]\displaystyle \frac{F_1}{F_2} = {\left(\frac{r_2}{r_1}\right)}^{2}[/tex].
Initial electromagnetic force [tex]F_1 = 8\times 10^{-9}\;\text{N}[/tex];Initial Separation [tex]r_1 = 20\;\text{cm}[/tex];Final Separation [tex]r_2 = 10\;\text{cm}[/tex].Final electromagnetic force:
[tex]\displaystyle F_2 = F_1 \cdot \left(\frac{r_2}{r_1}\right)^{2} = 8\times 10^{-9}\times \left( \frac{20}{10}\right)^{2} = 3.2\times 10^{-8}\;\text{N}[/tex].