Answers
Geothermal energy can be used only if an energy source is present.
Mining is required to use geothermal energy.
The depth of mining increases earthquake risk.
Thus, it is difficult to find geothermal energy sources that are close to the surface.
Related Questions
Sunita uses a lever of length 5m to lift a piece of stone weighing 1000N.
If the distance of the load from the fulcrum is Im, how much effort does she
apply to lift the piece of stone
Answers
Answer:
F = 250 [N] (Force exerted by Sunita)
Explanation:
First we must understand the use of the lever, in the attached picture we see that it is fulcrum and other features.
The moment that the load exerts with respect to the fulcrum should be calculated, as the distance is 1 [m].
\(M=F*d\\M=1000*1\\M=1000[N*m]\)
Now Sunita must exert the same moment using the remaining distance (4 [m]).
\(1000=F_{sunita}*4\\F_{sunita}=1000/4\\F_{sunita}=250 [N]\)
Can someone explain how to do the algebra for this question? I know everything else, I just don’t know how to rearrange the question to solve for v.
Answers
Answer:
Refer to the step-by-step Explanation.
Step-by-step Explanation:
Simplify the equation with given substitutions,
Given Equation:
\(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2\)
Given Substitutions:
\(\omega=v/R\\\\ \omega_{_{0}}=v_{_{0}}/R\\\\\ I=(2/5)mR^2\)\(\hrulefill\)
Start by substituting in the appropriate values: \(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2 \\\\\\\\\Longrightarrow mgh+(1/2)mv^2+(1/2)\bold{[(2/5)mR^2]} \bold{[v/R]}^2=(1/2)mv_{_{0}}^2+(1/2)\bold{[(2/5)mR^2]}\bold{[v_{_{0}}/R]}^2\)
Adjusting the equation so it easier to work with.\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)
\(\hrulefill\)
Simplifying the left-hand side of the equation:
\(mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)
Simplifying the third term.
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2}\cdot \dfrac{2}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)
\(\\ \boxed{\left\begin{array}{ccc}\text{\Underline{Power of a Fraction Rule:}}\\\\\Big(\dfrac{a}{b}\Big)^2=\dfrac{a^2}{b^2} \end{array}\right }\)
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2 \cdot\dfrac{v^2}{R^2} \Big]\)
"R²'s" cancel, we are left with:
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5}mv^2\)
We have like terms, combine them.
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{7}{10} mv^2\)
Each term has an "m" in common, factor it out.
\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)\)
Now we have the following equation:
\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)
\(\hrulefill\)
Simplifying the right-hand side of the equation:
\(\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac12\cdot\dfrac25\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\cdot\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15mv_{_{0}}^2\Big\\\\\\\\\)
\(\Longrightarrow \dfrac{7}{10}mv_{_{0}}^2\)
Now we have the equation:
\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)
\(\hrulefill\)
Now solving the equation for the variable "v":
\(m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)
Dividing each side by "m," this will cancel the "m" variable on each side.
\(\Longrightarrow gh+\dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2\)
Subtract the term "gh" from either side of the equation.
\(\Longrightarrow \dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2-gh\)
Multiply each side of the equation by "10/7."
\(\Longrightarrow v^2=\dfrac{10}{7}\cdot\dfrac{7}{10}v_{_{0}}^2-\dfrac{10}{7}gh\\\\\\\\\Longrightarrow v^2=v_{_{0}}^2-\dfrac{10}{7}gh\)
Now squaring both sides.
\(\Longrightarrow \boxed{\boxed{v=\sqrt{v_{_{0}}^2-\dfrac{10}{7}gh}}}\)
Thus, the simplified equation above matches the simplified equation that was given.
The Great Lakes are all part of what? The Mississippi River The St. Lawrence Seaway A large body of salt lakes The Missouri River
Answers
Answer:
St Lawrence Sea way
Explanation:
The great lake connects the middle of North America which is at the Canada-United states border connecting to the Atlantic Ocean through the St Lawrence River.
In hiking, what fitness component is required of you
Answers
When jumping straight down, you can be seriously injured if you land stiff-legged. One way to avoid injury is to bend your knees upon landing to reduce the force of the impact. A 63.5-kg man just before contact with the ground has a speed of 7.89 m/s. (a) In a stiff-legged landing he comes to a halt in 3.99 ms. Find the magnitude of the average net force that acts on him during this time. (b) When he bends his knees, he comes to a halt in 0.205 s. Find the magnitude of the average net force now. (c) During the landing, the force of the ground on the man points upward, while the force due to gravity points downward. The average net force acting on the man includes both of these forces. Taking into account the directions of the forces, find the magnitude of the force applied by the ground on the man in part (b).
Answers
Answer:
a) F = 1.26 10⁵ N, b) F = 2.44 10³ N, c) F_net = 1.82 10³ N directed vertically upwards
Explanation:
For this exercise we must use the relationship between momentum and momentum
I = Δp
F t = p_f -p₀
a) It asks to find the force
as the man stops the final velocity is zero
F = 0 - p₀ / t
the speed is directed downwards which is why it is negative, therefore the result is positive
F = m v₀ / t
F = 63.5 7.89 / 3.99 10⁻³
F = 1.26 10⁵ N
b) in this case flex the knees giving a time of t = 0.205 s
F = 63.5 7.89 / 0.205
F = 2.44 10³ N
c) The net force is
F_net = Sum F
F_net = F - W
F_net = F - mg
let's calculate
F_net = 2.44 10³ - 63.5 9.8
F_net = 1.82 10³ N
since it is positive it is directed vertically upwards
Popeye the Sailor man, who has a mass of 85 kg, ran ( at a constant rate ) up a flight of stairs that are 3.55 m high in 6 seconds. How many watts of power did he generate during his run ?
Answers
Given data
*The given mass of the Sailorman is m = 85 kg
*The given height is h = 3.55 m
*The given time is t = 6 s
*The value of the acceleration due to gravity is
\(g=9.8m/s^2\)The formula for the power generated by the Sailorman during his run is given as
\(\begin{gathered} P=\frac{W}{t} \\ =\frac{\text{mgh}}{t} \end{gathered}\)*Here W is the work done
\(\begin{gathered} P=\frac{85\times9.8\times3.55}{6} \\ =492.85\text{ W} \end{gathered}\)Please help I’m confused on this
Answers
Answer:
inversely proportional to
a package initially thrown horizontally at 40m/s at a height of 100m above the ground.Find the horizontal and vertical components of the velocity just before it hits the ground
Answers
Answer:
\(V = < 40 m/s, -20\sqrt{5}, 0 >\)
Explanation:
To find the time it takes for the package to hit the ground:
\(yf = yi +Vi*t + 0.5*a*t^2\\0 = 100 + 0 +0.5*-10*t^2\\t = \sqrt{20}s\)
The horizontal component is 40 m/s before it hits the ground because there are no external forces acting on it.
To get the vertical velocity:
\(Vf = Vi + a*t\\Vf = 0 + -10*\sqrt{20} \\Vf = -20\sqrt{5}\)
In terms of electric pressure, describe a charged capacitor.
Answers
Answer: The capacitor is fully charged when the voltage of the power supply is equal to that at the capacitor terminals. This is called capacitor charging; and the charging phase is over when current stops flowing through the electrical circuit.
If the Universe was born at the Big Bang, what existed before then?
Answers
Hey,
QUESTION)This is a complicated question that would be debated by many physicists. How to answer this question when we are struggling with the genesis of the universe? Many theories on the origin of the universe have been put forward, but the Bing Bang is probably, or at least to date, the most likely theory. If today the universe is expanding, some astronomers hypothesise that before the Bing Bang the universe already existed but that it was condensing, according to this hypothesis the Bing Bang would correspond to the limit point of compression of the universe.
But if we remain in the traditional theory the Bing Bang is at the origin of all the matter we know, as well as light. Before the Bing Bang, in other words before the universe, there was NOTHING.
4.2 Determine the reactions of the loads L and R. ↓ 5m
↓ 7 kN 6m 3 kN 4m R (8)
Answers
The reaction of load L is 0 (no horizontal force), and the reaction of load R is 10 kN (vertical upward force).
How to find reaction?To determine the reactions of the loads L and R, consider the equilibrium of the forces acting on the structure.
First, analyze the vertical equilibrium. The sum of the vertical forces must be zero:
ΣFy = R − 7 kN − 3 kN
ΣFy = 0
This gives:
R = 10kN
Next, analyze the horizontal equilibrium. The sum of the horizontal forces must be zero:
ΣFx = L
ΣFx = 0
This indicates that there is no horizontal force acting on the structure.
Therefore, the reaction of load L is zero (no horizontal force), and the reaction of load R is 10 kN (vertical upward force).
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Consider a system of two charges of magnitude 2 × 10-7 C and 4.5 × 10-7 C which is acted upon by a force of 0.1 N. What is the distance between the two charges?
Answers
To find the distance between two charges, we can use Coulomb's law, which states that the force between two charges is proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
The formula for Coulomb's law is:
F = (k * |q1| * |q2|) / r^2
where:
F is the force between the charges,
k is the electrostatic constant (k = 8.99 × 10^9 N m^2/C^2),
|q1| and |q2| are the magnitudes of the charges, and
r is the distance between the charges.
Given:
|q1| = 2 × 10^-7 C
|q2| = 4.5 × 10^-7 C
F = 0.1 N
k = 8.99 × 10^9 N m^2/C^2
We can rearrange the equation to solve for r:
r^2 = (k * |q1| * |q2|) / F
Plugging in the values:
r^2 = (8.99 × 10^9 N m^2/C^2 * 2 × 10^-7 C * 4.5 × 10^-7 C) / 0.1 N
r^2 = (8.99 × 2 × 4.5) * (10^9 * 10^-7 * 10^-7) / 0.1
r^2 = 80.91 * (10^9 * 10^-7 * 10^-7) / 0.1
r^2 = 80.91 * 10^(-7 + 9 - 1)
r^2 = 80.91 * 10^1
r^2 = 809.1
Taking the square root of both sides:
r = √809.1
r ≈ 28.46
Therefore, the distance between the two charges is approximately 28.46 units.
If the average hang time of a professional football kick is 4.60 s, then determine the average maximum height.
The average maximum height is what?
Answers
The average maximum height will be 103.7m.
What is a Projectile?A projectile is defined as an object that has an initial velocity and follows a path that dependent on the gravitational acceleration.
The gravitational force initially will act on the opposite direction until it reach the maximum height, and right after that, the gravitational force will accelerate the speed of the projectile.
The formular used will be;
\(H = \frac{1}{2} gt^{2}\)
In this case, the initial velocity u = 0;
where g = 9.8m/s2
t = 4.6s
\(H = \frac{1}{2} (9.8)(4.6)^{2}\)
H = 4.9 x 21.16
H = 103.7m.
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For the system of Problem3.18, determine the amount of energy transfer by heat, in kJ per kg of refrigerant.[Problem3.18A closed, rigid tank contains a two‐phase liquid–vapor mixture of Refrigerant 22 initially at−20°Cwith a quality of 50.36%. Energy transfer by heat into the tank occurs until the refrigerant is at a final pressure of 6 bar. Determine the final temperature, in°C. If the final state is in the superheated vapor region, at what temperature, in°C, does the tank contain only saturated vapor?]
Answers
Answer:
35.625° C
Explanation:
See attachment
a) Final temperature is 35.625° C
b) 0°
What does g stand for
Group of answer choices
gravity
The acceleration of gravity
The force of gravity
Answers
Answer:
the acceleration of gravity.
Answer:
g stand for the acceleration of gravity .
Explanation:
WHAT IS THE MEAING OF- Grouping Data
Answers
Grouping data refers to the process of categorizing or organizing data based on specific criteria or attributes.
It involves grouping similar data points together to gain a better understanding of patterns, relationships, and trends within the dataset. By grouping data, you can simplify complex information and derive meaningful insights from large amounts of data. The purpose of grouping data is to create subsets or clusters that share common characteristics.
This enables easier analysis, summarization, and comparison of data within each group. Grouping can be performed on various types of data, such as numerical, categorical, or time-based data. Grouping data allows for the exploration of data at different levels of granularity.
For example, you can group sales data by region to analyze regional performance, or group customer data by demographics to identify specific customer segments. This process helps in identifying outliers, detecting patterns, and making data-driven decisions.
Common techniques for grouping data include using functions like GROUP BY in SQL or utilizing data visualization tools to create charts or graphs that illustrate the grouped data. Grouping can be applied in various fields, such as marketing, finance, healthcare, and research, to uncover insights and support decision-making processes.
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William B. Hartsfield was a man of humble origins who became one of the greatest mayors of Atlanta. He served as mayor for six terms (1937–41, 1942–61), longer than any other person in the city's history. Hartsfield held office during a critical period when the color line separating the races began to change and the city grew . . . to a metropolitan population of one million. He is credited with developing Atlanta into the aviation powerhouse that it is today . . . . . . . On August 30, 1961, the city peacefully integrated its public schools. As a result, Atlanta began to acquire its reputation as "A City Too Busy to Hate."
–New Georgia Encyclopedia
During Hartsfield’s time in office, Atlanta became known as "A City Too Busy to Hate.” What factors supported this nickname? Check all that apply.
The city integrated its schools.
Atlanta became a leader in aviation.
The economy declined.
The population increased to one million.
Many people served as the city mayor.
Answers
Answer:
It's A, B, and D
A. The city integrated its school
B. Atlanta became a leader in aviation
D. The population increased to one million
Explanation:
(a) A hole of 1 cm in diameter is drilled in a plate of steel at 20°C. What happens to the diameter of the hole as the steel is heated to 100°C?
Answers
When heat is applied to a substance/material or steel in our case, a series of changes will occur, one of which is Expansion.
Hence the hole will expand from 1cm to a diameter that is greater.
Thermal expansion refers to the expansion or contraction of the dimensions of the solid, liquid or gas when their temperature is changed.
Types of Expansion Linear expansionAreal expansion and Volumetric volume.Learn more about expansion here:
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When a cannon fires a cannonball we observe Newton's third law. Which is the reaction force? A) The cannon moving forward B) The cannonball moving backwards C) The cannon moving backwards D) The cannonball moving forward
Answers
Answer:
I cant answer too complicated sorry
Explanation:
im sorry for not answering
Answer:
I
will
only
explain
Explanation:
The cannon is fired when an explosive charge is detonated, causing a sudden and immense increase in pressure. Is it not this pressure that causes the rapid acceleration of the cannonball and the recoil of the cannon, not an action–reaction between the cannon and the cannonball?
For purposes of this model, we can consider the expanding gas from the explosion to be part of the cannon, or as an intervening object between the cannon and the ball. So the gasses exert a force on the ball. The ball exerts a force back on the gasses. This is transferred to the cannon.
You could also imagine or build a (toy) "cannon" with a spring mechanism to propel the ball, rather than an explosion. You'd see very similar results.
In any case, the deeper point, which you will soon learn, is that momentum is a conserved quantity. Regardless of what mechanism applies the force on the ball and the cannon, after the ball is flying free the cannon must end up with as much backwards momentum as the ball has forward momentum.
If no cannonball is present when the charge is detonated, then the pressure dissipates much more quickly and the recoil is smaller but still present
Because air and exhaust gasses from the explosion are expelled from the cannon. These gasses have mass and carry momentum, therefore they exert a reaction force on the cannon just as a ball does.
HOPE IT HELPS
it's hard but not for memark me in brainliest answers please please pleaseThe monster wants to make himself known to the family in the cottage in chapters 9-12 of Frankenstein. He decides he can't do that until he masters something. What skill
must he master?
A. How to dress properly
B. Language
C. The rules of etiquette
D. Music
Answers
Answer:
c
Explanation:
During an experiment, Ellie records a measurement of 0.0034 m. How would
she write her measurement in scientific notation?
A. 3.4 x 10-3 m
B. 3.4 x 10-4 m
O C. 3.4 x 10-5 m
D. 3.4 x 10-2 m
Answers
Answer:
(A) She needs to move the decimal point by 3 places
WHAT IS THE FORMULA TO CALCULATE THE FORCE OF GRAVITY?
Answers
Answer:
See Image
Explanation:
F = force
G = gravitational constant
m_1 = mass of object 1
m_2= mass of object 2
r = distance between centers of the masses
Answer:
F=G{\frac{m_1m_2}{r^2}}
F = force
G = gravitational constant
m_1 = mass of object 1
m_2 = mass of object 2
r = distance between centers of the masses
FROM THE WEB
To calculate the force of gravity of an object, use the formula: force of gravity = mg, where m is the mass of the object and g is the acceleration of the object due to gravity. Since g is always 9.8 m/s^2, just multiply the object's mass by 9.8 and you'll get its force of gravity!
Safawi kicked a ball with an initial speed of 20 ms) at 30° angle. If the ball experienced a constant vertical acceleration of -9.81 ms?, calculate the ball's maximum height and distance. Explain how soccer player could apply the force of summation theory to optimize his kicks performance.
(10 marks)
Answers
Answer:
maximum height = 5.1 m distance traveled/horizontal displacement = 35.3m
Explanation:
Vy = sin 30º • 20 m/s
Vy = 10 m/s
Vx = cos 30º • 20m/s
Vx = 17.3
V final = V initial + acceleration • time
0 = 10m/s + (-9.81 m/s/s) • time
subtract 10 m/s from both sides
-10m/s = -9.81m/s/s • time
divide each side by -9.81m/s/s
t = 10/9.81 s or roughly 1.02 second
the time to reach max height is equal to 1.02 s
Height = 1/2 • acceleration • time^2 + Vy • time
Height = 1/2 • (-9.81 m/s/s) • 1.02s^2 + 10m/s • 1.02 s
Height = 5.1 m
the maximum height of the ball is equal to 5.1m
since the ball starts from an initial height of zero and has a final height of 0 once it reaches the ground, the time needed to reach max height is the same amount of time to fall back down to earth. thus, time total is equal to 1.02s multiplied by 2
t total = 1.02s • 2
t total = 2.04s
horizontal displacement = Vx • time total
horizontal displacement = 17.3m/s • 2.04 s
Horizontal displacement = 35.3m
Which statement describes a question that can guide the design of a
scientific investigation?
A. It asks about a cause-and-effect relationship between two
variables.
B. It asks about how the observations will be organized,
C. It asks about whether a controlled variable is necessary.
D. It asks about the preferred outcome of the investigation.
Answers
Answer:
The correct answer is:
It asks about a cause-and-effect relationship between two variables (A)
Explanation:
Scientific investigations are aimed as developing a hypothesis and proving the validity or not of the hypothesis developed. In order for these hypotheses to be tested, experiments must be done, and the experiments are designed based on the identification of a cause-and-effect relationship existing between two variables to be tested, where the "cause" is varied to various degrees and the "effect" of the variation is recorded. Therefore, knowing the cause-and-effect relationship will guide the experimental design, which will be aimed at manipulating the causes to see how these manipulations affect the second variable.
Answer:
A
Explanation:
alex is pushing a heavy box.The force he exerts is represented by the white arrow. In order to make his task easier in which direction should an additional force be applied?
Answers
Answer:
The other arrow/force should be in the same direction that Alex is pushing the heavy box.
Explanation:
If Alex is pushing the heavy box to the right, then another person helping him that is also pushing the heavy box to the right would lessen the amount that he has to push.
A robotic arm lifts a barrel of radioactive waste, as shown in the figure.
If the maximum torque delivered by the arm about the axis O is 3.00 x 10° N•m and the distance r is 3.00 m, what is the maximum mass m of the barrel?
Answers
The maximum mass of the barrel, with maximum torque of 3.0×10° N.m delivered about the axis is 0.102 kg.
What is mass?Mass is the quantity of matter a body contains. The S.I unit of mass is kilogram (kg). Mass can also be defined as the ratio of the force to the acceleration of a body.
To calculate the maximum mass of the barrel, we use the formula below.
Formula:
m = τ/dg........... Equation 1Where:
m = Maximum Mass of the barrel τ = maximum Torque deliveredd = Distanceg = Acceleration due to gravity.From the question,
Given:
τ = 3.00×10° N.md = 3.00 mg = 9.8 m/s²Substitute the values above into equation 1
m = (3.00×10°/3×9.8)m = 1/9.8 kg.m = 0.102 kg.Hence, the maximum mass of the barrel is 0.102 kg.
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15 points.
An object of mass 100 kg is observed to accelerate at a rate of 15
m/s/s. Calculate the force required to produce this acceleration.
Answers
Answer:
its 0.5 for all i beleive
Explanation:
glucose+oxygen--->carbon dioxide+water+energy= What reaction??
Fill in the answers to describe this chemical equation.
Name the reactants in this reaction.
Name the products in this reaction.
How many oxygen atoms are involved in this reaction?
Is this equation balanced, and how can you tell?
Is this reaction endothermic or exothermic, and how can you tell?
I REALLY NEED HELP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
combustion reaction
glucose,oxygen
carbon dioxide,water,energy
8
no. required balanced equation is:
C6H12O6+6O2--->6CO2+6H2O+energy
endothermic as it needs heat in the form of sunlight.
A cylindrical capacitor is made of two concentric cylinders. The inner cylinder has radius r1 = 4 mm, and the outer one a radius r2= 8 mm. The common length of the cylinders is L = 150 m. What is the potential energy stored in this capacitor when a potential difference V = 4 V is applied between the inner and outer cylinder?
Answers
Answer:
E = 9.62*10^-8 J
Explanation:
The energy stored in a capacitor is given by the following formula:
\(E=\frac{1}{2}CV^2\) (1)
E: energy stored
C: capacitance
V: potential difference of the capacitor = 4 V
The capacitance for a concentric cylindrical capacitor is:
\(C=\frac{2\pi \epsilon_o L}{ln(\frac{r_2}{r_1})}\) (2)
L: length of the capacitor = 150m
r2: radius of the outer cylinder = 8mm = 8*10^-3m
r1: radius of the inner cylinder = 4mm = 4*10^-3m
εo: dielectric permittivity of vacuum = 8.85*10^-12C^2/Nm^2
You replace the expression (2) into the equation (1) and replace the values of all parameters:
\(E=\frac{1}{2}(\frac{2\pi \epsilon_o L}{ln(\frac{r_2}{r_1})})V^2\\\\E=\frac{\pi \epsilon_o L}{ln(\frac{r_2}{r_1})}V^2\\\\E=\frac{\pi (8.85*10^{-12}C^2/Nm^2)(150m)}{ln(\frac{8*10^{-3}m}{4*10^{-3}m})}(4V)^2\\\\E=9.62*10^{-8}J\)
The energy stored in the cylindrical capacitor is 9.62*10-8 J
You are sitting at your dinner table and notice three peas have fallen off of your plate as shown. Each pea has a mass of 0.22g and d=3.6cm. A. Find the magnitude and direction (CCW from the +axis) of the net gravitational force on the pea labeled M1 B. Find the direction (CCW from the +axis) of the net gravitational force on the pea labeled m1
Answers
Answer:
force = 2.73 x 10^ -15 N
angle = 153.435
Explanation:
Let us redraw the diagram
Let us call
F13 = force on m1 due to m3
F12 = force on m1 due to m2
Now along the x-axis, we have
\(F_x=F_{13}\sin \theta\; \hat{i}\)and along the y-axis, we have
\(F_y=F_{13}\cos \theta+F_{12}\; \hat{j}\)Now,
\(F_{13}=G\frac{m_1m_3}{d^2+(2d)^2}\)and
\(F_{12}=G\frac{m_1m_2}{d^2}\)Therefore, the force along the x-axis becomes
\(\begin{gathered} F_x=F_{13}\sin \theta\; \hat{i} \\ \Rightarrow F_x=G\frac{m_1m_3}{d^2+(2d)^2}\sin \theta\; \hat{i} \end{gathered}\)and the force along the y-axis becomes
\(\begin{gathered} F_y=F_{13}\cos \theta+F_{12}\; \hat{j} \\ \Rightarrow F_y=G\frac{m_1m_3}{d^2+(2d)^2}\cos \theta+G\frac{m_1m_2}{d^2}\hat{\; j} \end{gathered}\)Since
\(\sin \theta=\frac{2d}{\sqrt[]{d^2+(2d)^2}}=\frac{2d}{d\sqrt[]{5}}=\frac{2}{\sqrt[]{5}}\)and
\(\cos \theta=\frac{d}{\sqrt[]{d^2+(2d)^2}}=\frac{d}{d\sqrt[]{5}}=\frac{1}{\sqrt[]{5}}\)The above equations become
\(F_x=G\frac{m_1m_3}{d^2+(2d)^2}\times\frac{2}{\sqrt[]{5}}\; \hat{i}\)\(\Rightarrow\boxed{F_x=G\frac{m_1m_3}{5d^2}\times\frac{2}{\sqrt[]{5}}\; \hat{i}}\)and
\(\boxed{F_y=G\frac{m_1m_3}{5d^2}\times\frac{1}{\sqrt[]{5}}+G\frac{m_1m_2}{d^2}\hat{j}}\)To find the numerical value, we now put
G = 6.67 x 10^-11
m_1 = m_2 = m_3 = 2.2 x 10^-4 kg
d = 0.036 m
into the above equations and get
\(F_x=(6.67\times10^{-11})\frac{(2.2\times10^{-4})^2}{5(0.036)^2}\times\frac{2}{\sqrt[]{5}}\; \hat{i}\)\(\boxed{F_x=4.46\times20^{-16}\; \; \hat{i}}\)and
\(F_y=(6.67\times10^{-11})\frac{(2.2\times10^{-4})^2}{5(0.036)^2}\times\frac{1}{\sqrt[]{5}}+(6.67\times10^{-11})\frac{(2.2\times10^{-4})^2}{(0.036)^2}\hat{j}\)\(\Rightarrow\boxed{F_y=2.7\times10^{-15}\; \hat{j}}\)Therefore, the net gravitational force is
\(F_{\text{tot}}=4.46\times20^{-16}\; \; \hat{i}+2.7\times10^{-15}\; \hat{j}\)the magnitude of this net force is
\(|F_{\text{tot}}|=\sqrt[]{(4.46\times20^{-16})^2+(2.7\times10^{-15})^2}\)\(\boxed{|F_{\text{tot}}|=2.73\times10^{-15}}\)Finally, we need to find the direction of this force.
To specify, the direction, we need to find the angle this force makes counterclockwise with respect the x-axis.
The angle is given by
\(\cos \theta=\frac{1}{\sqrt[]{5}}\)\(\Rightarrow\theta=63.435^o\)adding additional 90 degrees gives the angle with respect to the positive x-axis.
\(\theta+90^o=153.435^o\)Hence, the force is directed at about 153 degrees counterclockwise with respect to the x-axis.
