Answer:
The kinetic energy gained is 40[J]
Explanation:
This is a problem that applies the work and energy conservation. We must analyze the initial and final positions as well as the forces that act on the couch during displacement.
The working and energy conservation theorem says:
[tex]E_{k1} + W_{1-2}= E_{k2}[/tex]
The above equation tells us that kinetic energy plus the work done to move an object from one position to another will be equal to kinetic energy in the last position.
The kinetic energy in the initial position is zero since the couch is at rest, Ek1=0
The work will be given by the force that drives the couch multiplied by the distance, and the friction force that acts in the opposite direction to the displacement.
[tex]0+(200-180)*2= Ek2\\Ek2=20*2= 40 [J][/tex]
An object initially at rest accelerates at 5 meters per second2 until it attains a speed of 30 meters per second. What distance does the object traverse while accelerating?
Answer: 90m
Explanation:
Use Equation for distance:
S=a*t²/2
use eqation for acceleraton a=(Vf-Vs)/t
Vs- starting speed
Vf - final speed
a-accelaration
---------------------------------
a=5m/s²
Vs=0m/s
Vf=30m/s
use
a=(Vf-Vs)/t
to find time
t=(Vf-Vs)/a
t=30m/s/5m/s²
t=6s
Now calculate distance that object travel using:
S=(a*t²)72
s=(5m/s²*(6s)²)/2
S=90m
If an object initially at rest accelerates at 5 meters per second² until it attains a speed of 30 meters per second, then the distance traveled by the object would be 90 meters.
What are the three equations of motion?There are three equations of motion given by Newton,
v = u + at
S = ut + 1/2×a×t²
v² - u² = 2×a×s
As given in the problem an object initially at rest accelerates at 5 meters per second2 until it attains a speed of 30 meters per second.
By using the third equation of motion given by newton
v² - u² = 2×a×s
30² - 0² = 2*5*s
10s = 900
s = 900 / 10
=90 meters
Thus,If an object initially at rest accelerates at 5 meters per second² until it attains a speed of 30 meters per second, then the distance traveled by the object would be 90 meters.
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A golf club hits a 0.0459 kg golf ball
at rest. Afterwards the ball leaves
at 63.9 m/s. What impulse was
given to the ball?
(Unit = kg*m/s)
Answer:
2.933 kg m/s
Explanation:
impulse = change in momentum
impulse = mass ( final velocity - initial velocity )
= 0.0459 ( 63.9 - 0 )
= 0.0459 × 63.9
= 2.93301 kg m/s
or = 2.933 kg m/s up to 4 significant figures
The impulse given to the golf ball is [tex]2.9331 kgm/s[/tex].
calculated as the change in momentum from rest to [tex]63.9 m/s[/tex] using the golf ball's mass.
To determine the impulse given to the golf ball, we need to use the formula:
[tex]Impulse (J) = Change in Momentum (Δp)[/tex]
First, we calculate the initial momentum:
[tex]Initial momentum (pinitial) = mass (m) * initial velocity (vinitial)[/tex]
Since the golf ball is at rest initially, initial velocity [tex](vinitial) = 0 m/s:[/tex]
[tex]pinitial = 0.0459 kg * 0 m/s = 0 kgm/s[/tex]
Next, we calculate the final momentum:
Final momentum [tex](pfinal) = mass (m) * final velocity (vfinal)[/tex]
[tex]vfinal = 63.9 m/s:[/tex]
[tex]pfinal = 0.0459 kg * 63.9 m/s = 2.9331 kgm/s[/tex]
Now, we find the impulse by calculating the change in momentum:
[tex]Impulse (J) = Δp = pfinal - pinitial[/tex]
Impulse (J) = [tex]2.9331 kgm/s - 0 kgm/s = 2.9331 kgm/s[/tex]
Thus, the impulse given to the ball is [tex]2.9331 kgm/s.[/tex]
I WIIL GIVE BRAINLIEST
Which type of biotechnology is used by scientists when they alter the DNA of a plant to make it grow faster?
Group of answer choices
Genetic engineering because it is always helpful to society
Artificial selection because the DNA of the plant was changed
Genetic engineering because the genes of the plants were modified
Artificial selection because it always produces desirable traits
Answer:
Genetic engineering because the genes of the plants were modified.
Explanation:
We can eliminate the second and fourth ones right off of the bat because artificial selection is breeding organisms until they display a trait or a series of traits that is desired, but in this situation, the scientist directly altered the DNA. Genetic engineering, just like all other technologies, aren't necessarily helpful to society all of the time; they always have their draw backs. The answer has to be the third one because the DNA is directly altered, just like the answer choice says.
What is an example of light energy converted into electrical energy?
(Help, I have my exam in 1 day)
Answer:
Solar panel
Explanation:
You can often find solar panels on top of rooftops of buildings or apartments (usually in less developed countries), as because it consumes the light energy from sunlight and converts it into electrical energy which can be later used to run electrical energy in that specific building.
Two water balloons of mass 0.35 kg collide and bounce off of each other
without breaking. Before the collision, one water balloon moved at a velocity
of 2.5 m/s east, while the other moved at a velocity of 2.25 m/s west. After
the collision, one balloon moves at a velocity of 1.75 m/s west. What is the
velocity of the other water balloon?
O
A. 2 m/s west
O
B. 0.25 m/s east
O
C. 0.25 m/s west
O
D. 2 m/s east
Answer:
Option D
2 m/s East
Explanation:
From the law of conservation of momentum, the sum of initial momentum equals the sum of final momentum
Momentum, p=mv where m is the mass and v is the velocity
Since the masses are the same then
[tex]m(u_1+u_2)=m(v_1+v_2)[/tex]
Therefore
[tex]u_1+u_2=v_1+v_2[/tex]
where [tex]v_1[/tex] and [tex]v_2[/tex] are final velocities of objects while [tex]u_1[/tex] and [tex]u_2[/tex] are the initial velocities respectively
Taking East direction as positive then West as negative and by substitution
[tex]2.5+-2.25=v_1-1.75[/tex]
Therefore
[tex]v_1=2 m/s[/tex] hence East since it's positive
Answer:
2 m/s east
just did it ;D
Explanation:
How do I do number 8, plz respond quick, I have a big unit test on this and I’m rocking a 65 science average rn. Thank you for the help
Answer:
3 is the correct answer for number 8
Number three is the one. The same lines are there but they're all shifted toward the red end. They all show up at longer wavelengths than they should. That suggests that the distant Galaxy he's observing is speeding away from us.
If a space ship is traveling with a constant acceleration of 75 m/s^2 and travels for three weeks, how far did it travel and what was it's velocity before it stopped?
Answer:
The final velocity of the ship is, v = 136050000 m/s
The total distance covered, s = 6.94 x 10¹⁷ m
Explanation:
Given data,
The constant acceleration of the space ship, a = 75 m/s²
The time period of the space ship acceleration is t = 3 weeks
t = 1.814 x 10⁶ s
The initial velocity of the ship is u = 0 m/s
The final velocity of the ship is,
v = u + at
= 0 + 75 (1.814 x 10⁶)
= 136050000 m/s
The distance space ship traveled, can be calculated from the second equation of motion.
s = ut + ½ at²
= 0 + ½ 75 (136050000)²
= 6.94 x 10¹⁷ m
Hence, the total distance covered, s = 6.94 x 10¹⁷ m
To be a healthy family, which of the statements below is TRUE:
A.
Family members need to be perfect.
B.
Family members must include a mom, dad, and children.
C.
Family members try to work out differences together.
D.
Family members must never disagree.
Kgms^-1 ÷ m× (ms^-1)^2
Can u simplify this
Answer:
[tex]\displaystyle \frac{Kg\ m^2}{s^3}[/tex]
Explanation:
Physic Units
Physic magnitudes are expressed in international units in different systems. The most used by this modern times is the SI (International System of Units) which expressed length in meters, time in seconds and mass in kg, just to mention some of the most-used magnitudes.
The given expression is a composition of basic units:
[tex]\displaystyle \frac{Kg\ m\ s^{-1}}{m}(m\ s^{-1})^2[/tex]
Converting negative in positive powers:
[tex]\displaystyle \frac{Kg\ m\ }{m\ s}\left ( \frac{m}{s} \right )^2[/tex]
Expanding the square
[tex]\displaystyle \frac{Kg\ m\ }{m\ s}\left ( \frac{m^2}{s^2} \right )[/tex]
Simplifying by m and multiplying like factors
[tex]\displaystyle \frac{Kg\ m^2}{s^3}[/tex]
Object is going 22m/s and is 3kg find momentum
66 kgm/s
Explanation:We are given;
Velocity of the object as 22 m/sMass of the object as 3 kgWe are required to determine the momentum of the object;
We need to know that momentum is the product of mass and velocity of an object.Therefore; Momentum = Velocity × MassIn this case;
Momentum = 22 m/s × 3 kg
= 66 kgm/s
Thus, the momentum of the object is 66 kgm/s
f a light bulb produces 60.0 J of electrical energy and is 45% efficient, how much energy does it use?
a)133 J
b)1.33 J
c)0.75 J
d)2700 J
Answer:
133 j
Explanation:
what will happen to the solar particle as the particles enter magnetosphere?
Answer:
When the solar particles enters into the magnetosphere gets deflected.
Explanation:
When particles enter into the magnetosphere gets deflected because of the solar wind. After getting deflected they comes towards the earth's magnetic field. The Earth's outer space is live and also much dynamic. When solar wind as well as the plasma comes together in magnetosphere, electricity gets generated and also formation of electric field. The magnetosphere found to attract the charged particles only that are being emitted by the sun.
The magnitude of the gravitational field on the surface of a particular planet is 2g. The planet’s mass is half the mass of the Earth. What is the planet’s radius in terms of the radius Rg of Earth?
To find the radius of a planet with a gravitational field twice that of Earth's and half the mass, the radius is calculated to be half of Earth's radius.
Explanation:The magnitude of the gravitational field strength g on a planet is given by the equation g = G(M/R^2), where G is the universal gravitation constant, M is the planet's mass, and R is the planet's radius. Given that the gravitational field on the surface of the particular planet is 2g where g is Earth's gravitational field, and the planet's mass is half of Earth's mass, we can derive the planet's radius in terms of Earth's radius Rg. Setting up the proportion (G(1/2M_Earth)/(R^2)) / (G(M_Earth)/(Rg^2)) = 2, and simplifying, we find that R^2 = (1/4)Rg^2. Taking the square root of both sides gives us the final relation R = (1/2)Rg.
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Two men decide to use their cars to pull a truck stuck in mud. They attach ropes and one pulls with a force of 821 N at an angle of 32◦ with respect to the direction in which the truck is headed, while the other car pulls with a force of 1140 N at an angle of 26◦ with respect to the same direction.
What is the net forward force exerted on the truck in the direction it is headed?
Answer:
1737.8 N
Explanation:
Given information
[tex]F_1= 821 N[/tex]
[tex]F_2= 1140 N[/tex]
[tex]\theta_1=32^{\circ}[/tex]
[tex]\theta_2=26^{\circ}[/tex]
Net force, [tex]F_{net}=F_1 cos \theta_1+F_2 cos \theta_2=821cos 32^{\circ}+ 1140 cos 26^{\circ}=1737.833662 N \approx 1737.8 N[/tex]
What is the rate of change of position in which the same distance is traveled each second ?
Answer:
The rate of change of position in which the same distance is traveled each second is called uniform velocity.
Explanation:
When there is a change in the position coordinate of an object with respect to time, it is has a velocity associated with it.Similarly, when there is a change in the velocity component of the object with respect to the time, there is an acceleration associated with it.When the rate of change of position in which the same distance is traveled each second, the object is said to be in uniform velocity. Therefore, there is no acceleration acting on the object.Since there is no acceleration acting on the object, the net force on the object is zero.The rate of change of position where the same distance is traveled each second is known as speed, and when this rate is constant, the object has a constant speed.
Explanation:The rate of change of position in which the same distance is traveled each second is referred to as speed. Speed is a measure of how quickly an object moves from one place to another. It is calculated by dividing the distance covered by the time it takes to travel that distance. For instance, if a train travels 120 kilometers in 2 hours, its speed would be calculated as 120 divided by 2, giving a speed of 60 kilometers per hour.
In the case where the rate of change of position is constant over time, the object is said to be moving with constant speed. This means that the object covers equal distances in equal intervals of time, no matter how small these time intervals are. An example of this would be a car moving at a steady 50 kilometers per hour, implying that every hour, it travels exactly 50 kilometers, and in every second, it travels approximately 13.9 meters.
When a pitcher throws a baseball, it reaches a top speed of 45 m/s. If the
baseball takes 0.9 seconds to travel from the pitcher to the catcher, what is
its acceleration? (Assume the ball is moving at 0 m/s right before it leaves
the pitcher's hand.)
A. 45 m/s2
B. 50 m/s2
C. 55m/s 2
D. 40 m/s2
Answer:
B. 50 m/s²
Explanation:
Given:
Initial velocity of the ball is, [tex]u=0\ m/s[/tex]
Final velocity of the ball is, [tex]v=45\ m/s[/tex]
Time taken by the ball is, [tex]t=0.9\ s[/tex]
Acceleration is defined as the rate of change of velocity. So, the velocity of the ball is changing with time. So, acceleration is given as:
[tex]a=\frac{v-u}{t}[/tex]
Plug in 0 for 'u', 45 for 'v', 0.9 for 't' and solve for acceleration, 'a'. This gives,
[tex]a=\frac{45-0}{0.9}\\\\a=\frac{45}{0.9}\\\\a=50\ m/s^2[/tex]
Therefore, the acceleration of the ball is 50 m/s².
1- Is the d versus t2 graph linear. What is the relation between the acceleration and the slope?
Answer:The principle is that the slope of the line on a position-time graph reveals useful information about the velocity of the object. ... If the velocity is constant, then the slope is constant (i.e., a straight line). If the velocity is changing, then the slope is changing (i.e., a curved line
Explanation:
Which statement best describes insulators? Free electrons can move to other atoms Electrons within their atoms are strongly held by the nuclei Permits charged particles to move freely through it Most electrons within their atoms are unpaired
Answer:
The statement that best describes insulators is "Electrons within their atoms are strongly held by the nuclei"
Explanation:
Atoms are constituted by a nucleus with positive charge (protons and neutrons), around which negative charges (electrons) revolve.
Substances that have a huge amount of "free electrons" that can move through the material are called conductors. This is due to the low resistance to the movement of the load or electric current.
Materials that do not conduct electricity are called insulators. In this case the electrons are strongly bound to the nucleus and cannot move freely. In this way a great resistance to the flow of electric current is offered.
Finally, semiconductors are the materials that can have electrical properties of conductors or insulators.
So the statement that best describes insulators is "Electrons within their atoms are strongly held by the nuclei"
Answer:
it has a high resistivity because it opposes the movement of electrons
Explanation:
We are able to see an object when it:
A. is between our eyes and a light source.
B. emits infrared (heat) radiation.
C. reflects one or more visible light frequencies.
D. emits one or more visible light frequencies.
Answer:
C. reflects one or more visible light frequencies.
Explanation:
The color that we see is the color that is deflected from the RGBHSB.etc. This means that the light has all the colors within, and the object it hits absorbs all but one color, in which it deflects for our eyes to see.
~
A student finds an unlabeled bottle of liquid under
his kitchen sink. Which investigation would BEST
help him identify the unknown liquid as acidic,
basic, or neutral?
healing the unknown liquid to its boiling point
B. cooling the unknown liquid to its freezing point
C adding some of the unknown liquid to red litmus
paper
D. adding an equal amount of water to the
unknown liquid
Answer:
C. Adding some of the unknown liquid to red litmus paper.
Explanation:
Since the student doesn't know what the liquid is, it is not safe to experiment with it by boiling, cooling, or adding water to it. The safest option would be to add a small bit of the liquid to the litmus paper, which will identify the liquid as neutral, basic, or acidic.
The answer is C. Adding some of the unknown liquid to red litmus paper.
SP: Calculate the moment
exerted with the claw hammer if
the person exerts a force of 80N
and distance equals 25cm. Give
the unit
Answer:
Moment of the force is 20 N-m.
Explanation:
Given:
Force exerted by the person is, [tex]F=80\ N[/tex]
Distance of application of force from the point about which moment is needed is, [tex]d=25\ cm=\frac{25}{100}\ m=0.25\ m[/tex]
Now, we know that, moment of a force 'F' about a point at a perpendicular distance of 'd' from the same point is given as the product of the force and the perpendicular distance.
Therefore, the moment of the force about the end of the claw hammer is given as:
[tex]M=F\times d\\\\M=(80\ N)(0.25\ m)\\\\M=20\textrm{ N-m}[/tex]
Hence, the moment of the force exerted by the person about the end of the claw hammer is 20 N-m.
The required value of moment of force exerted on the claw hammer is of 20 N-m.
Given data:
The magnitude of force exerted by hammer is, F = 80 N.
The distance covered due to applied force is, s = 25 cm = 0.25 m.
The moment of force is termed as the turning effect produced by the applied force. In other words, moment is a term used to measure the tendency of linear force to rotate any object. The mathematical expression for the turning moment is given as,
M = F × s
Solving as,
M = 80 × 0.25
M = 20 N-m
Thus, we can conclude that the required value of moment of force exerted on the claw hammer is of 20 N-m.
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wich of these is not a sign of chemical change 1 A gas is given off
2 the material dissolves.
3 a color change occurs.
2. The material dissolves
Explanation:The Question tests the understanding of chemical change and whether we know the signs that show its occurrence.
First we need to know what is chemical change;
Chemical change is a type of change that involves formation of a new substance different from the original substance.Second we need to identify the signs that indicate the occurrence of a chemical change
Chemical change in chemical reactions is characterized by various signs which include;Production of bubbles Color change Formation of a precipitate Change of odor Change in temperature.Therefore, in this case, the material dissolving is not a sign that chemical change has taken place.The force of the players head on the ball is 1.5N upward, What is the force of the ball on the players head?
The force is 1.5N acting downward or -1.5N.
Why?
To answer this question, we need to remember the Newton's Third Law. This Law states that for every force applied upon an object, there is an equal force acting in the opposite direction. This Law is also called "action-reaction Law".
So, if the force of the players heads applied on the ball is equal to 1.5N (upward), the force applied by the force on the players heads will be exactly equal, but with opposite direction, or -1.5N (downward).
Have a nice day!
what chemical bond is formed when an equal exchange of electrons occurs?
A) covalent
B) hydrate
C) ionic
D) magnetic
An ionic bond is formed when there's an equal exchange of electrons between atoms. This differs from other bond types like covalent bonds, where electrons are shared. Sodium chloride (NaCl) is a typical example of this kind of bond.
Explanation:The chemical bond that's formed when an equal exchange of electrons occurs is the ionic bond. An ionic bond is a type of chemical bond that occurs when an atom transfers one or more electrons to another atom. This is different from a covalent bond where the electrons are shared, rather than exchanged. For example, when the sodium atom (Na) transfers an electron to the chlorine atom (Cl), they form an ionic bond and become a sodium chloride (NaCl) molecule.
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How much work can you do using a 600 watt stove and oven for 10 minutes
Answer:
360 kJ
Explanation:
Energy = power × time
E = 600 J/s × (10 min × 60 s/min)
E = 360,000 J
E = 360 kJ
Using a 600 watt stove and oven for 10 minutes results in an energy consumption of 0.1 kilowatt-hours (kWh),
Using the formula:
Energy (in watt-minutes) = Power (in watts)× Time (in minutes)
For a 600 watt stove:
Power = 600 wattsTime = 10 minutesEnergy = 600 watts× 10 minutes
= 6000 watt-minutes
However, energy consumption is usually expressed in kilowatt-hours (kWh). To convert watt-minutes to kilowatt-hours, use the following conversion:
1 watt-minute = 1/60,000 kilowatt-hour
Therefore:
Energy = 6000 watt-minutes× (1/60,000) kWh/watt-minute
= 0.1 kWh
The 600 watt stove and oven can do 0.1 kWh of work in 10 minutes.
if the Moon were twice as big, _______. A) its pattern of apparent shapes would probably be the same B) its pattern of apparent shapes would probably be reversed C) it probably would no longer revolve around Earth D) it would probably revolve in the opposite direction
(Sorry if the subject is wrong)
If the Moon were twice as big, its pattern of apparent shapes would be probably be reversed.
Option B
Explanation :The motion or the movement of the earth and that of the moon trajectory are the same of one another. There are many reasons for the great differences in the earth and the space. But the gravity plays a very major and an important role in controlling all the activities of these celestial bodies.
The projectile motion plays a very important and a crucial role. It is plays were the parabolic motions and the paths come into act. They also move in a definite speed in order to control the movement.
A cannon ball is fired horizontally with a velocity of 50 metre per sec from the top of a cliff 90m high. After how many seconds will it strike the plain at the foot of the cliff? with what velocity will it strike the ground?
To solve the problem, we use the equations of projectile motion. The cannonball takes approximately 4.28 seconds to hit the ground and has a velocity of 50m/s at impact.
Explanation:To solve this problem, we can use the equations of projectile motion. Since the cannonball is fired horizontally, its initial vertical velocity is zero, so it will only accelerate vertically due to gravity. We can use the equation h = (1/2)gt^2, where h is the height of the cliff (90m), g is the acceleration due to gravity (9.8m/s^2), and t is the time it takes for the cannonball to hit the ground.
Plugging in the values, we get 90 = (1/2)*(9.8)*t^2. Solving for t, we find that it takes approximately 4.28 seconds for the cannonball to strike the ground.
Since the cannonball is fired horizontally, its initial vertical velocity is zero, so its velocity just before hitting the ground will be equal to its horizontal velocity. The horizontal velocity remains constant throughout the motion, so the cannonball will have a velocity of 50m/s just before hitting the ground.
When Mr. Peterson first met his teenaged granddaughter, he thought she was
self-centered and silly. After spending more time with her, however, he now
thinks she is a great person. This is an example of the:
Question: when Mr. Peterson first met his teenage granddaughter, he thought she was self-centered and silly. after spending more time with her, however, he now thinks she is a great person. this is an example of:
A. fundamental attribution error
B. Mere exposure effect
C. Cognitive dissonance
D. Scapegoat theory
Answer:
when Mr. Peterson first met his teenage granddaughter, he thought she was self-centered and silly. after spending more time with her, however, he now thinks she is a great person. this is an example of: Mere exposure effect
Explanation:
The mere exposure effect is something on first exposure you dislike it, but after being spending more time with it you will start liking it. Moreover spending time with something or someone getting aware of that person make you believe that you have started liking it, despite the initial aversion. It is psychological phenomenon which with time build up a preference for the thing after getting familiar to them. Also, called as familiarity principle.
Answer: mere exposure effect
Explanation:
Which part of the manufacturing process involves heating and rolling blocks of steel into flat sheets and bars?
A. Forming
B. Finishing
C. Conditioning
D. Separating
Answer: Forming
Explanation: Metal forming is a process where materials are subjected to plastic deformation to obtain the required size, shape, and/or change the physical and chemical properties
To measure the mass of a planet with the same radius as Earth, an astronaut drops an object
from rest (relative to the planet) from an altitude of one radius above the surface. When the
object hits its speed is 4 times what it would be if the same experiment were carried out for
Earth. In units of Earth masses, the mass of the planet is:
A. 2
B. 4
C. 8
D. 16
E. 32
ans: D
Answer:
D. 16
Explanation:
For this you must the gravitational force equation, i.e.
[tex]\mathbf{F = \frac{Gm_{1}m_{2}}{r^{2}}}[/tex]
where [tex]\textrm{m}_{1}[/tex] and [tex]\textrm{m}_{2}[/tex] are mass of objects,
[tex]\textrm{r}[/tex] is the distance between objects
and [tex]\textrm{G}[/tex] is the universal gravitational constant which is approximately equal to [tex]\mathrm{6.67\times10^{-11} \frac{m^3}{kg\cdot s^{2}}}[/tex].
You must know that energy and its conservation in terms of gravitational forces.
Let mass of earth be equal to M and radius of earth as R.
Potential energy of an object of mass m at a distance r from center of earth = [tex]\mathbf{PE = -\frac{GMm}{r}}[/tex]
Kinetic energy of same object at any point of time = [tex]\mathbf{KE = \frac{1}{2}mv^{2}}[/tex] where v is the speed of the object.
Energy conservation states that total energy of a system is always constant.
Total energy = Potential energy + Kinetic energy
∴ Total energy initial = Total energy final
let the mass of object be m and mass of planet be [tex]\mathbf{M_{p}}[/tex] and initial distance between object and center of plant is equal to 2R. let the speed of object of object on earth equal to v.
Initial Kinetic energy is zero(0) as it is at rest so its speed is zero.
Total energy initially on earth= [tex]\mathrm{-\frac{GMm}{(2R)^{2}}+0}[/tex]
Total energy initially on planet= [tex]\mathrm{-\frac{GM_{p}m}{(2R)^{2}}+0}[/tex]
Total Energy finally on earth = [tex]\mathrm{-\frac{GMm}{R^{2}}+\frac{1}{2}mv^{2}}[/tex]
Total Energy finally on planet = [tex]\mathrm{-\frac{GM_{p}m}{R^{2}}+\frac{1}{2}m(4v)^{2}}[/tex]
Solving equation of earth
[tex]\mathrm{-\frac{GMm}{(2R)^{2}}+0=-\frac{GMm}{R^{2}}+\frac{1}{2}mv^{2}}[/tex]
[tex]\mathrm{-\frac{GMm}{4R^{2}}=-\frac{GMm}{R^{2}}+\frac{1}{2}mv^{2}}[/tex]
[tex]\mathrm{\frac{GMm}{R^{2}}-\frac{GMm}{4R^{2}}=\frac{1}{2}mv^{2}}[/tex]
[tex]\mathrm{\frac{3GMm}{4R^{2}}=\frac{1}{2}mv^{2}}[/tex]
[tex]\mathrm{\frac{3GM}{2R^{2}}=v^{2}}[/tex]
[tex]\therefore\mathbf{v^{2}=\frac{3GM}{2R^{2}}}[/tex] _________eq(1)
Solving equation of planet
[tex]\mathrm{-\frac{GM_{p}m}{(2R)^{2}}+0=-\frac{GM_{p}m}{R^{2}}+\frac{1}{2}m(4v)^{2}}[/tex]
[tex]\mathrm{-\frac{GM_{p}m}{4R^{2}}=-\frac{GM_{p}m}{R^{2}}+\frac{16}{2}mv^{2}}[/tex]
[tex]\mathrm{\frac{GM_{p}m}{R^{2}}-\frac{GM_{p}m}{4R^{2}}=8mv^{2}}[/tex]
[tex]\mathrm{\frac{3GM_{p}m}{4R^{2}}=8mv^{2}}[/tex]
[tex]\mathrm{\frac{3GM_{p}}{32R^{2}}=v^{2}}[/tex]
[tex]\therefore\mathbf{v^{2}=\frac{3GM_{p}}{32R^{2}}}[/tex] ___________eq(2)
Using eq(1) and eq(2)
[tex]\mathrm{\frac{3GM_{p}}{32R^{2}}=\frac{3GM}{2R^{2}}}[/tex]
[tex]\mathrm{\frac{M_{p}}{16}=M}[/tex]
[tex]\therefore\mathbf{M_{p}=16M}[/tex]
Therefore mass of planet is 16 times the mass of Earth.
The mass of the planet is 16 times that of Earth. This is calculated based on the speed of a dropped object on the planet compared to Earth, which indicates its gravity and mass.
Explanation:The speed of a dropped object on another planet is determined by the acceleration due to gravity on that planet, which is influenced by the planet's mass. If the speed of the object upon arriving at the ground is four times greater on this planet vs. Earth, that indicates that the gravity (and thus the mass) of this planet is 16 times that of Earth. Therefore, in units of Earth masses, the mass of the planet is 16.
To further elucidate, the speed of the object when it hits the ground is proportional to the square root of the mass of the planet. Thus, if the speed is 4 times higher than what it would be on Earth, the mass of the planet must be 4^2, or 16 times the mass of Earth. Hence, the correct option is D. 16.
Learn more about planetary mass here:https://brainly.com/question/34699802
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