Answers
We will have the following:
First, we find all the forces in x & y, that is:
\(\sum ^{}_{}F_x=0\Rightarrow\sum ^{}_{}F_x=F_f-N_1\colon N_1=F_f\)Here Ff is the frictional force and N1 the normal force on the point where the ladder is resting.
\(\sum ^{}_{}F_y=0\Rightarrow\sum ^{}_{}F_y=N_2-mg-Mg\colon N_2=(M+m)g\)Here N2 is the normal force of the resting point of the ladder on the ground. M is the mass of the person and m is the mass of the ladder.
Then we make sure that the ladder won't rotate, that is the momentum will be 0, that is:
\(\sum ^{}_{}\tau_i=mg\cos (\theta)(l/3)+mg\cos (\theta)(l/2)-N_2\cos (\theta)l+F_f\sin (\theta)l=0\)Here "l/3" represents the positons of the person to climb, and "l/2" represents the position of the center of mass of the ladder.
Then, we remember that we are given the static friction coefficient, and replace:
\(\sum ^{}_{}\tau_i=mg\cos (\theta)(l/3)+mg\cos (\theta)(l/2)-(M+m)g\cos (\theta)l+\mu_s(M+m)g\sin (\theta)l=0\)Then we divide the whole expression by cos(theta) in order to eliminate all extra trigonometric values and determie the angle:
\(\Rightarrow(\frac{M}{3}+\frac{m}{2})g-(M+m)g+\mu_s(M+m)g\tan (\theta)=0\)\(\Rightarrow(\frac{M}{3}+\frac{m}{2})-(M+m)+\mu_s(M+m)\tan (\theta)=0\)\(\Rightarrow\tan (\theta)=\frac{(M+m)-(\frac{M}{3}+\frac{m}{2})}{(M+m)\mu_s}\Rightarrow\tan (\theta)=\frac{(60\operatorname{kg}+10\operatorname{kg})-(\frac{60\operatorname{kg}}{3}+\frac{10\operatorname{kg}}{2})}{(60\operatorname{kg}+10\operatorname{kg})(0.50)}\)\(\Rightarrow\theta=\tan ^{-1}(\frac{45}{35})\Rightarrow\theta=\tan ^{-1}(\frac{9}{7})\)\(=\theta=52.12501635\ldots\Rightarrow\theta\approx52.1\)So, the angle would be approximately 52.1°.
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Related Questions
Louis Armstrong ride his bike 55km east time trial in 51 minutes what was his average velocity in KM/min?
Answers
Louis Armstrong's average velocity in the time trial was approximately 1.078 km/min.
How to determine average velocity?To calculate the average velocity, divide the total displacement by the total time taken. In this case, Louis Armstrong rode his bike 55 km to the east in a time trial lasting 51 minutes.
Average Velocity = Displacement / Time
Displacement = 55 km (since he rode 55 km to the east)
Time = 51 minutes
Average Velocity = 55 km / 51 min
To express the average velocity in km/min, convert the time from minutes to minutes.
1 hour = 60 minutes
Average Velocity = 55 km / 51 min × (1 hour / 60 min)
Average Velocity = 55 km / 51 min × (1/60) hour
Simplifying the expression:
Average Velocity = 1.078 km/min
Therefore, Louis Armstrong's average velocity in the time trial was approximately 1.078 km/min.
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Austin is interested in working for an intelligence branch of the government. A polygraph test is part of the interview
process. Though Austin intends to be honest, he is worried that the polygraph will say he is lying when he is not.
Austin's friend, Gabe, assures Austin that polygraph tests are infallible. Is Gabe right?
Answers
Answer:
Gabe is wrong in concluding that the polygraph tests are infallible. Even though the polygraph machine is a man-made machine, there is a small margin of error factored into it.
This error could be caused as a result of the anxiety of the test taker, the heart beat rate, the blood pressure etc which would lead to the answers provided by the person to be flagged as false despite being true.
In most cases, the test result will be declared inconclusive if there was an error in the readings.
Explanation:
Water diversion projects may involve the movement of water to dry regions using? A.canals
B.dams
C.reservoirs
D.sprinklers
Answers
Water diversion projects may involve the movement of water to dry regions using canals
Hence, option (a) is the correct choice.
Water diversions are made up of a system of structures and measures that intercept clear surface water runoff upstream of a project site, transport it around the work area, and discharge it downstream with minimal water quality degradation for either project construction operations or diversion construction.
Water diversion projects may involve the movement of water to dry regions using canals, reservoirs, and/or pipelines.
Dams can be used to store water for later use in these projects, but sprinklers are typically not involved in water diversion projects.
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A force F = (2xî + 4yĵ), where F is in newtons and x and y are in meters, acts on an object as the object moves in the x-direction from the origin to x = 4.99 m. Find the work W = ∫ F · dr done by the force on the object (in J).
Answers
Answer:
Work done, W = 24.9001 J
Explanation:
Given that,
Force, F = (2xî + 4yĵ) Where x and y are in meters
This force acts on an object as the object moves in the x-direction from the origin to x = 4.99 m.
We need to find the work done by the force on the object. It is given by :
\(W=\int\limits^a_b {F dr} \\\\W=\int\limits^{4.99}_0 {(2xi+4yj)dx} \\\\W=\int\limits^{4.99}_0 {2xi\ dx} \\\\W=x^2|_0^{4.99}\\\\\text{Applying limits}\\\\W=(4.99)^2-0^2\\\\W=24.9001\ J\)
So, the work done is 24.9001 J.
define the term change and state one negative change you may encounter as a student or as an employee in the future
Answers
Answer:
hey iam bored pls join
ID: 724 645 3790
Password: 1111
The term change refers to an alteration of present conditions.
What is change?The term change refers to an alteration of present conditions. When a change occurs, things cease to be the way they were. As a student, the complexity of academic work increases with time. This is a change that has taken place.
As an employee, you are given real world tasks to accomplish rather than mere mental exercises like when you were a student, this is change that has taken place.
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a 0.1 kg object oscillates as a simple harmonic motion along x axis with a frequency f=3.185 hz. At a position x1 , the object has a kinetic energy of o.7 j and a potential energy 0.3 J.The amplitude of oscillation A is:
Answers
Answer:
The total energy must be .7 J + .3 J = 1 J for a particle at the endpoint or midpoint of motion.
Also, omega = (k / m)^1/2
f = omega / (2 * pi)
omega^2 = 4 pi^2 * f^2 = k / m
k = 4 * pi^2 * f^2 * m = 40.05
Max KE or PE = 1/2 k A^2
A^2 = 2 * E / k = 2 * 1 / k = .0499
A = .223 meters
A carousel is (more or less) a disk of mass, 15,000 kg, with a radius of 6.14. What torque must be applied to create an angular acceleration of 0.0500 rad/s^2?round to 3 significant figures
(Plssss help me im suffering from severe brainrot)
Answers
To calculate the torque required to create an angular acceleration, we can use the formula:
Torque = Moment of Inertia × Angular Acceleration
The moment of inertia of a disk can be calculated using the formula:
Moment of Inertia = (1/2) × Mass × Radius^2
Given:
Mass = 15,000 kg
Radius = 6.14 m
Angular Acceleration = 0.0500 rad/s^2
First, calculate the moment of inertia:
Moment of Inertia = (1/2) × Mass × Radius^2
Moment of Inertia = (1/2) × 15,000 kg × (6.14 m)^2
Next, calculate the torque:
Torque = Moment of Inertia × Angular Acceleration
Torque = Moment of Inertia × 0.0500 rad/s^2
Now, let's plug in the values and calculate:
Moment of Inertia = (1/2) × 15,000 kg × (6.14 m)^2
Moment of Inertia ≈ 283,594.13 kg·m^2
Torque = 283,594.13 kg·m^2 × 0.0500 rad/s^2
Torque ≈ 14,179.71 N·m
Rounding to three significant figures, the torque required to create an angular acceleration of 0.0500 rad/s^2 is approximately 14,180 N·m.
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An electron with a velocity of 14.4 m/s in the positive y-direction enters a region where there is a uniform electric field of 201 N/C in the positive x-direction. The mass of the electron is 9.109 × 10−31 kg.
What is the y-component of the electron’s displacement 2.40 μs after entering the electric-field region if no other forces act on it in μm?
What is the x-component of the electron’s displacement 2.40 μs after entering the electric-field region if no other forces act on it in m?
Answers
1. The electron experiences acceleration and moves independently in the y-direction.
2. The y-component of the electron's displacement after 2.40 μs in the electric field is -8.11 μm.
3. The x-component of displacement remains zero.
To calculate the y-component and x-component of the electron's displacement, we need to consider the motion of the electron in the electric field. Let's break it down step by step:
1. Acceleration of the Electron:
The electric field causes a force on the electron given by the equation: F = qE, where F is the force, q is the charge of the electron, and E is the electric field.
Since the charge of an electron is -1.6 × \(10^-^1^9\) C, and the electric field is 201 N/C, we can calculate the force:
F = (-1.6 × \(10^-^1^9\)C) * (201 N/C)
= -3.216 × \(10^-^1^7\) N
Using Newton's second law, F = ma, we can find the acceleration (a) of the electron:
a = F / m
= (-3.216 × \(10^-^1^7\) N) / (9.109 ×\(10^-^3^1\) kg)
= -3.530 × \(10^1^3 m/s^2\)
2. Displacement in the y-direction:
Since no other forces act on the electron, its motion in the y-direction is independent of the electric field. The equation for displacement (y) under constant acceleration is:
y = (1/2) * a *\(t^2\)
Substituting the values, where the time (t) is 2.40 μs (2.40 ×\(10^-^6\) s), we can calculate the y-component of displacement:
y = (1/2) * (-3.530 ×\(10^1^3 m/s^2\)) * (2.40 ×\(10^-^6 s)^2\)
= -8.11 μm
Therefore, the y-component of the electron's displacement 2.40 μs after entering the electric-field region is -8.11 μm.
3. Displacement in the x-direction:
Since the electron's velocity is only in the y-direction initially, the x-component of the displacement remains zero. Without any forces acting in the x-direction, the electron continues to move in the y-direction without changing its x-position.
Hence, the x-component of the electron's displacement 2.40 μs after entering the electric-field region is 0 meters.
Please note that the calculations provided are based on the given values and the provided formulas for displacement and acceleration.
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A cat jumps horizontally from a 3.2 meter shelf at a velocity of 7m/s. How far from the base of the shelf does the cat land? At what velocity does the cat land? (Magnitude and Direction).
Answers
PLEASE ANSWER ASAP BEFORE MY TEACHER AND MY MOM KILLES ME PLEASE ASAP
The first person with the right answer gets to be a brainlest
In the attachment there is a density column where there is colour
Question: tell me why is the red at the bottom of the density column if it is the least dense
Answers
The most dense thing inside the column is the little star. It's pink, and it's resting on the bottom of the cylinder.
The red part under the star is the solid base that the cylinder is standing in. It's probably wood or plastic, it's not free to move, and it's not involved in the experiment.
Answer: That is not meant to be red, it‘s the bottom of the beaker. The star is at the very bottom of the beaker. it’s just the base of the beaker.
A radio is rated as 50 W. Calculate the energy transferred in Joules by the radio when it has been switched on for 2 minutes?
Answers
The energy transferred in Joules by the radio when it has been switched on for 2 minutes would be 6000 Joules.
Energy transferPower is defined as the rate of energy transfer or the rate at which work is done, and is given by the equation:
Power = Energy transferred / Time
Rearranging the equation to solve for energy transferred, we get:
Energy transferred = Power x Time
We are given:
Power = 50 W
Time = 2 minutes = 120 seconds
Therefore, the energy transferred by the radio when it has been switched on for 2 minutes is:
Energy transferred = Power x Time = 50 W x 120 s = 6000 J
In other words, the energy transferred by the radio is 6000 Joules.
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big ideas
key questions and terms notes
Answers
Answer:
what i and confused
Explanation:
Answer:
nerd
Explanation:
I H4+3 U
Find V. in the circuit of the following figure
Answers
Answer:
A5 A20 A32 5G A1 G A20 5G T mOBIL
What is an example of a scientific topics that requires knowledge of at least two branches of physics?
Answers
Explanation:
classical physics and modern physics.
Physics is the branch of science that deals with the interaction of energy and matter. Modern and Classical Physics are the two major branches of physics.
What is physics?Physics is the discipline of science that investigates the structure of matter and how the universe's fundamental constituents interact. It investigates objects ranging from the very small to the entire universe using quantum mechanics and general relativity.
One of the most crucial physics topics is kinematics. Kinematics is the study of an object 's direction of travel. Kinematics is only concerned with the motion of an object.
There is a vertical and a horizontal component to two-dimensional projectile motion, such as that of a football or other thrown object.
Throwing a rock or kicking a ball produces a projectile pattern of motion that includes both a vertical and a horizontal component.
Thus, these can be the topics that require the knowledge of physics.
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Question 3 of 15
Which of the following statements are not true about gravity? Check all that
apply.
A. Gravity exists in the whole universe.
B. Gravity exists only on Earth.
C. Gravity is a force that pulls two objects together.
D. Gravity exists between two objects that have mass.
E. Gravity doesn't exist between Earth and the sun.
Answers
The statement "B. Gravity exists only on Earth" and the statement "E. Gravity doesn't exist between Earth and the sun" is not true about gravity.
Gravity is a fundamental force of nature that exists in the whole universe, not just on Earth. It is a force that acts between any two objects that have mass. This means that statement "C. Gravity is a force that pulls two objects together" and "D. Gravity exists between two objects that have mass" are both true. Gravity plays a significant role in the functioning of our solar system. The sun's gravitational force acts on the planets, including Earth, keeping them in their orbits. Similarly, Earth's gravitational force attracts objects towards its center, giving weight to objects on its surface. Gravity is the force that holds Earth in orbit around the sun and is responsible for the planets' motion in the solar system. Gravity is a universal force that exists throughout the universe, acts between objects with mass, and plays a crucial role in celestial bodies' movements, including the interaction between Earth and the sun.
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Need help for this Asap please
Answers
The coefficient of static friction between the block of wood and the table is 0.449.
How to calculate the frictionThe weight of the block of wood is Mg = 4.0 kg × 9.81 m/s^2 = 39.24 N.
The coefficient of static friction μs is given by the equation μ_s = fs/N, where N is the normal force from the table.
Since the block is not accelerating vertically, we know that N = Mg, so we have:
μs = fs/N = 17.64 N / 39.24 N = 0.449
Therefore, the coefficient of static friction between the block of wood and the table is 0.449.
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Pretty Easy question please answer only 20 minutes left:
A summary of the results of a scientific investigation is called a:
observation
research
hypothesis
conclusion
Answers
Answer:
D. Conclusion.
Explanation:
Gold forms a solid solution with silver. Since the densities of pure gold and silver are 19.32 g/cm³ and 10.49 g/cm³, respectively, calculate the number of gold atoms per cubic centimeter for a silver-gold alloy containing 10% Au and 90% Ag by weight.
Answers
There are 3.37 × \(10^{22}\) gold atoms per cubic centimeter in the silver-gold alloy.
The density of a binary alloy can be calculated using the following equation:
ρ = w1ρ1 + w2ρ2
where,
ρ = density of the alloy
w1 and w2 = weight fractions of the two components (in this case, gold and silver)
ρ1 and ρ2 = densities of the pure components.
We are given that the alloy contains 10% gold and 90% silver by weight, so we can calculate the weight fractions as:
\(w_{Au}\) = 0.10
\(w_{Ag}\) = 0.90
We are also given the densities of pure gold and silver as:
ρ_Au = 19.32 g/\(cm^{3}\)
ρ_Ag = 10.49 g/\(cm^{3}\)
Now we can substitute these values into the density equation to find the density of the alloy:
ρ = \(w_{Au}\)ρ_Au +\(w_{Ag}\)ρ_Ag
ρ = (0.10)(19.32 g/\(cm^{3}\)) + (0.90)(10.49 g/\(cm^{3}\))
ρ = 11.08 g/\(cm^{3}\)
Next, we need to calculate the number of gold atoms per cubic centimeter in the alloy.
To do this, we can use Avogadro's number and the atomic weights of gold and silver:
\(N_A\) = 6.022 × \(10^{23}\) atoms/mol
Aum = 196.97 g/mol
Agm = 107.87 g/mol
The number of gold atoms:
\(n_{Au}\) = (\(w_{Au}\)ρ/ Aum) × \(N_{A}\)
Substituting the values, we get:
\(n_{Au}\) = (0.10 × 11.08 g/\(cm^{3}\)/ 196.97 g/mol) × 6.022 × \(10^{23}\) atoms/mol
\(n_{Au}\) ≈ 3.37 × \(10^{22}\) atoms/\(cm^{3}\)
Therefore, there are approximately 3.37 × \(10^{22}\) gold atoms per cubic centimeter in the silver-gold alloy.
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A child playing by the side of a well is throwing a stone vertically into the well with an initial velocity of 5 m/s. if the stone falls into the water 3 s later, find the height, h, of the point which the stone is thrown from the surface of the water. (g=10 m/s2)
a) 15m
b)30m
c)45m
d)60m
Answers
The height of the well is 30m
We are given that ,
The initial velocity of the stone = u = 5m/s
The stone fall into well in time = t = 3s
The acceleration due to gravity = g = 10 m/s²
To get the height of the stone which is thrown from the surface of the water in the well by equation,
h = ut + 1/2 gt²
Where, u is initial velocity in m/s, h is height in m, t is time in secs, g is acceleration due to gravity which is vertically upward direction i.e. (-10m/s²)
h = (5m/s) (3s) + 1/2 (-10m/s²)(3s)²
h = (15m) - (5m/s²)(9s²)
h = -30 m
Therefore, the height of the stone which is thrown upward is 30 m . And here, we can neglect the negative sign due to height is never be in negative.
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If f(x)=5x+40, what is f(x) when x =-5?
Answers
Answer:
given - x = (-5)To find - Value of the equation
Solution -
5x + 40
Putting value of x = (-5) in equation
5(-5) + 40
-25 + 40
15
An object is projected with speed of 4ms at an angle of 60° to horizontal. Calculate the time of flight of the object. (g=10ms2)
Answers
0.8 seconds
Explanation:
time of flight = 2u/g
u=4m/s
g=10
= 8/10
= 0.8 sec
just a trial...not sure!!!
Given :
∅ = 60⁰
u = 4 m/s
g = 10m/s²
to find :
T = ?
Solution :
as per formula,
\(t = \frac{2u \: sin \theta}{g} \)
now put the value : \(t \: = \frac{2 \times 4 \times sin \: 60}{10} \)
as we know \( sin60 \: = \frac{ \sqrt{3} }{2} \)
therefore,
\(t \: = \frac{8 \times \frac{ \sqrt{3} }{2} }{10} \)
as we solve this we get,
\(t \: = \frac{ 2\sqrt{3} }{5} \)
that's t = 0.69 sec
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Select the correct answer from each drop-down menu. Because of location, the has become a center for transportation. The is also a center for transportation and home to the nation’s busiest airport.
Answers
Because of location, the Hartsfield Jackson international airport has become a center for transportation. The is also a center for transportation and home to the nation’s busiest airport.
What is transportation?It should be noted that transportation simply means the movement of people and animals from one location to another. It should be noted that there are different means of transportation such as rail, air, road, etc.
In this case, because of location, the Hartsfield Jackson international airport has become a center for transportation. The is also a center for transportation and home to the nation’s busiest airport. This is located in Atlanta Georgia.
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Select the correct answer from each drop-down menu. Because of location, the has become a center for transportation. The is also a center for transportation and home to the nation’s busiest airport.
a. Dallas International Airport.
b. Denver International Airport.
c. John Kennedy International Airport
d. Hartsfield Jackson international airport
An object of height 5cm is placed 20cm in front of pin hole camera from a cubic box of side 6cm . Determine the height of the image formed
Answers
True False: Marke each statement as true or false.
shift
1. Light intensity affects the rate of photosynthesis.
in
2. Energy is required by all organisms for life.
3. The ability of a plant to repair tissue depends on respiration.
4. The gas needed for photosynthesis is carbon dioxide (CO2).
5. Plants only carry on photosynthesis, not respiration.
6. Respiration can occur without photosynthesis.
Answers
Answer:
1) true 2) true 3) true 4) true 5) false 6) false
Explanation:
According to Newton's second law, if you increase the mass but the force is the same, what happens to the acceleration?
Audio Recording 50 KB
acceleration decreases
Оа
Ob
Ос
acceleration increases
acceleration remains the same
Answers
Simple Answer. Mass cannot change.
Force=Acceleration
The way in which one atom interacts with another atom is mostly influenced by the configuration of the
A. electrons farthest from the nucleus.
B. protons in the center of the nucleus.
C. electrons closest to the nucleus.
D. protons on the outer edge of the nucleus.
Answers
The way in which one atom interacts with another atom is mostly influenced by the configuration of the electrons farthest from the nucleus.
Option A.
What is atom?An atom can be defined as the smallest part of a substance that cannot be broken down chemically. Each atom has a nucleus (center) made up of protons (positive particles) and neutrons (particles with no charge).
The arrangement of electrons in orbitals and shells around the nucleus is referred to as the electronic configuration of the atom.
Thus, we can conclude that the way in which one atom interacts with another atom is mostly influenced by the configuration of the electrons farthest from the nucleus.
The remaining options do not fit the empty space properly, and they include;
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after landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 51.0 cmcm . the explorer finds that the pendulum completes 101 full swing cycles in a time of 136 ss .part awhat is the magnitude of the gravitational acceleration on this planet?express your answer in meters per second per second.view available hint(s)for part aactivate to select the appropriates template from the following choices. operate up and down arrow for selection and press enter to choose the input value typeactivate to select the appropriates symbol from the following choices. operate up and down arrow for selection and press enter to choose the input value typegplanetgplanet
Answers
The magnitude of the acceleration due to gravity of the planet is 11.06 m/s², if the pendulum completes 101 full swing cycles in 136 seconds.
Length of the pendulum, l = 51.0 cm = 0.51 m
Time taken to complete 101 full swings cycle is 136 seconds, so
Time period of the pendulum, T = 136/101 = 1.35 sec
Let the value of gravitational acceleration on the planet, = gₓ
We know the equation of simple pendulum is: T = 2π√(l/g)
1.35 = 2π√(0.51/g)
Squaring of both sides,
1.35² = (2π)²×(0.51/gₓ)
1.82 = 20.13/gₓ
gₓ = 20.13/1.82
gₓ = 11.06 m/s²
--The given question is incorrect, the correct question is:
"after landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 51.0 cm . the explorer finds that the pendulum completes 101 full swing cycles in a time of 136 s. What is the magnitude of the gravitational acceleration on this planet? Express your answer in meters per second per second."--
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Running at 2 m/sec, Jack, the 45-kg quarterback, collides with Leon, the 90-kg tackle, who is traveling towards him at 7.0 m/sec. Upon colliding, Leon continues to travel forward towards Jack, at 1.0 m/sec. How fast is Jack knocked backwards?
Answers
Given:
The mass of Jack is,
\(m_1=45\text{ kg}\)The initial speed Jack is,
\(u_1=2\text{ m/s}\)The mass of Leon is
\(m_2=90\text{ kg}\)The initial speed of Leon is
\(u_2=7.0\text{ m/s}\)The final speed of Leon after the collision is
\(v_2=1.0\text{ m/s}\)To find:
How fast is Jack knocked backward?
Explanation:
The initial momentum of Jack and Leon is,
\(\begin{gathered} P_i=m_1u_1+m_2u_2 \\ =45\times2+90\times7.0 \\ =720\text{ kg.m/s} \end{gathered}\)If the speed Jack after the collision is
\(v_1\)the final momentum is
\(\begin{gathered} P_f=m_1v_1+m_1v_2 \\ =45\times v_1+90\times1.0 \\ =45v_1+90\text{ kg.m/s} \end{gathered}\)Applying, The total linear momentum before the collision is the sum of the momentums of each of the football players. So,
\(\begin{gathered} 45v_1+90=720 \\ v_1=\frac{720-90}{45} \\ v_1=14\text{ m/s} \end{gathered}\)Hence, Jack is knocked backward at 14 m/s.
2 A rectangular storage tank 4 m long by 3 m wide is filled with paraffin to a depth
of 2 m. Calculate:
a the volume of paraffin
c the weight of paraffin
b the mass of paraffin
d the pressure at the bottom of the tank due
to the paraffin
1m
Answers
For a rectangular storage tank filled with paraffin to a depth of 2 m, the volume, weight, mass of paraffin, and pressure at the bottom of the tank are:
a. The volume is 24 m³.
b. weight is 240,000 N,
c. mass is 24,490 kg, and
d. pressure is 23,530 Pa.
a) The volume of paraffin in the rectangular storage tank can be calculated using the formula:
Volume = Length x Width x Depth
Given:
Length = 4 m
Width = 3 m
Depth = 2 m
Substituting the values into the formula, we have:
Volume = 4 m x 3 m x 2 m
Volume = 24 m³
Therefore, the volume of paraffin in the tank is 24 cubic meters.
b) The weight of the paraffin can be calculated using the formula:
Weight = Volume x Density x Acceleration due to gravity
The density of paraffin varies, but we can assume a typical value of 10,000 kg/m³. The acceleration due to gravity is approximately 9.8 m/s². Substituting these values into the formula:
Weight = 24 m³ x 10,000 kg/m³ x 9.8 m/s²
Weight = 240,000 N
Therefore, the weight of the paraffin in the tank is 240,000 Newtons.
c) The mass of the paraffin can be calculated using the formula:
Mass = Density x Volume
Substituting the given values:
Mass = 10,000 kg/m³ x 24 m³
Mass = 24,490 kg
Therefore, the mass of the paraffin in the tank is 24,490 kilograms.
d) The pressure at the bottom of the tank due to the paraffin can be calculated using the formula:
Pressure = Weight / Area
The area of the bottom of the tank is equal to the length multiplied by the width. Substituting the values:
Area = 4 m x 3 m
Area = 12 m²
Pressure = 240,000 N / 12 m²
Pressure = 20,000 Pa
Therefore, the pressure at the bottom of the tank due to the paraffin is 20,000 Pascals (Pa).
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ASAP
What is the area under the curve for the histogram below?
Answers
The area under the curve for the histogram in this problem is given by the following option:
B. 97.
How to obtain the area of the histogram?The histogram is composed by rectangular bins, hence the total area under the histogram is given by the sum of the areas of each bin.
The area of a rectangle of base b and height h is given by the multiplication of these dimensions, as follows:
Area = b x h.
From the histogram given in this image, all the bins have a base of 1, hence the total area is given by the sum of the heights of the histogram.
Thus the total area is calculated as follows:
Area = 5 + 7 + 11 + 15 + 17 + 14 + 12 + 9 + 4 + 3 = 97.
Meaning that option B is correct.
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