When a wheel rolls at 6.0 m/s on a horizontal surface, its kinetic energy is 255.6 J.
\(I = M * r^2+4*1/3*m*r^2\\M=3.4Kg\\m=1.4kg\\Now, (3.4 + (4/3*1.4))r^2=5.26r^2\\K.E.=1/2(M+4m)r^2+1/2*I*w^2\\=4.5V^2+2.63V^2\\=7.1V^2\\=255.6J\\\)
Kinetic energy is defined as the energy possessed by an object as a result of its velocity or speed. The formula for kinetic energy is 1/2(mass x velocity squared), where the mass is the amount of matter in an object and the velocity is the speed at which the object is moving.
Kinetic energy is also important in the study of collisions, as the conservation of kinetic energy is an essential principle in understanding how energy is transferred between objects. The amount of kinetic energy that an object has is directly proportional to its mass and velocity. This means that the greater the mass and the faster an object is moving, the more kinetic energy it has.
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because relative humidity is dependent on air temperature, it is ____________ in the cooler mornings and ____________ in the warmer afternoons.
Because relative humidity is dependent on air temperature, it is generally higher in the cooler mornings and lower in the warmer afternoons.
This is because warm air can hold more water vapor than cool air, so as the temperature rises in the afternoon, the air has the capacity to hold more moisture. This means that the same amount of water vapor in the air will result in a lower relative humidity when the temperature is higher. Conversely, in the cooler mornings, the air has less capacity to hold moisture, so the same amount of water vapor in the air will result in a higher relative humidity.
It's important to note, however, that this pattern is not always true and can be affected by other factors such as wind, precipitation, and geography. Additionally, relative humidity is not the same as absolute humidity, which refers to the actual amount of water vapor in the air, regardless of temperature.
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Nitrogen , Carbon, Hydrogen, Calcium , Oxygen and Iron are all examples of a(n)
Answer:
All four words are the name of elements.
Hydrogen, oxygen, carbon, nitrogen, calcium, and iron are all important substances found in the body and in environments. They can be combined with each other, and with other substances to form larger compounds.
But i think the answer is nucleic acids..
Explanation:
Well, hope it helps you..
I tried to answer it..
Your welcome in advance..
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A.Calculate the wavelength of the photon absorbed by COCO in the following vibration-rotation transition: nn = 0, ll = 2 →n→n = 1, ll = 3.
Express your answer to four significant figures and include the appropriate units.
B.Calculate the wavelength of the photon absorbed by COCO in the following vibration-rotation transition: nn = 0, ll = 3 →n→n = 1, ll = 2.
Express your answer to four significant figures and include the appropriate units.
C.Calculate the wavelength of the photon absorbed by COCO in the following vibration-rotation transition: nn = 0, ll = 4→n→n = 1, ll = 3.
However, I can explain the general concepts and equations involved in calculating the wavelength of photons absorbed during vibration-rotation transitions.
In molecular spectroscopy, the wavelength of a photon absorbed during a transition can be determined using the equation: λ = c / ν
where λ is the wavelength, c is the speed of light in a vacuum (approximately 3.00 x 10^8 meters per second), and ν is the frequency of the absorbed radiation.
To calculate the frequency of the absorbed radiation, you would need to consider the energy levels associated with the initial (nn = 0, ll = 2) and final (nn = 1, ll = 3) states of the vibration-rotation transition for each case.
The frequency can be determined using the equation:
ν = (E_final - E_initial) / h
where ν is the frequency, E_final is the energy of the final state, E_initial is the energy of the initial state, and h is Planck's constant (approximately 6.63 x 10^-34 joule-seconds).
By substituting the frequency into the wavelength equation, you can calculate the corresponding wavelength of the absorbed photon.
Please note that the actual numerical calculations would require specific energy values and molecular parameters for COCO, which I don't have access to in real-time.
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Humpty Dumpty (5 kg) is about to a bungee jump from a 50-meter high bridge. Feeling nervous, he paces back and forth with a velocity of 2 m/s. What is Humpty Dumpty's GRAVITATIONAL POTENTIAL ENERGY before jumping?
Answer:
E = 2450 J
Explanation:
Given that,
Mass of Humpty Dumpty, m = 5 kg
He jumps from a 50 m high bridge.
Feeling nervous, he paces back and forth with a velocity of 2 m/s.
We need to find Humpty Dumpty's gravitational potential energy before jumping. The formula is given by :
\(E=mgh\\\\E=5\times 9.8\times 50\\\\E=2450\ J\)
So, the required gravitaional potential energy is 2450 J.
If a rock falls for 5 seconds near the surface of the earth and with no air friction, it will reach a velocity of
Answer: -49m/s.
Explanation:
As the rock only falls, we will assume that the initial vertical velocity is zero.
We neglect the air friction, so the only force acting on the rock is the gravitational force, this means that the acceleration is -g = -9.8m/s^2.
Then we can write:
a(t) = -9.8m/s^2
To write the velocity of the rock, we must ingrate over time and get:
v(t) = (-9.8m/s^2)*t + v0
where v0 is the initial vertical velocity, and as we said above, v0 = 0m/s
Then the vertical velocity as a function of time is:
v(t) = (-9.8m/s^2)*t
Now, the question is:
"...If a rock falls for 5 seconds near the surface of the earth and with no air friction, it will reach a velocity of..."
Then we need to evaluate the velocity equation in t = 5 seconds.
v(5s) = (-9.8m/s^2)*5s = -49m/s.
How does Health & Physical Education relate to any other subject you now study in
school?
Answer:
Health relates to science because
in science you study, research, and knowledge in this case, health science, which helps you under stand more about how humans and animals function. And Physical education relates to science because , you study the way of human movement, think of push-ups as a example.
I hope I helped U ´꓃ ` U
find the distance if Jerry runs at speed 8 km/hr in 2.5 hours
The distance will be 20km.
Like any other equation, the formula speed = distance time can be changed.
There are three possible arrangements for the formula:
Distance is determined by speed and time.
Time = Speed x Distance
Speed given = 8km/Hr
Time = 2.5 hours
Distance = Speed * Time
= 8 * 2.5
= 20 km
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Answer:
12.4274 miles or 20 kilometers
Explanation:
\(distance = time\) × \(speed\)
distance = 2.5hr × 8 kph
2.5 × 8 = 20 Note: this is if we solve with kilometers.
Let's solve with miles now.
Let's convert kph to mph.
Let's solve for mph, in this case, mph will be x, and y will be kph.
x = y ÷ 1.609344
x = 8 kph ÷ 1.609344
8 kph ÷ 1.609344 = 4.97097 mph
x = 4.97097 mph
Now, x will be distance. y will be time and z will be speed.
Let's solve for x:
x = y × z
y = 2.5
z = 4.97097
x = 2.5 × 4.97097
4.97097 × 2.5 = 12.4274
x = mph
x = 12.4274
x = 12.4274 mph
miles = hours × mph
12.4274 = 2.5 × 4.97097 = x
x = mph
x = 12.4274
x = 12.4274 mph
Hence, the right answer is 12.4274 miles or 20 kilometers.
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Correct me if I'm wrong :(
Happy to help!
What is entered in block 24j of the cms-1500 claim if the provider is a member of a group practice?
What is entered in block 24j of the cms-1500 claim if the provider is a member of a group practice is national provider identifier (NPI).
What is national provider identifier (NPI)?A National Provider Identifier is a unique 10-digit identification number issued to health care providers in the United States by the Centers for Medicare and Medicaid Services.
What is block 24j?The box 24j Shaded is used to identify the non-NPI if indicated by a qualifier in 24i.
The box 24j displays the NPI of the Rendering Provider.
Thus, what is entered in block 24j of the cms-1500 claim if the provider is a member of a group practice is national provider identifier (NPI).
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a diverging lens has a focal length of magnitude 20.0 cm. (a) locate the images for object distances of (i) 40.0 cm, (ii) 20.0 cm, and (iii) 10.0 cm. for each case, state whether the image is (b) real or virtual and (c) upright or inverted. (d) for each case, find the magnification.
It is only necessary to know the direction of two of the three rays in order to graphically depict the formation of an image in a thin lens with virtual image.
(i) The one that strikes the lens perpendicular to the optical axis of the lens is one of them. When this is refracted in the lens, the image focus will not be affected. Its trajectory won't be altered by this.
(ii) The third and final one is the one that crosses the object focus (or its extension does), which, following refraction, will move in a direction parallel to the optical axis of the lens.
Accordingly, depending on how an object or body is positioned in relation to the lens, one type of image will generally be formed in the lenses. The image will always be virtual, smaller than the body, and to the right in divergent lenses.
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During an isothermal process, 10 j of heat is removed from an ideal gas. What is the work done by the gas in the process?
The work done in the isothermal process is 10 joule.
We need to know about the isotherm process to solve this problem. The isotherm process can be described as a process where the initial temperature system will be the same as the final temperature. Hence, the internal energy change will be zero.
ΔU = 0
Hence,
ΔU = Q - W
0 = Q - W
Q = W
It means that the heat transferred is the same as the work done.
From the question above, we know that the heat transferred is 10 joule. Thus, the work done in the isothermal process is 10 joule.
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I have the mass but I can't find (b) or (c)
In 1986, a gargantuan iceberg broke away from the Ross Ice Shelf in Antarctica. It was approximately a rectangle 160 km long, 40.0 km wide, and 250 m thick.
(a) What is the mass of this iceberg, given that the density of ice is 917 kg/m3?
(b) How much heat transfer (in joules) is needed to melt it?
(c) How many years would it take sunlight alone to melt ice this thick, if the ice absorbs an average of 100 W/m2, 12.00 h per day?
Answer:
i only wrote this for points
Explanation:
Which of the following accurately states the claim made by special relativity?
A. The speed of light in a vacuum is the same for stationary frames
of reference.
B. The speed of light in a vacuum is faster for accelerating frames of
reference.
C. The speed of light in a vacuum is the same for all frames of
reference.
D. The speed of light in a vacuum is slower for frames of reference
that have a constant velocity.
Answer:
The Answer is C
The speed of light in a vacuum is the same for all frames of reference.
Explanation:
Answer:
C .The speed of light in the vacuum is same for all frames of reference.
Explanation:
What do you understand by frame of reference?A set of abstract coordinate system that explains the position or motion of something mathematically and physically by the set of reference points and geometric points.
What is Special relativity ?
It explains the effect on mass ,time and space by the speed . It also relates the speed of light , mass and energy.
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Assuming that the smallest measurable wavelength in an experiment is 0. 450 fm , what is the maximum mass of an object traveling at 479 m⋅s−1 for which the de broglie wavelength is observable?
The maximum mass of an object traveling at 479 m⋅s−1 for which the de broglie wavelength is observable, is 3.82×10⁻²⁷ kg.
What is De Broglie equation?To find the wavelength of a wave, Broglie given an equation. This equation for wavelength is,
\(\lambda=\dfrac{h}{mv}\)
Here, (h) is the planks constant, m is mass and (v) is the velocity.
Assuming that the smallest measurable wavelength in an experiment is 0. 450 fm. The speed of the object is 479 m⋅s−1.
Put the values in the formula,
\(\lambda=\dfrac{h}{mv}\\ 0.450\times10^{-15}=\dfrac{6.63\times10^{-34}}{m\times479}\\m=3.07\times10^{-21}\rm \;kg\)
Thus, the maximum mass of an object traveling at 479 m⋅s−1 for which the de broglie wavelength is observable, is 3.82×10⁻²⁷ kg.
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In 1993, the gold reserves in the United States were about 8.490 × 106
kg. If all
that gold were made into a thick wire with a cross-sectional area of 1cm2
, its
total resistance would be about 6.60 × 102 Ω. If the same operation were
applied to the gold reserves of Germany, France, and Switzerland, the
resistances would be 2.40 × 102 Ω, 2.00 × 102 Ω, and 2.00 × 102 Ω,
respectively. Now consider all four resistors connected as shown in the circuit
diagram below. Find the equivalent resistance.
The equivalent resistance of the circuit is 65.98 Ω.
What is Resistor?
A resistor is an electrical component that limits or regulates the flow of electrical current in a circuit. It is designed to provide a specific amount of resistance to the flow of electrons, measured in ohms, and is typically made of a material that can resist the flow of electricity, such as carbon or metal. Resistors are used in a wide range of electronic devices and circuits, from simple LED flashers to complex computer systems.
To find the equivalent resistance of the circuit, we need to use the formula for resistors in parallel:
1/Req = 1/R1 + 1/R2 + 1/R3 + 1/R4
where Req is the equivalent resistance, and R1, R2, R3, and R4 are the resistances of the four resistors.
Substituting the given values, we get:
1/Req = 1/6.60 × 102 + 1/2.40 × 102 + 1/2.00 × 102 + 1/2.00 × 102
1/Req = 0.01515
Req = 65.98 Ω
Therefore, the equivalent resistance of the circuit is 65.98 Ω.
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The particles of a liquid are packed more closely together than the particles of a gas and therefore don't have as much movement. O A True O B. False no links
Answer:
A. True
Explanation:
We are talking about motion of solid, liquid and gas particles.
Now, for gas particles, due to the fact that it's particles are far apart from one another, it usually vibrates and thus moves freely at speeds that are higher than those of liquids of solids. For liquids, their particles are not as far apart as those of gases and so they vibrate, move about, and then slide past each other while solids are the most densely packed and so they vibrate but do not move from one place to the other like gases and liquids.
Thus, we can see that particles of liquid are more closely packed than gases and as such don't have same movement speed.
let's suppose I have a glacier moving at a rate of 64m per day. What would be the steps to converting it to Kilometers per Hour? Also, expressing the km/h using two significant figures
Answer: \(2.7*10^{-2} km/h\)
Explanation:
First you need to know the units that your quantity has. Velocity is given in length divided by time. So to transform from m/day to km/h we need to convert separately length from m to km and time from day to h. For length we have:
1km -------- 1000m
x ------------ 64m
x = 64/1000 = 64*\(10^{-3}\) km
Next we convert the time:
1 day = 24h
And now we just make the proper substitution:
\(64\frac{m}{day} = \frac{64m}{1 day} = \frac{64*10^{-3} km}{24 h} = \frac{64*10^{-3}}{24} \frac{km}{h} = 2.7*10^{-2} km/h\)
Note that our result has two significant figures (2.7) since 10 to -2 does not count as significant figures.
Bill Nye- Static Electricity Answer Key?
. ASSERTION: WHEN ASTRONAUTS THROW SOMETHING IN SPACE, THAT OBJECT WOULD CONTINUE MOVING IN THE SAME DIRECTION AND WITH THE SAME SPEED. REASON: THE ACCELERATION OF AN OBJECT PRODUCED BY A NET APPLIED FORCE IS DIRECTLY RELATED TO THE MAGNITUDE OF THE FORCE, AND INVERSELY RELATED TO THE MASS OF THE OBJECT.
Both the assertion and the reason given are true.If the mass of the object is less, the acceleration produced by the force will be more. Hence, the acceleration produced by the force is directly proportional to the magnitude of the force and inversely proportional to the mass of the object.
The given assertion: When astronauts throw something in space, that object would continue moving in the same direction and with the same speed; and the given reason: The acceleration of an object produced by a net applied force is directly related to the magnitude of the force, and inversely related to the mass of the object are both correct.Astronauts are capable of throwing objects in space because they are beyond Earth's gravity and do not have to deal with any significant air resistance. In the absence of other forces like friction or air resistance, the initial velocity will be conserved, and the object will continue to move with the same speed and direction. The object would continue to move in a straight line with the same speed because no external force acts on it to change the object's state of motion.Newton's second law states that the force of an object is directly proportional to its acceleration, but inversely proportional to its mass. F=ma, where F is force, m is mass, and a is acceleration. Therefore, if the mass of the object is less, the acceleration produced by the force will be more. Hence, the acceleration produced by the force is directly proportional to the magnitude of the force and inversely proportional to the mass of the object.
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n the process of nailing up a heavy framed poster, a student pushes the poster straight in toward the wall; the poster is sliding downward at a constant speed.
Draw a free-body diagram of the poster. Assume that the wall is to the right of the student.
A free-body diagram of the heavy framed poster will include the following forces: gravitational force (weight) acting vertically downward, normal force exerted by the wall acting horizontally to the right, friction force acting vertically upward, and the applied force by the student acting horizontally to the left.
In the given situation, the poster is sliding downward at a constant speed, which means the net force acting on it is zero.
The gravitational force (weight) acting on the poster is balanced by the friction force between the poster and the wall.
The normal force exerted by the wall and the applied force by the student pushing the poster inwards are also balanced.
Summary: The free-body diagram for the heavy framed poster includes four forces: gravitational force (downward), normal force (rightward), friction force (upward), and the applied force by the student (leftward). These forces are balanced, resulting in the poster sliding downward at a constant speed.
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A collision cart runs off the edge of a lab table that is 0.95 meters high and lands 0.40 meters from the base of the table. Calculate the speed of the collision cart when it leaves the table. Let g =10m/s²
Answer/Explanation:
given values we can generate the equations:
x = vx*t
y = 0.95 - 1/2*g*t^2
where x refers to displacement in horizontal direction, y refers to displacement in vertical direction, and t is time, while vx is velocity of the cart in the x direction, and g is the acceleration due to gravity = 9.8 m/s^2
At it's landing point we have x = 0.4, y = 0:
0.4 = vx*t
0 = 0.95 - 1/2*9.8*t^2
Therefore combining the equations and solving:
t = 0.44 s s
vx = 0.91 m/s
Dizzy is speeding along at 22.8 / as she approaches the level section of track near the loading dock of the Whizzer roller coaster ride. A braking system abruptly brings the 328 car (rider mass included) to a speed of 2.9 / over a distance of 5.55 . Determine the braking force applied to Dizzy's car
The braking force applied to Dizzy's car is approximately 50,600 Newtons in the opposite direction to the car's motion.
What is braking force?Braking force is the force applied by a vehicle's brakes to slow down or stop the vehicle. To determine the braking force applied to Dizzy's car, we can use the equation:
force = mass x acceleration
where the acceleration is the rate at which the car's velocity changes during braking.
First, we need to calculate the initial velocity of the car before braking:
v0 = 22.8 m/s
Next, we need to calculate the final velocity of the car after braking:
vf = 2.9 m/s
The change in velocity, or delta-v, is:
delta-v = vf - v0 = 2.9 m/s - 22.8 m/s = -19.9 m/s
Note that the negative sign indicates a decrease in velocity.
We also need to calculate the time it takes for the car to come to a stop. We can use the equation:
delta-x = (v0 + vf) / 2 x t
where delta-x is the distance traveled during braking, which is given as 5.55 m.
Rearranging the equation, we get:
t = 2 x delta-x / (v0 + vf)
Substituting the given values, we get:
t = 2 x 5.55 m / (22.8 m/s + 2.9 m/s) = 0.393 s
Now we can calculate the acceleration:
acceleration = delta-v / t = (-19.9 m/s) / (0.393 s) = -50.6 m/s^2
Again, the negative sign indicates a deceleration or braking acceleration.
Finally, we can calculate the force applied to the car:
force = mass x acceleration
The mass of the car is not given, but we can assume it is approximately the same as the average mass of a roller coaster car, which is around 1000 kg.
Substituting the values, we get:
force = 1000 kg x (-50.6 m/s^2) = -50,600 N
Therefore, the braking force applied to Dizzy's car is approximately 50,600 Newtons in the opposite direction to the car's motion.
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I AM TIMED !! 30 POINTS Which is the smallest possible particle of an element?
O molecule
O atom
O compound
O matter
Answer:
atoms
Explanation:
they are the smallest
Electrical energy is supplied to a string of lights. What forms of energy are lost?
Answer:
In what forms is the electrical energy that is supplied to a string of decorative lights dissipated? It is converted to thermal energy and light energy.
Answer:
Energy loss. When energy is transformed from one form to another, or moved from one place to another, or from one system to another there is some energy loss. This means that when energy is converted to a different form, some of the input energy is turned into a highly disordered form of energy, like heat.
Energy losses in lights are very large; most of the input energy is lost in the form of heat energy.
Explanation:
A 45 kg student is riding on a 7kg skateboard with a velocity of +4 m/s. The student jumps off the skateboard with a velocity of 1 m/s. Find the velocity of the skateboard after the student jumped off
According to conservation of momentum,
(m1+m2) v = m1v1 + m2v2
Thus, velocity of the skateboard, v2= 36m/s
How to calculate the velocity of skateboard?As per the law of conservation of momentum in an isolated system the total momentum of two or more bodies acting upon each other remains constant unless an external force is applied.
Thus,
(m1+m2) v = m1v1 + m2v2
v2= (m1+m2) v - m1v1 /m2
= (45+7) (4) -(45) (1) /7
= 253/7 = 36m/s
Hence, velocity of the skateboard, v2= 36m/s
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An object is thrown vertically upward to a height of 10m. Calculate it's
A) velocity with which it is was thrown upward
B) Time taken by the object to reach the highest point.
(a)To calculate the initial velocity of the object with which it is thrown upward, we can use kinematic equation as follows, v 2 = u 2 − 2 g h Here, v is the final velocity, u is the initial velocity, g is the acceleration due to gravity and h is the height attained by the object.
What would it take to get the stone slab to move? Propose an
idea and explain how it would work in the context of Newton's
laws.
In order to get a stone slab to move, one would have to apply force to it. This can be done in a number of ways, depending on the situation. Here are a few possible laws that could be proposed for moving a stone slab:1. Newton's first law of motion: This law states that an object at rest will stay at rest unless acted upon by an external force. Therefore, to move a stone slab, one would need to apply a force to it.
This could be done by pushing it, pulling it, or applying a force from a lever or other mechanical device. Newton's second law of motion: This law states that the force required to accelerate an object is directly proportional to its mass. Therefore, to move a stone slab, a greater force would be required if it is more massive. This could be accomplished by using more people to push or pull the slab, or by using a larger lever or other mechanical device.. Friction: Friction is the force that opposes motion between two surfaces that are in contact with each other. In order to move a stone slab, one would need to overcome the friction between it and the surface it is resting on. This could be accomplished by reducing the friction (for example, by using rollers or lubricant), or by applying a greater force to overcome the friction.Work: Work is defined as the product of force and distance. Therefore, in order to move a stone slab, one would need to apply a force over a certain distance.This could be accomplished by pushing or pulling the slab over a distance, or by using a lever or other mechanical device to apply force over a greater distance.These are just a few possible laws that could be proposed for moving a stone slab. Ultimately, the best approach will depend on the specific situation and the resources available.For such more question on Newton's second law
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A 10 gram ball is rolling at 3 m/s. The ball has __________ energy. Calculate it. A 10 gram ball is held 2 meters from the ground. It has __________ energy. Calculate it. You serve a volleyball with a mass of 2100 g. The ball leaves your hand with a velocity of 30 m/s. The ball has ____________ energy. Calculate it. A toy baby carriage is sitting at the top of a hill that is 21 m high. The carriage with the baby has a mass of 200 grams . The carriage has ____________ energy. Calculate it. A toy car is traveling with a velocity of 4 m/s and has a mass of 1120 g. The car has ___________energy. Calculate it. A cinder block is sitting on a platform 20 m high. It has a mass of 790 grams. The block has _____________ energy. Calculate it. There is a bell at the top of a tower that is 5 m high. The bell has a mass of 190 grams. The bell has ____________ energy. Calculate it. A toy roller coaster is at the top of a 2 m hill and has a mass of 9660 grams. The coaster (at this moment) has ____________ energy. Calculate it.
Answer:
a) KINETIC ENERGY K = 0.045 J , b) POTENTIAL ENERGY U = 0.196 J ,
c) KINETIC ENERGY K = 9.45 10⁵ J, d) POTENTIAL ENERGY , U = 41.16 J ,
e) POTENTIAL ENERGY U = 154.84 J , f) ENERGY IS POTENTIAL U = 9.31 J
g) energy is POTENTIAL U = 189.336 J
Explanation:
a) The ball is moving with a speed, so it has KINETIC ENERGY
K = ½ m v²
K = ½ 10 10⁻³ 3²
K = 0.045 J
b) The ball is at a given height therefore it has POTENTIAL GRAVITATORY ENERGY
U = m g y
U = 10 10-3 9.8 2
U = 0.196 J
c) The ball has speed so it has KINETIC ENERGY
K = ½ m v²
K = ½ 2,100 30²
K = 9.45 10⁵ J
d) The baby carriage is at a height whereby the POTENTIAL ENERGY
U = mg h
U = 0.200 9.8 21
U = 41.16 J
e) the concrete block is at a height that has POTENTIAL ENERGY
U = m g h
U = 0.790 9.8 20
U = 154.84 J
f) the hood has height, the ENERGY IS POTENTIAL
U = 0.190 9.8 5
U = 9.31 J
g) The roller coaster has height and speed, therefore the mechanical energy has a scientific part and a potential part, in general the speed at the top of the mountain is very small, so we can consider that almost all the energy is POTENTIAL
The value they give allows calculating the potential energy
U = 9.660 9.8 2
U = 189.336 J
The answer to all the questions on potential energy and kinetic energy have been done below;
A) We are told that the ball is rolling. An object in motion has kinetic energy. Formula for kinetic energy is;
K = ½mv²
We have; m = 10 g = 0.01 kg and v = 3 m/s
K = ½ × 0.01 × 3²
K = 0.045 J
B) We are told that the ball is held at a height. This means it is at rest and any object at rest has Potential Energy. Formula for potential energy is;
PE = mgh
We have; m = 10g = 0.01 kg and h = 2 m
PE = 0.01 × 9.8 × 2
PE = 0.196 J
C) Like in A above, the ball is in motion. Thus, it has kinetic energy.
K = ½ × 2.1 × 30²
K = 945 J
D) The baby carriage is sitting at rest and therefore has potential energy.
PE = 0.2 × 9.8 × 21
PE = 41.16 J
E) The toy car is in motion and has kinetic energy. Thus;
K = ½ × 1.12 × 4²
K = 8.96 J
F) The cinder block is sitting at rest and has potential energy. Thus;
PE = 0.79 × 9.8 × 20
PE = 154.84 J
G) The bell is at the top of the tower and is at rest and thus has potential energy.
PE = 0.19 × 9.8 × 5
PE = 9.31 J
g) The rollercoaster is at the top at rest and so has potential energy.
PE = 9.66 × 9.8 × 2
PE = 189.336 J
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An axially loaded short column has length of 3.5m carries factored load of 1600KN. Concrete fc'=28MPA and Fy=420 MPA. Maximum aggregate size is 19mm. Calculate the suitable dimensions for tied and spiral columns.qr 1. Calculate • Required loads • Stresses • Gross area • Area of steel • Design satisfies risk assessment against use Appropriate reinforcement SELECTION • All relevant checks to make design safe
The suitable dimensions for tied and spiral columns of Required loads, Stresses, Gross area, Area of steel are 1142.86 kN, 12.6 MPa, 90.89 m².
The required loads can be determined by dividing the factored load by the appropriate load factor. For this example, let's assume a load factor of 1.4. Required loads = Factored load / Load factor
= 1600 kN / 1.4
= 1142.86 kN
Determine the allowable stresses: a concrete compressive strength of fc' = 28 MPa, the allowable compressive stress (fa) can be calculated using the formula:
= 0.45 * 28 MPa
= 12.6 MPa
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A force, F, of 25 N is acting in the direction of a= [6, 1). a) Find a unit vector in the direction of a. b) Find the Cartesian vector representing the force, 7, using your answer from part a). c) The force f is exerted on an object moving from point (4,0) to point (15, 0), with distance in metres. Determine the mechanical work done.
a) The unit vector in the direction of a is (0.993, 0.117).
b) The Cartesian vector representing the force is (24.825, 2.925).
c) The mechanical work done is 275 Joules.
What is the unit vector in the direction of a? How can the force be represented in Cartesian vector form? What is the value of the mechanical work done?The unit vector in the direction of vector a can be found by dividing vector a by its magnitude. In this case, vector a = [6, 1], so the magnitude of a is √(6² + 1²) = √37. Dividing vector a by its magnitude yields (6/√37, 1/√37), which simplifies to approximately (0.993, 0.117).
To find the Cartesian vector representation of the force, we multiply the unit vector from part a) by the magnitude of the force, F = 25 N. The result is (0.993 * 25, 0.117 * 25), which simplifies to (24.825, 2.925).
To determine the mechanical work done, we use the formula W = F * d * cos(θ), where W is the work done, F is the force, d is the displacement, and θ is the angle between the force and displacement vectors.
In this case, the force is F = 25 N, and the displacement is the difference between the x-coordinates of the two points, which is 15 - 4 = 11 meters. Since the force and displacement are in the same direction (θ = 0°), cos(θ) = 1.
Plugging in the values, we get W = 25 * 11 * 1 = 275 Joules.
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What does a capacitor do in a circuit?
A. It stores and releases charge.
B. It increases voltage.
C. It reduces current.
D. It overcomes resistance.
A capacitor stores and releases charge in a circuit. Capacitors are a fundamental component in electronic circuits that can store and release charge, helping to smooth out voltage fluctuations and filter out unwanted frequencies in a signal.
A capacitor is an electronic component that consists of two conductive plates separated by a dielectric material. When a voltage is applied across the plates, the capacitor stores charge on its plates. The amount of charge that a capacitor can store is determined by its capacitance, which is measured in Farads (F).
When the voltage source is removed, the capacitor retains its charge, and when it is connected to a circuit, the capacitor releases the stored charge. This makes the capacitor useful for smoothing out voltage fluctuations, filtering out unwanted frequencies in a signal, and temporarily storing energy.
The amount of charge stored in a capacitor can be calculated using the formula Q = CV, where Q is the charge in coulombs, C is the capacitance in Farads, and V is the voltage across the capacitor in volts.
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