Answer:
1. 100 J
2. 225 J
Explanation:
We'll begin by calculating the mass of the object. This can be obtained as follow:
Velocity (v) = 5 ms¯¹
Kinetic energy (KE) = 25 J
Mass (m) =?
KE = ½mv²
25 = ½ × m × 5²
25 = ½ × m × 25
25 = 25m / 2
Cross multiply
25m = 25 × 2
25m = 50
Divide both side by 25
m = 50 / 25
m = 2 Kg
1. Determination of the kinetic energy when the velocity is doubled.
Mass (m) = 2 Kg
Velocity (v) = double the initial velocity
= 2 × 5 ms¯¹
= 10 ms¯¹
Kinetic energy (KE) =?
KE = ½mv²
KE = ½ × 2 × 10²
KE = ½ × 2 × 100
KE = 100 J
2. Determination of the kinetic energy when the velocity increased three times.
Mass (m) = 2 Kg
Velocity (v) = three times the initial velocity
= 3 × 5 ms¯¹
= 15 ms¯¹
Kinetic energy (KE) =?
KE = ½mv²
KE = ½ × 2 × 15²
KE = ½ × 2 × 225
KE = 225 J
Sí un auto viaja a 8m/s determine Tiempo en llegar a 200km de distancia Distancia que recorre en 40 minutos
Answer:
a. Tiempo = 25000 segundos
b. Distancia = 19200 metros
Explanation:
Dados los siguientes datos;
Velocidad = 8 m/s
Distancia = 200 km a metros = 200 * 1000 = 200,000
Para encontrar el tiempo para cubrir la distancia anterior;
Tiempo = distancia/velocidad
Tiempo = 200000/8
Tiempo = 25000 segundos
b. Para encontrar la distancia recorrida en 40 minutos;
Tiempo = 40 minutos a segundos = 40 * 60 = 2400 segundos
Distancia = velocidad * tiempo
Distancia = 8 * 2400
Distancia = 19200 metros
Amy throws a softball through the air. What are the different forces acting on the ball while it’s in the air?
The softball experiences
force as a result of Amy’s throw. As the ball moves, it experiences
from the air it passes through. It also experiences a downward pull because of
.
Answer:
1.the friction of air, gravity2.gravity
Answer:
The softball experiences an applied force as a result of Amy’s throw. As the ball moves, it experiences drag from the air it passes through. It also experiences a downward pull because of gravity.
Explanation:
Plato
What is matter made of.
Answer:
Matter is made up of atoms
Answer:
Mater is made up of atoms.
Explanation:
Atoms come together to form molecules,which are the building blocks for all types of matter.
If the radius of curvature of a mirror is 15m and the distance of the object from the mirror is 10m. Find the distance of the image from the mirror and the magnification of the object in meter
Answer:
Data given.
focal length (f)=15m÷2=7.5m
Distance of the object(U)=10m
Image distance (v)=?
Magnification (M)=?
Solution:
From:
1/f=1/u+1/v
1/7.5=1/10+1/v=75
then v=75m
Magnification, M=u/v
=75/10=7.5
Then magnification=7.5
Answer:
v = 30 m and m = 3
Explanation:
Given that,
The radius of curvature of the mirror, R = 15 m
Focal length, f = 7.5 m
Object distance, u = -10 m
We need to find the image distance and the magnification of the object.
Using mirror's formula,
[tex]\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}\\\\\dfrac{1}{v}=\dfrac{1}{f}+\dfrac{1}{u}\\\\\dfrac{1}{v}=\dfrac{1}{(7.5)}+\dfrac{1}{(-10)}\\\\v=30\ m[/tex]
The magnification of the object in mirror is given by :
[tex]m=\dfrac{-v}{u}\\\\m=\dfrac{-30}{-10}\\\\m=3[/tex]
So, the distance of the image from the mirror and the magnification of the object are 30 m and 3 respectively.
Un alambre de plástico, aislante y recto mide 10 cm de longitud y tiene una densidad de carga de +150 nC/m, distribuidos de manera uniforme por toda su longitud. Se encuentra sobre una mesa horizontal. A) Encuentre la magnitud y la dirección del campo eléctrico que produce este alambre en un punto que está 8 cm directamente arriba de su punto medio. B) Si el alambre ahora se dobla para formar un círculo que se coloca aplanado sobre la mesa, calcule la magnitud y la dirección del campo eléctrico que produce en un punto que se encuentra 6 cm directamente arriba de su centro.
Answer:
English only
Explanation:
When solving problems related to Electric Fields, care must be taken about symmetries. In our particular case when we take a look to at the drawings of the attached file, we realize:
1.-By symmetry each dx associated at a, has an opposite dx with point b as reference. The respective dE ( the charge is uniform ) is the same, as the charge of the wire is positive the force and the Field on a test charge (+) located at h will be upward, therefore the components dEx will cancel each other and the Electric Field becomes E = Ey = ∫ 2×dE× cosθ
The solutions:
A) Ey = 4623 N/C
B) Ey = 19.34 N/C
E = Ey = ∫ 2×dE× cosθ
Here cosθ = h/ d ⇒ cosθ = h/√h² + x² dE = K× dQ / d²
d² = h² + x²
k = 8.9 ×10⁹ Nm²C⁻² ; dQ = λ×dx λ = 150×10⁻⁹ C h = 0.08 m
Then by substitution
Ey = 2 ∫[K× λ×dx/ (h² + x²) ] × h / √h² + x²
reordering that equation:
Ey = 2×K×λ×h ∫ dx / [√ ( h² + x² ) ]³ (2)
To solve the integral we make use of a change of variables
x = h × tanα then x² = h² ×tan²α and dx = h× sec²α dα
plugging that values in equation (2)
Ey = 2×K×λ×h ∫ h× sec²α× dα / [√ ( h² + h²tan²α)]³
Ey = 2×K×λ×h² ∫ sec²α× dα / [ h × √ (1 + tan²α)]³ 1 + tan²α = sec²α
Ey = 2×K×λ×h²× ∫ (sec²α / h³× sec³α )×dα
Ey = 2×K×λ/h × ∫ ( 1 / secα dα
Ey = 2×K×λ/h × sinα now we αneed to come back to our original variables:
as x = h × tanα tanα = x/h then x is the opposite leg in a right triangle and h the adjacent one then the hypothenuse is √ (h² + x²) then sin α = x/ √ (h² + x²)
Ey = 2×K×λ/h × x/ √ (h² + x²) |₀⁰°⁰⁵
Ey = 2×8.9×10⁹× 150×10⁻⁹× 5×10⁻²/8× 10⁻²× √ 10⁻² ( 8 + 5 ) N/C
Ey = 4623 N/C
To answer the second question again we will make use of symmetries if you look at drawing ( Figure 2 ) you see that again the components in direction of x-axis cancel each other and the components in y-axis direction will add. Then
Ey = ∫ dE× cosθ
following the same procedure we will find:
Ey = ∫ [K×λ × dl/d²] × h/ d
The importan point here is that the radius of the circle is
2×π×r = 0.01 ( the length of the wire) ⇒ r = 0.16×10⁻² m
And we need to take into account that the integration is over the circle and the length of the circle is 0.01 m or ××2×π×r. All other factors are constant. Then by substitution
Ey = [K×λ ×h× / ( √ r² + h²)³ ] × 10⁻² N/C
Ey = 8.9 × 10⁹ × 150× 10⁻⁹ × 6× 10⁻² × 10⁻² / √ 10⁻² ( 0.16 + 6)
Ey = 0.8 × 10² / 6
Ey = 19.34 N/C
what force to be required to accelerate a car of mass 120 kg from 5 m/s to 25m/s in 2s
Answer:
[tex]f = m \frac{v1 - v2}{t} \\ = 120 \times \frac{25 - 5}{2} \\ = 120 \times \frac{20}{2} \\ = 120 \times 10 \\ = 1200N \\ thank \: you[/tex]
5. A person standing on a 50 m cliff throws a rock upward at 26.5 m/s. How long will it take for the rock to reach the ground? Hint: determine the final velocity first.
Answer:
53 seconds
Explanation:
26.5/50
0.53 seconds
It will take approximately 5.42 seconds for the rock to reach the ground from a 50 m cliff when thrown upward with an initial velocity of 26.5 m/s.
The time it takes for the rock to reach its highest point. We can use the equation:
Final velocity (v) = Initial velocity (u) + Acceleration (a) × Time (t)
0 = 26.5 - 9.8 × t
9.8 × t = 26.5
t = 26.5 ÷ 9.8
t = 2.71 seconds
Now, we double the time to account for the time it takes for the rock to reach its highest point and fall back down:
Total time = 2 × t
Total time ≈ 2 × 2.71
Total time = 5.42 seconds
Therefore, it will take approximately 5.42 seconds for the rock to reach the ground from a 50 m cliff when thrown upward with an initial velocity of 26.5 m/s.
To know more about the velocity:
https://brainly.com/question/34025828
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Which would be used to measure the distance between the earth and a planet ,meter ruler or a measuring tape? Why?
Answer:
parallax
Due to foreshortening, nearby objects show a larger parallax than farther objects when observed from different positions, so parallax can be used to determine distances. To measure large distances, such as the distance of a planet or a star from Earth, astronomers use the principle of parallax.
Light strikes a smooth wooden tabletop.
What happens to the light after it is reflected?
The light rays bounce off the table and all move in the same direction.
The light rays bounce off the table and move in different directions.
The light rays pass through the table and all move in the same direction.
The light rays pass through the table and move in different directions.
Answer:
For smooth surface:The light rays bounce off the table and all move in the same direction.
What is this?
Picture
Answer:
may be upside down alphabet :"T"
Explanation:
Your mass is 80 kg on Earth. What would your MASS
be on Planet Roethler, which has twice as much
gravity as on Earth?
40 kg
160 kg
80 kg
Mass doesn't change. It doesn't matter where you are.
If your mass is 80 kg when you're on Earth, then your mass is 80 kg. It doesn't matter where you are, where you used to be, or where you're going tomorrow.
How much energy does it take to boil water for pasta? For a one-pound box of pasta
you would need four quarts of water, which requires 15.8 kJ of energy for every degree Celsius (°C) of temperature increase. Your thermometer measures the starting
temperature as 48°F. Water boils at 212°F.
a. [1 pts] How many degrees Fahrenheit (°F) must you raise the temperature?
b. [2 pts] How many degrees Celsius (°C) must you raise the temperature?
c. [2 pts] How much energy is required to heat the four quarts of water from
48°F to 212°F (boiling)?
Answer:
a. 164°F
b. [tex]91.\overline 1 \ ^{\circ} C[/tex]
c. [tex]140.\overline 4[/tex] kJ
Explanation:
The starting temperature of the water, T₁ = 48F
The temperature at which the water boils, T₂ = 212°F
a. The difference between the initial and the boiling water temperature, ΔT = T₂ - T₁
Therefore;
ΔT = 212°F - 48°F = 164°F
The temperature by which he temperature must be raised, ΔT = 164°F
b. 48°F = ((48 - 32)×5/9)°C = (80/9)°C = [tex]8.\overline 8 \ ^{\circ} C[/tex]
212°F = ((212 - 32)×5/9)°C = 100°C
∴ ΔT = 100°C - [tex]8.\overline 8 \ ^{\circ} C[/tex] = [tex]9.\overline 1 \ ^{\circ} C[/tex]
c. The heat capacity of the water = The heat required to increase four quartz of water by 1 °C = 15.8 kJ
∴ The heat required to raise four quartz of water by [tex]9.\overline 1 \ ^{\circ} C[/tex], ΔQ = 15.8 kJ/°C × [tex]9.\overline 1 \ ^{\circ} C[/tex] = [tex]140.\overline 4[/tex] kJ.
how much does a car weighr if each tyre cover of 4cm^2 and exert a pressure of 100000Nm^-2 on the ground it is physics questions
Answer:
Weight = 160 N
Explanation:
The weight of an object is a measure of the gravitational force on the object. So that weight is synonymous to the force applied by the object.
i.e Weight = mass x gravitational force
Also, the pressure of an object is the ratio of its force to area covered by the object. So that;
P = [tex]\frac{F}{A}[/tex]
Given that: area = 4 [tex]cm^{2}[/tex] (0.0004 [tex]m^{2}[/tex]), and pressure = 100 000 N[tex]m^{-2}[/tex].
Then;
F = PA
= 100 000 N[tex]m^{-2}[/tex] x 0.0004 [tex]m^{2}[/tex]
F = 40 N
The force applied on the ground by each of the four tyres of the car is 40 N.
Thus, the weight of the car = 4 x 40 N
= 160 N
A gas is enclosed in a confainer fitted with a piston of cross sectional area 0.10 the pressureof the gas is maintained in 8000 when hat is slowlh transferred the piston is pushed up through a distance of 4.0cm If 42j of heat is transferred to the system during expansion wht is the change im internal energy of th system
Answer:
10 Joule
Explanation:
The solution and answer are well written in the Pic above.
Is it possible to get a body accelerated even if it is moving with uniform speed? justify.
Answer:Yes, A body can have constant speed but still accelerate as in case of uniform circular motion. In uniform circular motion speed remains constant and direction of velocity changes with every point in the direction of tangent drawn from that point.
Explaination:
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How do space probes make it past the asteroid belt without crashing into asteroids?
Answer:
The thing is space is really vast like really big so even though the asteroid belt looks really cramped it isn't. There's a lot of space between asteriods and using simple navigation and maneuvering, space probes can easily make it through without the threat of crashing.
Explanation:
What is displacement?
An objects overall change in position
The total measure of how far one travels
a change in direction
Answer:
An object overall change in position
Explanation:
ans maybe corre6
An ice skater pushes harder with her legs and begins to move faster. Which two laws best describes this
Answer:
Newton' second law and third law describes the situation.
Explanation:
According to the Newton's second law, the force applied on a body is proportional to the rate of change of momentum of the body.
According to the Newton's third law, for every action there is an equal and opposite reaction.
When ice skater pushes harder means more force is applied so he moves fast and more be the action force more be the reaction force.
Thus, Newton' second law and third law describes the situation.
three condensers are connected in series across a 150 volt supply, the voltages across them are 40,50 and 60 volts respectively, and the charge on each condenser is 6×10^-8 c.calculate (a) the capacitance of each condenser (b)the effective capacitance of the combination
Answer:
(a) 1.5 nF, 1.2 nF, 1 nF
(b) 0.4 nF
Explanation:
V = 150 V
V' = 40 V, V'' = 50 V, V''' = 60 V, q = 6 x 10^-8 C
(a) C' = q/V' = 6 x 10^-8 / 40 = 1.5 x 10^-9 F
C'' = q/V'' = 6 x 10^-8 / 50 = 1.2 x 10^-9 F
C''' = q/V''' = 6 x 10^-8 / 60 = 1 x 10^-9 F
(b) The effective capacitance is
[tex]\frac{1}{C}=\frac{1}{C'}+\frac{1}{C''}+\frac{1}{C'''}\\\\\frac{1}{C}=\frac{10^9}{1.5}+\frac{10^9}{1.2}+\frac{10^9}{1}\\\\C = 0.4\times 10^{-9} F[/tex]
& What is meant by expansion effect of heating?
Answer:
it's when heat demolished the object
a man is running on the straight road with the uniform velocity of3m/s.calculate its acceleration
Answer:
9m is this the way calculator its acceleration
A man is running on the straight road with the uniform velocity of 3 m/s.
To find out:Acceleration produced by the man.
Solution:Given, the man is running with uniform velocity of 3 m/s.So the velocity did not change.It remains constant.We know, acceleration is the change of velocity per unit time.Since there is no change in velocity in this case, so there will be no acceleration.So, the acceleration produced by the man is zero.Answer:The acceleration produced by the man is zero.3.00 m^3 of water is at 20.0°C.
If you raise its temperature to
60.0°C, by how much will its
volume expand?
Water
B = 207•10-6 0-1
(Unit = m^3)
Answer:
[tex]\triangle V = 0.02484m^3[/tex]
Explanation:
Given
[tex]V_1 = 3.00m^3[/tex] --- initial volume
[tex]T_1 = 20.0^oC[/tex] --- initial temperature
[tex]T_2 = 60.0^oC[/tex] --- final temperature
[tex]\gamma = 207*10^{-6[/tex] --- coefficient of thermal expansion:
Required
The change in volume
To do this, we make use of cubic expansivity formula
[tex]\triangle V = \gamma * V_2 * (T_2 - T_1)[/tex]
So, we have:
[tex]\triangle V = 207 * 10^{-6} * 3.00 * (60.0 - 20.0)[/tex]
[tex]\triangle V = 207 * 10^{-6} * 3.00 * 40.0[/tex]
[tex]\triangle V = 0.02484m^3[/tex]
The volume will expand by [tex]0.02484m^3[/tex]
What process forms the Mid-Atlantic Ridge?
A. Radioactive decay
B. Seafloor spreading
C. Radiometric dating
D. Sediment formation
Answer:
B. seafloor spreading
Explanation:
divergent motion between the Eurasian and North American, and African and South American Plates. ... In this way, as the plates move further apart new ocean lithosphere is formed at the ridge and the ocean basin gets wider
geological society
Why are the largest craters we find on the Moon and Mercury so much larger than the largest craters we find on the Earth
Answer:
Because Moon and Mars has no atmosphere.
Explanation:
Moon and Mars has no atmosphere, so there is no friction on the falling object due to the atmosphere. The speed of the falling object is more at Moon and Mars.
When a small object impact on the surface of moon or Mars with high speed, the size of crater is large than the earth as out earth has atmosphere.
A cannon sitting on level ground is aimed at 45.0 degrees relative to the horizontal. It fires a test shot at a target located 100.0 meters away from the cannon on the same level ground. The test overshoots the target by 20.0 meters. Which of the following angles can the cannon be adjusted to to hit the target. You may neglect air resistance and assume the cannon always delivers the same initial velocity to the cannonball .
A. 35.9 deg
B. 49.1 deg
C. 28.2 deg
D. 52.8 deg
E. 22.7 deg
Answer:
C. 28.2 deg
Explanation:
The horizontal range of a projectile is given as:
[tex]R = \frac{v^2Sin2\theta}{g}[/tex]
where,
R = Range
v = speed
θ = angle of launch
g = acceleration due to gravity = 9.81 m/s²
First, we will find the launch speed (v) by using the initial conditions:
R = 120 m
θ = 45°
Therefore,
[tex]120\ m = \frac{v^2Sin 90^o}{9.81\ m/s^2}\\\\v = \sqrt{(120\ m)(9.81\ m/s^2)}\\\\v = 34.31\ m/s[/tex]
Now, consider the second scenario to hit the target:
R = 100 m
Therefore,
[tex]100\ m = \frac{(34.31\ m/s)^2Sin2\theta}{9.81\ m/s^2}\\\\Sin2\theta = \frac{(100\ m)(9.81\ m/s^2)}{(34.31\ m/s)^2}\\\\2\theta = Sin^{-1}(0.833)\\\\\theta = \frac{56.44^o}{2}\\\theta = 28.22^o[/tex]
Hence, the correct option is:
C. 28.2 deg
The power of the kettle was 1.5 kW. The 0.2kg heating element took 5 seconds to heat from 20 °C to 100 °C. Calculate the specific heat capacity of water using this information.
Answer:
Specific heat capacity, c = 468.75 J/Kg°C
Explanation:
Given the following data;
Power = 1.5 kW to Watts = 1.5 * 1000 = 1500 Watts
Time = 5 seconds
Mass = 0.2 kg
Initial temperature = 20°C
Final temperature = 100°C
To find specific heat capacity;
First of all, we would have to determine the energy consumption of the kettle;
Energy = power * time
Energy = 1500 * 5
Energy = 7500 Joules
Next, we would calculate the specific heat capacity of water.
Heat capacity is given by the formula;
[tex] Q = mcdt[/tex]
Where;
Q represents the heat capacity or quantity of heat. m represents the mass of an object. c represents the specific heat capacity of water. dt represents the change in temperature.dt = T2 - T1
dt = 100 - 20
dt = 80°C
Making c the subject of formula, we have;
[tex] c = \frac {Q}{mdt} [/tex]
Substituting into the equation, we have;
[tex] c = \frac {7500}{0.2*80} [/tex]
[tex] c = \frac {7500}{16} [/tex]
Specific heat capacity, c = 468.75 J/Kg°C
Two drums of the same size and same height are taken.
i)what will be the difference in liquid pressure on their bases if A of them is completely filled and B is half filled and kept at the same place.
ii) what will be the difference in liquid pressure on their bases if both A and B are filled with water completely but one of them is kept at nepal and another in india?why?
iii) what will be the difference in liquid pressure on their bases if A is filled with water and B is filled with salty water and kept at delhi in the same position?why?
Answer:
i) The pressure acting on the base of B will be half the pressure acting on the base of A
ii) The pressure acting on the base of B will be the same as the pressure acting on the base of A
iii) The pressure on the base of drum A will be slightly less than the pressure on the base of drum B
Explanation:
The pressure acting on the base of the drum, P = h·ρ·g
Where;
h = The level of the liquid in the drum
[tex]h_{max}[/tex] = The height of the drums
ρ = The density of the liquid in the drum
g = The acceleration due to gravity ≈ 9.81 m/s²
i) If A is completely filled, we have [tex]h_A[/tex] = [tex]h_{max}[/tex]
Therefore, [tex]P_A[/tex] = [tex]h_{max}[/tex]×[tex]\rho_{liquid}[/tex]×g
If B is half filled, we have, [tex]h_B[/tex] = (1/2)·[tex]h_{max}[/tex]
[tex]P_B[/tex] = (1/2) × [tex]h_{max}[/tex]×[tex]\rho_{liquid}[/tex]×g
Therefore, [tex]P_B[/tex] = (1/2) × [tex]P_A[/tex]
The pressure acting on the base of B will be half the pressure acting on the base of A
ii) If both A and B are each filled with water (the same liquid), then the pressure on their bases will be [tex]P_A[/tex] = [tex]h_{max}[/tex]×[tex]\rho_{water}[/tex]×g = [tex]P_B[/tex], the same, given that the acceleration due to gravity, g, is constant and the same in Nepal and India
iii) If A is filled with water, and B is filled with salty water, we have that, the density of salty water is slightly higher than water, therefore, we get;
[tex]P_A[/tex] = [tex]h_{max}[/tex]×[tex]\rho_{water}[/tex]×g < [tex]P_B[/tex] =
The pressure on the base of drum A will be less than the pressure on the base of drum B.
Please help me with this!!!
Answer:
Its all about figuring out what numbers you times by
Explanation:
soooooooooo just x the numbers until you get it right, and i'm guessing your in a school soooo ask your teacher aswell :)
In an experiment the mass of a calorimeter is 36.35 g . Express in micrometer ,millimetre and kg.
Answer:
1. 36.35 g = 36.35E15 micrometer.
II. 36.35 g = 363.5 millimetre.
III. 36.35 g = 0.03635 kilogram.
Explanation:
Given the following data;
Mass of calorimeter = 36.35 gramsTo convert the mass in grams (g) to;
I. Micrometer
Conversion:
1 g = 1 exp 15 um
36.35 g = X um
Cross-multiplying, we have;
X = 36.35 * 1 exp 15 = 36.35 exp 15 um
36.35 g = 36.35E15 micrometer
II. Millimetre
Conversion:
1 g = 1 milliliter
36.35 g = X milliliter
Cross-multiplying, we have;
X = 36.35 * 1 = 36.35 milliliter
Next, we would convert milliliter to millimetre;
1 milliliter = 10 millimetre
36.35 milliliter = X millimetre
Cross-multiplying, we have;
X = 36.35 * 10 = 363.5 millimetre
36.35 g = 363.5 millimetre
III. Kilogram
Conversion:
1000 grams = 1 kilogram
36.35 g = X kilogram
Cross-multiplying, we have;
X * 1000 = 36.35 * 1
Dividing both sides by 1000, we have;
X = 36.35/1000 = 0.03635 kilogram
36.35 g = 0.03635 kilogram
Note:
g is the symbol for grams.Exp (E) means exponential = 10um is the symbol for micrometer.10. If the mass of the Earth is... increased by a factor of 2, then the Fgrav is ______________ by a factor of _______. ... increased by a factor of 3, then the Fgrav is ______________ by a factor of _______. ... decreased by a factor of 4, then the Fgrav is ______________ by a factor of _______.
Answer:
If the mass of the Earth is increased by a factor of 2, then the Fgrav is increased by a factor of 2.
If the mass of the earth is increased by a factor of 3, then Fgrav is increased by a factor of 3.
If the mass of the earth is decreased by a factor of 4, then the Fgrav is decreased by a factor of 4
Explanation:
In order to solve this question, we must take into account that the force of gravity is given by the following formula:
[tex]F_{g0}=G \frac{mM_{E0}}{r^{2}}[/tex]
So if the mass of the earth is increased by a factor of 2, this means that:
[tex]M_{Ef}=2M_{E0}[/tex]
so:
[tex]F_{gf}=G \frac{2mM_{E0}}{r^{2}}[/tex]
Therefore:
[tex]\frac{F_{gf}}{F_{g0}}=\frac{G \frac{2mM_{E0}}{r^{2}}}{G \frac{mM_{E0}}{r^{2}}}[/tex]
When simplifying we end up with:
[tex]\frac{F_{gf}}{F_{g0}}=2[/tex]
so if the mass of the Earth is increased by a factor of 2, then the Fgrav is increased by a factor of 2.
If the mass of the earth is increased by a factor of 3
So if the mass of the earth is increased by a factor of 2, this means that:
[tex]M_{Ef}=3M_{E0}[/tex]
so:
[tex]F_{gf}=G \frac{3mM_{E0}}{r^{2}}[/tex]
Therefore:
[tex]\frac{F_{gf}}{F_{g0}}=\frac{G \frac{3mM_{E0}}{r^{2}}}{G \frac{mM_{E0}}{r^{2}}}[/tex]
When simplifying we end up with:
[tex]\frac{F_{gf}}{F_{g0}}=3[/tex]
so if the mass of the Earth is increased by a factor of 3, then the Fgrav is increased by a factor of 3.
If the mass of the earth is decreased by a factor of 4
So if the mass of the earth is decreased by a factor of 4, this means that:
[tex]M_{Ef}=\frac{M_{E0}}{4}[/tex]
so:
[tex]F_{gf}=G \frac{mM_{E0}}{4r^{2}}[/tex]
Therefore:
[tex]\frac{F_{gf}}{F_{g0}}=\frac{G \frac{mM_{E0}}{4r^{2}}}{G \frac{mM_{E0}}{r^{2}}}[/tex]
When simplifying we end up with:
[tex]\frac{F_{gf}}{F_{g0}}=\frac{1}{4}[/tex]
so if the mass of the Earth is decreased by a factor of 4, then the Fgrav is decreased by a factor of 4.