Answer:
The magnitude of the net electric field inside the solution is 3.704 N/C
Explanation:
Given;
average drift speed, v = 3 x 10⁻⁷ m/s
mobility of the bromide ions, μ = 8.1 x 10⁻⁸ (m/s)(N/C)
The magnitude of the net electric field inside the solution is given by the equation below;
[tex]E = \frac{v}{\mu}[/tex]
where;
E is the magnitude of the net electric field inside the solution
Substitute the given values and solve for E
[tex]E = \frac{v}{\mu}\\\\E = \frac{3*10^{-7}}{8.1*10^{-8}}\\\\ E = 3.704 \ N/C[/tex]
Therefore, the magnitude of the net electric field inside the solution is 3.704 N/C
What does the measurement unit N stand for?
Explanation:
The newton (symbol: N) is the International System of Units (SI) derived unit of force.
Answer:
The newton is the SI unit of force, and is the force which will accelerate one kilogram one metre per second squared. The symbol of the newton in SI is N. The newton is also the unit of weight
Explanation:
I hope it helps
A fully loaded elevator at maximum capacity weighs 2400 lbs. The counterweight weighs 1000 lbs. The elevator always starts from rest at its maximum acceleration of g/4 whether it is going up or down. (a) What force does the wall of the elevator shaft exert on the motor if the elevator starts from rest and goes up
Answer:
2250lb
Explanation:
Using
1000-T=(1000/g)(g/4)
So
T = 750lb
Then
750+F-2400= 2400/9
So F= 2250lb
Emily wanted to see what battery lasted the longest. She put each battery into a clock and recorded the time that the clock stopped. She used Duracell, Energizer, Kroger brand, and EverReady. Iv,Dv, Control, consistent
Answer:
This question is asking to identify the following variables:
Independent variable (IV): Battery
Dependent variable (DV): Time the clock stopped
Constant: Same clock
Control: No stated control
Explanation:
The independent variable in an experiment is the variable that is subject to manipulation or change by the experimenter. In this experiment, the independent variable is the BATTERIES (Duracell, Energizer, Kroger brand, EverReady).
The dependent variable is the variable that responds to the changes made to the independent variable. It is the variable that the experimenter measures. In this case, the dependent variable is the TIME IT TAKES FOR THE CLOCK TO STOP.
Constants or control variable is the variable that the experimenter keeps constant or unchanged for all groups throughout the experiment in order not to influence the outcome of the experiment. The constant in this case is the SAME CLOCK USED.
Control group is the group that does not receive the experimental treatment or independent variable in an experiment. In this case, all groups received a different kind of battery.
PLEASE HURRY!!!
WILL MARK!!!
Which statement describes a difference between the lower mantle and oceanic crust?
Answer:
Its C on edge
Explanation:
trust me
The energy stored in a wooden log transforms when the log is burned. Which of the following explanations BEST describes how the chemical energy stored in the log compares to the heat and light energy produced by burning?
A. chemical energy is the same and additional energy is produced as heat and light.
B. chemical energy is more than the amount of heat and light
C. the amount of chemical energy is less than the amount of heat and light energy
D. the amount of chemical energy equals the amount of heat and light energy.
Answer:
D. the amount of chemical energy equals the amount of heat and light energy.
Explanation:
Given that the first law of thermodynamics affirmed that energy is neither created nor destroyed however, it can be transformed from one form to another. In other words, while, during the transformation of energy, no energy is lost, the input energy is also equal to output energy.
Hence, the chemical energy stored in the log is EQUAL to the heat and light energy produced by burning.
100 POINTS.
PLEASE EXPLAIN YOUR ANSWER.
Explanation:
Draw free body diagrams for each mass.
There are 3 forces on the disk: weight force mg pulling down, normal force N pushing up, and tension force T pulling right.
There are 2 forces on the cylinder: tension force T pulling up and weight force 3mg pulling down.
Sum of forces on the disk in the centripetal direction:
∑F = ma
T = m v²/r
Sum of forces on the cylinder in the vertical direction:
∑F = ma
T − 3mg = 0
T = 3mg
Substituting:
3mg = m v²/r
3gr = v²
v = √(3gr)
Plug in values:
v = √(3 × 10 m/s² × 0.800 m)
v = √24 m/s
v ≈ 4.90 m/s
By what factor is the heat flow increased if a window 0.550 mm on a side is inserted in the door? The glass is 0.450 cmcm, and the glass has a thermal conductivity of 0.80 W/(m⋅K)W/(m⋅K). The air films on the two sides of the glass have a total thermal resistance that is the same as an additional 12.0 cmcm of glass.
This question is incomplete, the complete question is;
A carpenter builds a solid wood door with dimensions 1.95 m × 0.99 m × 4.5 cm . Its thermal conductivity is k=0.120W/(m.K). The air films on the inner and outer surfaces of the door have the same combined thermal resistance as an additional 1.6 cm thickness of solid wood. The inside air temperature is 19.0°C , and the outside air temperature is -6.50°C .
a) What is the rate of heat flow through the door?
b) By what factor is the heat flow increased if a window 0.550 m on a side is inserted in the door? The glass is 0.450 cm , and the glass has a thermal conductivity of 0.80 W/(m.K). The air films on the two sides of the glass have a total thermal resistance that is the same as an additional 12.0 cm of glass.
Answer:
a) the rate of heat flow through the door is 97 watts
b) The factor of increased heat flow is 1.353
Explanation:
Given that;
room dimension = 1.95m × 0.99m × 4.5cm,
thermal conductivity = 0.120 w/m.k
additional thickness of solid wood Δt = 1.6 cm
a)
first we determine the effective thickness of the door;
t = 4.5cm + 1.6 cm = 61 cm ≈ 0.061 m
Now rate of heat flow is given by the relation
Q = KA( (TH -TC)/L)
= 0.12 × (1.95 m × 0.99 m) × ( (19°C - (-6.50°C)) / 0.061m)
= 0.23166 × 418.0327
= 96.8414 watts
Q = 97 watts
therefore the rate of heat flow through the door is 97 watts
b)
by intensity the glass of thickness 0.450 cm
the effective thickness is
L = 0.45cm + 12 cm = 12.45 cm = 0.1245 m
additionally area of glass A = (0.550 m)²
A = 0.3025 m²
Now
Qglass = KA ((TH-TC)/L)
= 0.80 w/m.k × 0.3025 m² × (19°C - (-6.50°C)) / 0.1245m)
= 0.242 × 204.819
Qglass = 49.57 watt
Qwood = KA ((TH-TC)/L)
area of wooden door = (1.95×0.99) - 0.3025 m² = 1.628m²
so Qwood = 0.12 × 1.628 × (19°C - (-6.50°C)) / 0.061m)
= 0.19536 × 418.0327
Qwood = 81.67 watt
Q = Qglass + Qwood
Q = 49.57 watt + 81.67 watt
Q = 131.24 watt
The factor of increased heat flow is;
f = 131.24 watt / 97 watts
f = 1.353
Two planets, Dean and Sam, orbit the Sun. They each have with circular orbits, but orbit at different distances from the Sun. Dean orbits at a greater average distance than Sam. According to Kepler's Third Law, which planet will have a longer orbital period? Group of answer choices Dean Sam Since they both have circular orbits, they will have the same orbital periods. There isn't enough information to tell.
Answer:
The correct answer is Dean has a period greater than San
Explanation:
Kepler's third law is an application of Newton's second law where the force is the universal force of attraction for circular orbits, where it is obtained.
T² = (4π² / G M) r³
When applying this equation to our case, the planet with a greater orbit must have a greater period.
Consequently Dean must have a period greater than San which has the smallest orbit
The correct answer is Dean has a period greater than San
Answer:
According to the law of universal gravitation, any two objects are attracted to each other. The strength of the gravitational force depends on the masses of the objects and their distance from each other.
Many stars have planets around them. If there were no gravity attracting a planet to its star, the planet's motion would carry it away from the star. However, when this motion is balanced by the gravitational attraction to the star, the planet orbits the star.
Two solar systems each have a planet the same distance from the star. The planets have the same mass, but Planet A orbits a more massive star than Planet B.
Which of the following statements is true about the planets?
A.
Planet B will keep orbiting its star longer than Planet A.
B.
Planet A has a longer year than Planet B.
C.
Planet A orbits its star faster than Planet B.
D.
Planet B is more attracted to its star than Planet A.
Explanation:
A Me and Ed's Pizza has 16 slices. John eat 7/12pieces of pizza. Harold
finished 4/23 pieces of pizza. If there was only 23of a piece left over, how
much pizza did Betty eat?
Answer:
Explanation:
Total number of slices in the pizza = 16
Total number ate by John,
J = 7/12 * 16 = 28/3 = 9.3
Total number ate by Harold,
H = 4/23 * 16 = 2.783
Total number left over
L = 1/23 * 16 = 0.696
Total number ate by Betty
B = ?
All we have to do to get the total number eaten by Betty is to sum up that eaten by Harold and John, including the left over, then subtract it from the total pizza slices.
Betty = Total - (Harold + John + Left Over)
Betty = 16 - (9.3 + 2.783 + 0.696)
Betty = 16 - 12.779
Betty = 3.221
Therefore, Betty ate 3.221 of the total pizza as a whole
Newtons third lawWhat action-reaction forces are involved when a rocket engine fires? Why doesnt a rocket need air to push on? Atction force:_______ Reaction Force:________
Answer: action forc roketorce
reaction force is engine fires
Two trains, each having a speed of 33 km/h, are headed at each other on the same straight track. A bird that can fly 60 km/h flies off the front of on train when they are 60 km apart and heads directly for the other train. On reaching the other train, the (crazy) bird flies directly back to the first train, and so forth. What is the total distance the bird travels before the trains collide?
Answer:
66 km
Explanation:
Given that:
The speed of the two trains = 33 km/h
The speed of the bird = 60 km/h
The distance apart between the two trains = 60 km
From the given information, we are being told that the two trains are going at the same speed. Therefore, they will definitely collide at 30 km
We know that:
speed of the train = distance traveled × time
Making the time t the subject of the formula:
time = speed of the train / distance traveled
time = 30 km / 33 km/h
time = 0.909 / hr
Thus, the bird flying at a given speed of 60 km/h in a time of 0.909 / hr will cover a total distance of :
distance (d) = speed of the bird/ time
distance (d) = [tex]\dfrac{60 \ km/hr}{0.909 \ /hr}[/tex]
distance (d) = 66 km
A solid, insulating sphere of radius 40.0 cm has positive charge distributed uniformly throughout its volume. The electric field at a distance of 80.0 cm from the center of the sphere is 6.00 N/C. What is the electric field at a distance of 20.0 cm from the center of the sphere (in N/C)
Answer:
The correct answer to the following question will be "12.0 N/C".
Explanation:
As we know,
Charged from the inside of the sphere throughout consideration of the electrical field or inside sphere.
⇒ [tex]E_0=\frac{KQ}{r_0^{2}}[/tex]
Now,
⇒ [tex]Q=\frac{E_0r_0^{2}}{k}[/tex]
On putting the values in the above formula, we get
⇒ [tex]=\frac{6.00\times 80.0}{9\times 10^9}(\frac{10^{-2}}{2})^2[/tex]
⇒ [tex]=4.267\times 10^{-10} \ C[/tex]
Electric field within the sphere at that same distance of 20.0 cm from either the core.
⇒ [tex]E_i=\frac{kQr_i}{R^3}[/tex]
On putting the values, we get
⇒ [tex]=\frac{(9\times 10^9)(4.267\times 10^{-10})(20.0)}{(80.0)^3(\frac{10^{-2}}{1} )^2}[/tex]
⇒ [tex]=12.0 \ N/C[/tex]
8. An object that is traveling 50m/s slows down with an
acceleration rate of -3.5m/s/s. This took place over a period of 4s.
What was the objects final velocity? *
Answer:
36 m/s
Explanation:
Given:
v₀ = 50 m/s
a = -3.5 m/s²
t = 4 s
Find: v
v = at + v₀
v = (-3.5 m/s²) (4 s) + 50 m/s
v = 36 m/s
How is a scientific law different than a scientific theory ?
Answer: scientific law is the description of an observed phenomenon. It doesn't explain why the phenomenon exists or what causes it. The explanation of a phenomenon is called a scientific theory
hope this helps
plz mark brainleist
What is the minimum amount of energy required to completely melt a 7.25-kg lead brick which has a starting temperature of 18.0 °C? The melting point of lead is 328 °C. The specific heat capacity of lead is 128 J/(kg∙C°); and its latent heat of fusion is 23,200 J/kg.a. 1.68 × 105 J b. 2.88 × 105 J c. 4.56 × 105 J d. 5.96 × 105 J e. 7.44 × 105 J
Answer: c. 4.56 × 105 J
Explanation:
Given that
mass of lead brick, m= 7.25kg
Temperature T1 = 18.0 °C
Temperature T2 = 328 °C
specific heat capacity of lead, c = 128 J/(kg∙C°)
latent heat of fusion Lfusion =23,200 J/kg
Amount of energy Q =?
Using the formulae
Amount of energy ,Q =mc ( T2-T1)+ mLfusion
7.25kg x 128 J/(kg∙C°) x (328-18°C) + 7.25kg x 23200 J/kg
=455880J
=4.56 x 10^5 J
The minimum amount of energy required is 4.56 × 10^5 J.
Calculation of the minimum amount of energy:Since
mass of lead brick, m= 7.25kg
Temperature T1 = 18.0 °C
Temperature T2 = 328 °C
specific heat capacity of lead, c = 128 J/(kg∙C°)
latent heat of fusion =23,200 J/kg
So
we know that
Amount of energy ,Q =mc ( T2-T1)+ mLfusion
7.25kg x 128 J/(kg∙C°) x (328-18°C) + 7.25kg x 23200 J/kg
=455880J
=4.56 x 10^5 J
hence, The minimum amount of energy required is 4.56 × 10^5 J.
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What force causes oppositely charged particles to attract each other?
A. Magnetic force B. Compression
C. Electrical Force D. Gravity
Answer:
The electromagnetic force.
Answer:
It is electrical force
Explanation:
i got it wrong on A P E X with magnetic hope this helps!
3. Why do we revise laws?
Answer:
Everyone is held accountable to the same laws, and those laws protect our fundamental rights. This is the foundation of the rule of law in the United States. We need new laws because life and the world keep revolving and changing. We therefore need new laws to match the latest trending events in the country.
in a closed system three objects have the following momentum: 11 kg* m/s, -65 kg*m/s and -100 kg m/s. the objects collide and move together. What is the total momentum after the collision? 55 kg*m/s 275 kg * m/s -55kg * m/s -275 kg m/2
Explanation:
The momentum of the three objects are as follow :
11 kg-m/s, -65 kg-m/s and -100 kg-m/s
Before collision, the momentum of the system is :
[tex]P_i=11+(-65)+(-100)\\\\P_i=-154\ kg-m/s[/tex]
After collison, they move together. It means it is a case of inelastic collision. In this type of collision, the momentum of the system remains conserved.
It would mean that, after collision, momentum of the system is equal to the initial momentum.
Hence, final momentum = -154 kg-m/s.
Philip drives his car at a velocity of 28 m/s he applies the break which slows the vehicle down at a rate of six. 4 m/s2 and it causes it’s to slow to stop how long does it take for the car to stop answer to the nearest 10th?
Two ropes are attached to a tree, and forces of F⃗ 1=2.0iˆ+4.0jˆN and F⃗ 2=3.0iˆ+6.0jˆN are applied. The forces are coplanar (in the same plane). (a) What is the resultant (net force) of these two force vectors? (b) Find the magnitude and direction of this net force.
Answer:
We can see that the 2 forces are being applied in the same direction
So the resultant force will be larger than the given forces
Resultant force = (2i + 4j) + (3i + 6j)
R = 5i + 10j
Magnitude of the resultant force :
R² = i² + j²
R² = 25 + 100
R = [tex]\sqrt{125}[/tex] = [tex]5\sqrt{5}[/tex]
Direction of the resultant force:
Tan Θ = Vertical component of force / Horizontal component of force
Tan Θ = 10 / 5
Tan Θ = 2
Θ = Arctan (2)
Θ = 63.4 degrees
Direction is 63.4 degrees in the NE direction
Kindly mark Brainliest
A) The resultant ( net force ) = 5i + 10 j
B) The magnitude and direction of this net force
magnitude of net force = 5√5 direction of net force = 63.4° NEGiven that :
The vector forces are coplanar ( In the same plane and direction )
A) resultant force = (2i + 4j) + (3i + 6j) = ( 2 + 3 ) i + ( 4 + 6 ) j
= ( 5 i + 10 j )
B ) Calculate The magnitude and direction of the net force
i) Magnitude of the force
R² = ( i² + j² )
= ( 5² + 10² )
= 25 + 100
∴ R = √ (25 + 100) = 5√5
ii) Determine the direction of resultant force
Tan ∅ = opposite / adjacent ( vertical force ( j ) / horizontal force ( i ) )
= 10 / 5 = 2
∅ = arctan ( 2 ) ≈ 63.4°
∴ direction of resultant force = 163.4° NE
Hence we can conclude that the resultant ( net force ) = 5i + 10 j and The magnitude and direction of this net force
magnitude of net force = 15 direction of net force = 1.107° NELearn more : https://brainly.com/question/24034108
It was once recorded that a Jaguar
left skid marks that were 290 min
length. Assuming that the Jaguar
skidded to a stop with a constant
acceleration of -8.90 m/s2,
determine the speed of the Jaguar
before it began to skid.
Answer:
71.85 m/s
Explanation:
Given the following :
Length of skid marks left by jaguar (s) = 290 m
Skidding Acceleration (a) = - 8.90m/s²
Final velocity of jaguar (v) = 0
Speed of Jaguar before it Began to skid =?
Hence, initial speed of jaguar could be obtained using the formula :
v² = u² + 2as
Where
v = final speed of jaguar ; u = initial speed of jaguar(before it Began to skid) ; a = acceleration of jaguar ; s = distance /length of skid marks left by jaguar
0² = u² + (2 × (-8.90) × 290)
0 = u² + (-5,162)
u² = 5162
Take the square root of both sides
u = √5162
u = 71.847 m/s
u = 71.85m/s
3. Does the Sun's light that reaches Earth produce a true continuous rainbow? If not, what colors
would you expect our sun's light to be missing if the outer atmosphere is pure Hydrogen?
Answer:
when there is no water in the atmosphere or when no drops are formed there is no rainbow..
he hydrogen transition lines would be missing in the visible range, the RED region
Explanation:
The sunlight that reaches the Earth is scattered by the atmosphere and radiated, as the atmosphere has mainly nitrogen, the radiated light is blue, this light does not produce a rainbow.
The sunlight must reach a drop of water that disperses the colors according to the refractive index of the water and in this way produces a rainbow, so when there is no water in the atmosphere or when no drops are formed there is no rainbow..
If the atmosphere were composed of Hydrogen, the hydrogen transition lines would be missing in the visible range, this corresponds to the so-called Balmer series and they are in the RED light region.
At which point in time does an object with the motion represented in the graph have an
instantaneous acceleration of -2 m/s^2?
Answer:
4s.
Explanation:
Hello,
In this case, considering that the instantaneous acceleration is computed via the change in the velocity divided by the change in the time, at 4 s we can evidence that the instantaneous acceleration is -2m/s² since the initial velocity at t=0s is 8m/s and at t=4s the velocity is 0 m/s, meaning that such decrease accounts for a deceleration process which is represented by a negative acceleration, and the value is:
[tex]a=\frac{0m/s-8m/s}{4s-0s}\\ \\a=-2m/s^2[/tex]
Best regards.
Which of the following are evidence of what happened in the past?
A.
volcanoes and plate movement
B.
weathering and rain
C.
weather and erosion
D.
earthquakes and climate
Answer:
A
Explanation:
volcanoes and plate movement
Car B is following car A as they are moving along a straight path with vA=40 mph and vB=45 mph. At the moment when the distance between the cars is 45 ft brakes are applied simultaneously in both cars. Car A decelerates with aA=−22 ft/s2 and car B with aB=−20 ft/s2. What is the distance between the cars when they are both stopped?
Answer:
s = 14.3 ft
Explanation:
First we need to calculate the distances traveled by both the cars. We use third equation of motion for that:
2as = Vf² - Vi²
where,
a = acceleration
s = distance
Vf = Final Velocity
Vi = Initial velocity
FOR CAR A:
Vi = Va = (40 mph)(5280 ft/1 mile)(1 h/3600 s) = 58.66 ft/s
Vf = 0 ft/s
a = aA = - 22 ft/s²
s = sa = ?
Therefore,
2(- 22 ft/s²)(sa) = (58.66 ft/s)² - (0 ft/s)²
sa = 78.2 ft
FOR CAR B:
Vi = Vb = (45 mph)(5280 ft/1 mile)(1 h/3600 s) = 66 ft/s
Vf = 0 ft/s
a = aB = - 20 ft/s²
s = sb = ?
Therefore,
2(- 20 ft/s²)(sb) = (66 ft/s)² - (0 ft/s)²
sb = 108.9 ft
Since, the car A was initially 45 ft ahead of car B. Therefore,
sa = 45 ft + 78.2 ft = 123.2 ft
Now, the distance between the cars will be:
s = sa - sb
s = 123.2 ft - 108.9 ft
s = 14.3 ft
A displacement vector points in a direction of θ = 23° left of the positive y-axis. The magnitude of this vector is D = 155 m. Refer to the figure. Enter an expression for the x-component vector, Dx, in terms of D, θ, and the unit vectors i and j.
Answer:
Dₓ = -155 sin 23° i + 0 j
Explanation:
The diagram showing the vector has been attached to this response.
As shown in the diagram,
The vector D has an x-component (also called horizontal component) of -D sinθ i. i.e
Dₓ = -D sin θ i [The negative sign shows that D lies in the negative x direction]
Where;
D = magnitude of D = 155m
θ = direction of D = 23°
Therefore;
Dₓ = -155 sin 23° i
Since Dₓ represents the x component, its unit vector, j component has a value of 0.
Therefore, Dₓ can be written in terms of D, θ and the unit vectors i and j as follows;
Dₓ = -155 sin 23° i + 0 j
The x-component of the vector is written as [tex]D_x = (-60.56 \ i + 0j)\ m[/tex].
The given parameters;
direction of the vector, θ = 23°magnitude of the vector, D = 155 mThe x-component of the vector is calculated as;
[tex]D_x = D \ \times sin\theta \\\\D_x = 155 \times sin(23)\\\\D_x = 60.56 \ m[/tex]
Since the direction of the vector is in negative x-axis, the x-component of the vectors is written as;
[tex]D_x = (-60.56 \ i + 0j)\ m[/tex]
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Which figure shows vector A - vector B?
Answer:
The first and the last answer
An elephant pushes with 200 N on a load of trees. it then pushes these trees for 10 N. How much work did the elephant do?
Answer:
the answer is 2000Nm
Explanation:
wprk done = force × distance moved
w.d = 200N × 10m
w.d = 2000Nm
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A car is going 70 MPH down the road and hits a tree. The passenger is not wearing a seatbelt and goes through the windshield, explain why the driver remained in the car and the passenger did not. Be sure reference Newton’s first law in your explanation
Answer:
Inertia is the reason that people in cars need to wear seat belts. Instead, the riders continue moving forward with most of their original speed because of their inertia. If the driver is wearing a seat belt, the seat belt rather than the windshield applies the unbalanced force that stops the driver's forward motion.
Answer:
Explanation:
The driver was able to stay in the car because he or she had a seat belt on, the passenger did not have a seat belt on, therefore they were not able to stay in the car. Newton’s first law states “An object in motion stays in motion unless acted on by another force”. Therefore the passenger was yoinked out of the car.
b. How tar from the li u
b. Obtain the value of g from the motion of the moon assuming that its period
of rotation round the earth is 27 days 8 hours and the radius of its orbit is
60.1 times the radius of the earth.
0.
7.2 m. Compute
Answer:
Approximately [tex]9.79\; \rm m \cdot s^{-2}[/tex] at the surface of the earth, given that the radius of the earth is known to be approximately [tex]6.371\times 10^{6}\; \rm m[/tex]. Assumptions: the earth is a sphere, the orbit of the moon is circular, and that the gravitational pull of the earth is the only force on the moon.
Explanation:
Convert the orbital period of the moon around the earth to seconds:
[tex]\begin{aligned}t &= (27\; \text{day} \times 24\; \text{hours} \cdot \text{day}^{-1} + 8\; \text{hour})\times 3600\; \rm \text{s}\cdot \text{hour}^{-1}\\ &= 2361600\; \text{s} \end{aligned}[/tex].
Calculate the angular velocity of the moon around the earth using the formula[tex]\displaystyle \text{angular velocity} = \frac{2\pi}{\text{orbital period}}[/tex]:
[tex]\begin{aligned}\omega = \frac{2\pi }{t} = \frac{2\pi}{2361600\; \rm s} \approx 2.66056\times 10^{-6}\; \rm s^{-1}\end{aligned}[/tex].
Let [tex]m(\text{moon})[/tex] denote the mass of the moon. Let [tex]g[/tex] denote the gravitational field strength at the surface of the earth (not at the position of the moon.) Let [tex]r[/tex] denote the radius of the earth.
The orbital radius of the moon would thus be [tex]60.1\, r[/tex]. Note that in the gravitational field due to a single spherical mass, the field strength is inversely proportional to the square of distance from the center of that mass.
The surface of the earth is at a distance of [tex]r[/tex] away from the center of the earth. The distance between the moon and the center of the earth would then be [tex]60.1[/tex] times that number (that is: [tex]60.1\, r[/tex].)The gravitational field at the surface of the earth is [tex]g[/tex]. Therefore, at the position of the moon ([tex]60.1[/tex] times further away from the center of the earth compared to the earth surface,) the gravitational field strength would be:
[tex]\displaystyle \left( \frac{r^2}{(60.1\, r)^2} \right)\, g = \frac{g}{60.1^2}[/tex],
Hence, the gravitational pull of the earth on the moon would be [tex]\displaystyle \frac{m(\text{moon})\, g}{60.1^2}[/tex].
Assume that the gravitational pull of the earth is the only force on the moon. That gravitational pull would then be the equal (in size) to the net force on the moon. That is:
[tex]\displaystyle \text{Net force on the moon} = \frac{m(\text{moon})\, g}{60.1^2}[/tex].
On the other hand, the rotation (assumed to be perfectly circular) of the moon would give the net force on the moon in terms of:
the mass of the moon, the angular speed of the rotation, andthe radius of the orbit.[tex]\displaystyle \text{Net force on the moon} = m(\text{moon})\, \omega^2\, (60.1\, r)[/tex].
Combine the two expressions for the net force on the moon to obtain an equation for [tex]g[/tex]:
[tex]\displaystyle \frac{m(\text{moon})\, g}{60.1^2} = m(\text{moon})\, \omega^2\, (60.1\, r)[/tex].
Simplify and solve for [tex]g[/tex]:
[tex]\displaystyle g = 60.1^3 \, \omega^2\, r[/tex].
The angular velocity of this rotation, [tex]\omega[/tex], has already been found to be approximately [tex]2.66056\times 10^{-6}\; \rm s^{-1}[/tex]. Look up the radius of the earth: [tex]r = 6.371\times 10^{6}\; \rm m[/tex]. Evaluate this expression for [tex]g[/tex]:
[tex]\begin{aligned}g &= 60.1^3 \, \omega^2\, r \\ &\approx 60.1^3 \times \left( 2.66056\times 10^{-6}\; \rm s^{-1}\right) \times 6.371\times 10^{6}\;\rm m \\ &\approx 9.79\; \rm m \cdot s^{-1}\end{aligned}[/tex].
