Answers
Answer:
95 calories
Explanation:
A medium-sized apple has only 95 calories but plenty of water and fiber.
Related Questions
you made $100,000 this year. you have $0 in adjustments, $11,500 in deductions and $7,300 in exemptions. What is your taxable increase?
Answers
The tax rate you will pay is displayed in tax brackets for each category of taxable income.
Thus, For instance, in 2022, the first $10,275 of your taxable income is subject to the lowest tax rate of 10% if you are single.
Up until the maximum amount of your taxable income, the following portion of your income is taxed at a rate of 12%.
As taxable income rises, the tax rate rises under the progressive tax system. Overall, this has the result that taxpayers with higher incomes often pay a greater rate of income tax than taxpayers with lower incomes.
Thus, The tax rate you will pay is displayed in tax brackets for each category of taxable income.
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A wave traveling at 5.00x10^4 meters per second has a wavelength of 2.50x10^1 meters what is the frequency of the wave
Answers
Answer:
Frequency of the wave = 2 x 10³ hz
Explanation:
Given:
Velocity of wave = 5 x 10⁴
Wavelength = 2.5 x 10¹
Find:
Frequency of the wave
Computation:
Frequency of the wave = Velocity of wave / Wavelength
Frequency of the wave = [5 x 10⁴] / [2.5 x 10¹]
Frequency of the wave = 2 x 10³ hz
The frequency of a wave traveling at 5.00 x 10⁴ meters per second and a wavelength of 2.50x10¹ meters is 2 × 10³ Hz
HOW TO CALCULATE FREQUENCY:
The frequency of wave can be calculated by dividing the speed of the wave by its wavelength.λ = v/f
Where,
V= velocity of the wavef = frequencyλ = wavelengthAccording to this question, a wave is traveling at 5.00 x 10⁴ m/s and has a wavelength of 2.50 x 10¹ meters. The frequency can be calculated as follows:f = v ÷ λf = 5 × 10⁴ ÷ 2.5 × 10¹f = 2 × 10³HzTherefore, the frequency of a wave traveling at 5.00 x 10⁴ meters per second and a wavelength of 2.50x10¹ meters is 2 × 10³Hz.Learn more at: https://brainly.com/question/19601903?referrer=searchResults
STEM
Science Challenge
Rockin’ Around the Park
You are a geologist who teaches at a university. You receive the following letter from a local park
ranger.
Dear Professor Rubble,
Our park has some magnificent rock formations along our hiking trails. We receive many questions
from park visitors about how these rock formations were created, and how long it took for them to
form. One visitor even claimed that the same exact rock formation existed near her home thousands
of kilometers away. How can this be possible?
To answer these questions, can you help us develop a model of the Earth processes that shape and
change Earth’s surface that we can display in our nature center? We would also like an article to
accompany the model. The article should explain the model, as well as the time and spatial scales
involved in the processes that form and change rocks on Earth’s surface.
Yours sincerely,
Flint Cobblestone
Q) 1 :How is it possible that identical rock formations can exist thousands of kilometers apart?
Q) 2 :What clues would you look for in the identical rock formations to prove that they formed at the same
time? How might you incorporate this information in your model?
Q) 3 :What processes could have separated the rock formations over time?
Q) 4 :How might you incorporate this information in your model?
Q) 5 :The park contains mountain ranges. How could you determine how and when the mountain ranges
formed?
Q) 6 : How could you incorporate this information in your model?
Q) 7 : Do weathering and erosion cause fast or slow changes to Earth’s surface? Do they affect large or
small areas?
Some types of weathering and erosion occur quickly. A landslide, for example, can quickly transport
and break down Earth materials. Other types of weathering and erosion take place over millions of
years. These processes occur on both large scales (example, mountain ranges) and small scales
(example: a boulder). You could have two separate models to show different time and spatial scales.
One model might show the slow weathering and erosion of a rock using drops of water to simulate
rainfall. The second model might show the fast weathering and erosion of a mountainside during a
landslide triggered by an earthquake.
Q) 8 : How might you include this information in your model?
To model weathering, you could put rocks in a container and shake it many times. You could use
water or a fan to model erosion by rivers or wind.
Q) 9 : Which rock cycle processes will you include in your model? How will you model the sources of energy
that drive these processes?
Models should include weathering, erosion, deposition, compaction, cementation, melting, cooling,
heat, and pressure. Students might use a fan to model wind energy or a source of heat to model
energy from Earth’s interior.
Q) 10 : How will you model processes that occur on different time and spatial scales?
Develop Your Model
Use your information from the questions to construct your model and
prepare your article for the park to display at their nature center.
Models will vary, but should include processes that describe the cycling of Earth materials and the
flow of energy that drives the cycling. Examples of processes include weathering, erosion, deposition,
compaction, cementation, melting, crystallization, pressure, deformation, subduction, and seafloor
spreading.
Evaluate Your Model
After completing your model, identify the model elements in the table below.
Model Elements Descriptions
Components
(What are the different
parts of my model?)
Relationships
(How do the components
of my model interact?)
Connections
(How does my model help
me understand the
phenomenon?)
As the final part of your homework, construct an article that will accompany your model at the park’s
nature center. Your article should explain how Earth processes shape and change rocks on Earth’s
surface at different time and spatial scales.
Outline your article in the space below. Organize your central ideas into a structure that facilitates
understanding. Next, add relevant content including the evidence and reasoning that supports each
central idea. When you are finished with your outline, write your article in your Science Notebook.
Students’ articles should show an understanding that geoscience processes have changed Earth’s
surface at varying time and spatial scales. They should use evidence and reasoning to construct their
explanations for how the mountains and the rock formations in the park formed. They should identify
and describe the time and spatial scales involved (slow, large-scale, fast, small-scale).
Congratulations! You have reached the end of the science challenge.
Answers
Answer:
Hope this helps ;) don't forget to rate this answer !
Explanation:
It is possible that identical rock formations can exist thousands of kilometers apart because of the rock cycle, a process that involves the continuous transformation of rocks through various stages such as weathering, erosion, deposition, and more.
To prove that the identical rock formations formed at the same time, geologists can look for clues such as the presence of the same type of minerals, the same layering or structure, and similar levels of weathering or erosion. This information can be incorporated into the model by including representations of these clues and explaining their significance in the rock cycle.
Processes that could have separated the rock formations over time include tectonic movement, erosion, and weathering. These processes can be incorporated into the model by including representations of tectonic plates and showing how they can move and collide, as well as by including examples of erosion and weathering and explaining their role in the rock cycle.
To determine how and when mountain ranges formed, geologists can study the rock formations, the types of minerals present, and the levels of weathering and erosion. This information can be incorporated into the model by including representations of different types of rock formations and explaining how they were formed through processes such as mountain building and erosion.
Weathering and erosion can cause both fast and slow changes to Earth's surface, and can affect both large and small areas. To include this information in the model, you could have two separate models to show different time and spatial scales. One model might show the slow weathering and erosion of a rock, while the second model might show the fast weathering and erosion of a mountainside during a landslide.
To model weathering and erosion, you could put rocks in a container and shake it many times to simulate weathering, or use water or a fan to model erosion by rivers or wind. You could also use a source of heat to model energy from Earth's interior, or a fan to model wind energy.
In your model, you should include processes that describe the cycling of Earth materials and the flow of energy that drives the cycling. These processes include weathering, erosion, deposition, compaction, cementation, melting, crystallization, pressure, deformation, subduction, and seafloor spreading.
In your article, you could start by introducing the rock cycle and explaining the various processes involved. You could then describe how these processes shape and change rocks on Earth's surface at different time and spatial scales, using examples to illustrate your points. You could also include information about the clues that geologists look for to determine the history of a rock formation, and how these clues can be used to understand the rock cycle. Finally, you could conclude by summarizing the key points and explaining the significance of the rock cycle in understanding the Earth's surface.
Explain the process of refraction of light
Answers
The process of refraction of light occurs when light rays bends when travelling between media of different densities.
What is refraction of light?
Refraction of light is the bending of light rays or the change in the direction of light rays as it travels between media of different densities.
Light waves travel faster in media of less density than media of more density.
The change in density of the media makes light waves to be bend towards or away from the normal.
For example, when light travels from less dense air to more dense water, the light rays are bent towards the normal. However, when light rays travel from water to air, the light rays are refracted away from the normal.
In conclusion, refraction of light waves occur when light crosses the boundary of media of different densities.
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A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 3 feet/sec. How fast is the top of the ladder moving down the wall when the base of the ladder is 7, 15, and 24 feet from the wall?
Answers
The velocity of the ladder when the base of the ladder is 7, 15, and 24 feet from the wall is -0.875, -2.25, and -10.286 respectively.
Given, the length of the ladder= 25 ft
Let x be the distance between the wall and the ladder and h be the height of the ladder from the ground
x² + h² = (25)²
x² +h²= 625
h²= 625- x²
h= \((625- x^{2})^{1/2}\)
\(\frac{dh}{dx}\) = \(\frac{1}{2}\) \((625- x^2)^{-1/2} * (-2x)\)
\(\frac{dh}{dx}\) = \(\frac{-x}{\sqrt{ (625-x^2)}}\)
We have dx/dt= 3 ft/sec
Therefore, by applying the chain rule, we can get the value of dh/dt as:
dh/dt= dh/dx *dx/dt
=\(\frac{-x}{\sqrt{ (625-x^2)}}*3\)
=\(\frac{-3x}{\sqrt{ (625-x^2)}}\)
Now substituting the different values of x in the acquired equation
When x= 7, dh/dt= \(\frac{-7}{8}\) ft/sec= -0.875 ft/sec
When x= 15, dh/dt= \(\frac{-9}{4}\) ft/sec= -2.25 ft/sec
When x= 24, dh/dt= \(\frac{72}{7}\) ft/sec= -10.286 ft/sec
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The mass of the Moon is 0.0123 time the mass of the Earth and its radius is about 0.272 times the radius of the Earth.Calculate the escape velocity on the Moon. Show any work that you do.
Answers
Given data:
* The mass of the Moon is 0.0123 times of mass of Earth as,
\(\begin{gathered} M^{\prime}=0.0123\times M_E \\ M^{\prime}=0.0123\times5.97\times10^{24} \\ M^{\prime}=0.0734\times10^{24}\text{ kg} \end{gathered}\)where M_E is the mass of Earth,
* The radius of the Moon is 0.272 times the mass of Earth as,
\(\begin{gathered} R^{\prime}=0.272\times R_E \\ R^{\prime}=0.272\times6400\times10^3 \\ R^{\prime}=1740.8\times10^3\text{ m} \end{gathered}\)where R_E is the radius of Earth,
Solution:
The escape velocity of the object from the surface of the Moon is,
\(v_e=\sqrt[]{\frac{2GM^{\prime}}{R^{\prime}}}\)where G is the gravitational constant, M' is the mass of Moon, and R' is the radius of Moon,
Substituting the known values,
\(\begin{gathered} v_e=\sqrt[]{\frac{2\times6.67\times10^{-11}\times0.0734\times10^{24}}{1740.8\times10^3}} \\ v_e=0.0237\times10^5ms^{-1} \\ v_e=2.37\times10^3ms^{-1} \\ v_e=2.37kms^{-1} \end{gathered}\)Thus, the escape velocity on the Moon is 2.37 Kilometers per second.
A roller coaster is at a peak of 20m and has a mass of 900kg. What is the potential energy of the roller coaster?
O 100000 J
10000 J
O 9.8 J
O 176400 J
Answers
The potential energy of the roller coaster is 176,400 J (joules).
The potential energy of an object is given by the formula PE = mgh, where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height or vertical position of the object.
In this case, the roller coaster is at a peak of 20m and has a mass of 900kg. The acceleration due to gravity, g, is approximately 9.8 \(m/s^2\).
Using the formula, we can calculate the potential energy:
PE = mgh
= (900 kg)(9.8 \(m/s^2\))(20 m)
= 176,400 J
Therefore, the potential energy of the roller coaster is 176,400 J (joules).
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A hiker with a skin surface area of 1.3 m² is protected from hypothermia (the cold) by a close-fitting sleeping bag 30 mm thick. If her skin temperature is 34°C and she can safely lose 85 W of heat by conduction through the sleeping bag, what is the lowest outside temperature for which the sleeping bag provides adequate protection? Ignore heat losses due to convection or radiation. Coefficient of thermal conductivity of the sleeping bag = 0.019 Wm¹¹°C-¹
Answers
Answer: The lowest outside temperature for which the sleeping bag provides adequate protection is approximately 89.61°C below the hiker's skin temperature of 34°C.
Explanation:
To find the lowest outside temperature for which the sleeping bag provides adequate protection, we need to determine the rate of heat loss through conduction and compare it to the heat loss the hiker can safely tolerate.
The rate of heat loss through conduction can be calculated using the formula:
Q = (k * A * ΔT) / d
Where:
Q is the rate of heat transfer (in Watts)
k is the coefficient of thermal conductivity (0.019 Wm¹¹°C-¹ in this case)
A is the surface area (1.3 m² in this case)
ΔT is the temperature difference (in this case, the difference between the skin temperature and the outside temperature)
d is the thickness of the sleeping bag (30 mm, which needs to be converted to meters by dividing by 1000)
Let's plug in the values:
Q = (0.019 * 1.3 * ΔT) / (30 / 1000)
The hiker can safely lose 85 W of heat, so we can set up the equation:
85 = (0.019 * 1.3 * ΔT) / (30 / 1000)
To solve for ΔT, we can rearrange the equation:
ΔT = (85 * (30 / 1000)) / (0.019 * 1.3)
ΔT ≈ 89.61°C
Examine the image and assess the relationship of the atoms shown by
Answers
The reactants in the given chemical equation are methane (CH₄) and oxygen (O₂), while the products are carbon dioxide (CO₂) and water (H₂O).
During a chemical reaction, the atoms of the reactants reorganize to form new compounds in the products. A chemical change is this atomic rearrangement.
What is a change in chemistry?A chemical change is the transformation of one or more substances into new ones with distinct chemical and physical properties. New substances are created when the original substances' atoms are rearranged and new chemical bonds are formed during a chemical change.
Typically, a transfer of energy in the form of heat, light, or sound occurs in conjunction with this kind of change. Reactions like combustion, oxidation, decomposition, and synthesis are all examples of chemical changes. Physical changes, on the other hand, involve alterations in a substance's physical properties without altering its chemical composition.
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do humans have the right to alter and colonize unique environments on another planet? explain your answer.
Answers
Answer:
We may have people making habitats on asteroids ... I know that humans will colonize the solar system and one day go beyond. Richard Gott has estimated that the human race could survive for another 7.8 million years, but it is not likely to ever colonize other planets.
To be sure there are many daunting challenges facing prospective space colonists such as protection from exposure to deadly radiation levels, the impact on the human body while living and working in cramped, low-gravity environments for extended periods of time and the psychological toll of isolation and confinement.
According to me we can't colonize other planets which is against humanity
momentum is closely related to
Answers
Answer:
Momentum is mainly related to forces
how to protect the ozone layer?
Answers
Answer:
\(\huge{\purple{\underline{\underline{\bf{\pink{Answer}}}}}}\)
we have to protect ozone layer because it is like blanket for earth . It protects the earth form uv rays that are coming from the sunwe have to take some preventive. measures like
Use ecofriendly things that Doesnot contain (cfc) . It is the major reason for ozone DeplitionEffects of uv rays
Uv rays are very harmful . If it directly comes in contact with human it cause skin cancer , eyes irritation etc.Hope it helps.
The pressure at the bottom of a jug filled with water does NOT depend on the
__________.
A) depth of the liquid
B) acceleration due to gravity
C) density of water
D) surface area of the water
E) none of the above
Answers
Answer:
D
Explanation:
because of the the side of the bottom
what is threshold of hearing?
-> The minimum sound pressure level at which a sound of a given frequency can be perceived by the human ear is known as threshold of hearing.
Answers
Explanation:
The absolute threshold of hearing is the minimum sound level of a pure tone that an average human ear with normal hearing can hear with no other sound present. The absolute threshold relates to the sound that can just be heard by the organism.
A ball is dropped from rest. Its energy is transformed from ________.
Answers
Answer:
gravitational potential energy
When the ball falls, some of its gravitational potential energy is converted to other forms of energy, such as kinetic energy and rotational energy. When it rebounds, these other forms of energy is converted back to gravitational potential energy.
Explanation:
How much work is done to push a car 20m using a 200 N force?
W =
J
How much power did you developed in pushing the car in 30 s?
P =
W
Answers
Answer:
F=200N d=20m t=30s
W=F*d
W=200*20
W=4000J
P=W/t
P=4000/30
P=400/3
P=133.333333334 W
What is the relationship between unbalanced and motion?
Answers
The relationship between unbalanced forces and motion is that unbalanced forces cause motion.
When there is an unbalanced force acting on an object, it will accelerate in the direction of the net force.
The magnitude and direction of the motion are directly influenced by the magnitude and direction of the unbalanced force.
In the absence of any opposing forces, an unbalanced force will result in continuous acceleration, causing the object to move faster and faster.
This relationship is described by Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
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a drop of oil of volume 10^_10m^3 spreads out water to make a circular film of radius 10^_1m. what is the thickness of the film.
Answers
The answer is 10^-6 m
A step-by-step solution is below:
The volume of the oil is 10^-10 m^3. The radius of the oil film is 10^-1 m. The thickness of the oil film is the volume divided by the area. The area of a circle is pi * r^2. The thickness of the oil film is 10^-10 m^3 / (3.14 * 10^-2 m^2) = 10^-6 m.
What conditions determine which process occurs in a cell?
Answers
The conditions that determine which process occurs in a cell are largely based on the environment and the needs of the cell.
What is cell?A cell is the basic unit of life. It is the smallest unit of an organism that is capable of independent functioning. Cells are composed of a variety of molecules, including proteins, lipids, carbohydrates, and nucleic acids. Cells are able to carry out functions such as energy production, metabolism, growth and division, movement, and communication.
These conditions include the availability of nutrients, the presence or absence of specific signaling molecules, the amount of oxygen, and the temperature. In addition, the genetic makeup of the cell and its response to internal and external cues can also determine which processes occur.
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In the far future, astronauts travel to the planet Saturn and land on Mimas, one of its 62 moons. Mimas is small compared with the Earth's moon, with mass Mm = 3.75 ✕ 1019 kg and radius Rm = 1.98 ✕ 105 m, giving it a free-fall acceleration of g = 0.0636 m/s2. One astronaut, being a baseball fan and having a strong arm, decides to see how high she can throw a ball in this reduced gravity. She throws the ball straight up from the surface of Mimas at a speed of 43 m/s (about 96 mph, the speed of a good major league fastball)."
Required:
a. Predict the maximum height of the ball assuming g is constant and using energy conservation. Mimas has no atmosphere, so there is no air resistance.
b. Now calculate the maximum height using universal gravitation.
c. How far off is your estimate of part (a)? Express your answer as a percent difference and indicate if the estimate is too high or too low.
Answers
Answer:
a)\(h_{max}=14536.16 m\)
b)\(h = 15687.9 m\)
c)\(PD=7.62\%\) The estimate is low.
Explanation:
a) Using the energy conservation we have:
\(E_{initial}=E_{final}\)
we have kinetic energy intially and gravitational potential energy at the maximum height.
\(\frac{1}{2}mv^{2}=mgh_{max}\)
\(h_{max}=\frac{v^{2}}{2g}\)
\(h_{max}=\frac{43^{2}}{2*0.0636}\)
\(h_{max}=14536.16 m\)
b) We can use the equation of the gravitational force
\(F=G\frac{mM}{R^{2}}\) (1)
We have that:
\( F = ma \) (2)
at the surface G will be:
\(G=\frac{gR^{2}}{M}\)
Now the equation of an object at a distance x from the surface.
is:
\(F=\frac{mgR^{2}}{(R+x)^{2}}\)
\(m\frac{dv}{dt}=\frac{mgR^{2}}{(R+x)^{2}}\)
Using that dv/dt is vdx/dt and integrating in both sides we have:
\(v_{0}=\sqrt{\frac{2gRh}{R+h}}\)
\(h=\frac{v_{0}^{2}R}{2gR-v_{0}^{2}}\)
\(h=15687.9\)
c) The difference is:
So the percent difference will be:
\(PD=|\frac{14536.16-15687.9}{(14536.16+15687.9)/2}*100%\)
\(PD=7.62\%\)
The estimate is low.
I hope it helps you!
You apply a constant 15 N force while pushing a box through a distance of 2.5 m across the floor.
a) How much work, in Joules, did you do?
b) If the box, starting from rest only gains 23 J of kinetic energy, how much of the work that you
did was converted into thermal energy through friction?
Answers
Answer:
Total work done =force X displacement = 15 N X 2.5 m [ given F=15 N & d=2.5 m] W = 37.5 joules
Explanation:
this is just what i was able to find
If we drop 2 objects of different weights from the same height, which one will reach the ground faster?
Answers
If we drop 2 objects of different weights from the same height, both of them will reach the ground at the same time.
Gravity, at the surface of a body like Earth, provides an acceleration to bodies and this acceleration is constant and its value is equal to 9.8m/s². This is because the Earth attracts big objects more than little ones, but the big ones have more inertia, which cancels out. So, all the bodies on the earth's surface fall at the same acceleration of 9.8m/s²
This acceleration due to gravity,g is independent of the mass of the body. The time of flight for any freely falling object depends on the value of acceleration due to gravity and its initial speed. So both the bodies reach the ground at the same time.
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Particles q1 = -53.0 uc, q2 = +105 uc, andq3 = -88.0 uc are in a line. Particles qi and q2 areseparated by 0.50 m and particles q2 and q3 areseparated by 0.95 m. What is the net force onparticle q3?Remember: Negative forces (-F) will point LeftPositive forces (+F) will point Right-53.0 C+105 με-88.0 με91+92930.50 m0.95 m
Answers
We have the next diagram
r12=0.5
r23=0.95
r13=1.45
Using Columb's law the net force of the particle q3 will be equal to the sum of the forces on particle q3 from particle q1 and q2.
the force between q1 and q3
\(\begin{gathered} F_{13}=k\text{ }\frac{q_1\cdot q_3}{r^2_{13}} \\ F_{13}=9\times10^9\text{ }\frac{(-53\times10^{-6}\cdot-88\times10^{-6})}{1.45^2} \\ F_{13}=19.96N \end{gathered}\)then for between q2 and q3
\(\begin{gathered} F_{23}=k\text{ }\frac{q_2\cdot q_3}{r^2_{23}} \\ F_{23}=9\times10^9\text{ }\frac{(105\times10^{-6})\cdot(-88\times10^{-6})}{0.95^2} \\ F_{23}=-92.14N \end{gathered}\)Then we analyze
\(F_3=F_{13}+F_{23}=19.96-92.14=-72.18\)The force is 72.18N to the left
Which of the following phenomena provides evidence for the particle theory of light?
Refraction of light through a prism
Interference patterns produced from light through a double slit
Polarization of light in sunglasses
Ejection of electrons from metals illuminated with different frequencies of light
Answers
Answer:
The ejection of electrons from metals illuminated with different frequencies of light (photoelectric effect)
Explanation:
Ejection of electrons from metals illuminated with different frequencies of light provides evidence for the particle theory of light
What is photoelectric effect ?
The photoelectric effect proves that light has particle-like activity. The photoelectric effect happens when photons are shone on metal and electrons are ejected from the surface of that metal. The electrons that are ejected are determined by the wavelength of light which determines the energy of photons.
correct answer is
Ejection of electrons from metals illuminated with different frequencies of light
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How can a tennis ball and a bowling ball have the same momentum ?
Answers
A tennis ball and a bowling ball can have the same momentum. This is because, it depends upon both the mass of object and velocity of object.
What is Momentum?Momentum can be defined as the mass in motion. All objects which have mass so, if an object is moving in space, then it has some amount of momentum which has its mass in motion. The amount of momentum which an object has depend upon two variables which include how much stuff is moving that is the mass of object and how fast the stuff is moving that is the speed.
A fast-moving tennis ball may have the same momentum as a slow-bowling ball. It is important to understand here that the momentum of an object which depends on the product of the mass and velocity of an object, but not the mass or the velocity alone.
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Write two or three sentences to describe the conductivity of a conductor. Explain its conductivity in terms of the electrons in it.
Answers
The conductivity of a conductor refers to its ability to conduct electrical current.
A material that has high conductivity allows electrical charges to flow through it easily and with little resistance, while a material with low conductivity does not allow electrical charges to flow as easily and has more resistance.
The conductivity of a conductor is determined by the number of free electrons in the material, as well as how easily these electrons can move through the material.
In a conductor, the atoms are closely packed together and the electrons are not tightly bound to the atoms, allowing them to move freely through the material and carry an electrical charge. This facilitates the flow of electrical current through the material, resulting in high conductivity.
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A sprinter accelerates from the starting line in the 100 meter dash at a rate of 7.0ft/s and reaches a velocity of 28.2 ft/s. What amount of time did it take to reach the final velocity?
Answers
The time taken for the sprinter to reach the final velocity is 5.68 s.
What is velocity?
This can be defined as the ratio of displacement of a body to time. The S.I unit of velocity is m/s.
The time taken for the sprinter to reach its final velocity can be calculated using the formula below.
Formula
S = (v+u)t/2.................... Equation 1Where:
S = Total distance covered by the sprinterv = Final velocityu = Initial velocityt = time taken to reach its final velocitymake t the subject of the equation
t = 2S/(v+u)................. Equation 2From the question,
Given:
S = 100 mu = 7 ft/sv = 28.2 ft/sSubstitute these values into equation 2
t = 2(100)/(28.2+7)t = 200/35.2t = 5.68 sHence, The time taken for the sprinter to reach the final velocity is 5.68s
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In Figure below, m₁=2.00kg and m₂-4.00kg. Consider the pulley to be frictionless. (a) If m₂ is released, what will its acceleration be? (b) What is the tension in the string? m₂ 55 m₂
Answers
(a) When m₂ is released, its acceleration will be approximately -3.27 m/s².
(b) The tension in the string is approximately -13.08 N.
To determine the acceleration of m₂ when it is released and the tension in the string, we need to consider the forces acting on the system.
(a) Acceleration of m₂:
Since the pulley is assumed to be frictionless, the tension in the string is the same on both sides of the pulley. We can consider the system consisting of m₁ and m₂ as one body. The net force acting on this system is the difference between the weight of m₁ and the weight of m₂:
Net force = m₁g - m₂g
Applying Newton's second law, F = ma, where F is the net force and a is the acceleration, we have:
m₁g - m₂g = (m₁ + m₂)a
Rearranging the equation to solve for the acceleration, we get:
a = (m₁g - m₂g) / (m₁ + m₂)
Substituting the given values, m₁ = 2.00 kg and m₂ = 4.00 kg, and the acceleration due to gravity, g = 9.8 m/s², we can calculate the acceleration:
a = ((2.00 kg)(9.8 m/s²) - (4.00 kg)(9.8 m/s²)) / (2.00 kg + 4.00 kg)
a = (19.6 N - 39.2 N) / 6.00 kg
a = -19.6 N / 6.00 kg
a = -3.27 m/s²
Therefore, when m₂ is released, its acceleration will be approximately -3.27 m/s². The negative sign indicates that the acceleration is in the opposite direction of the gravitational force.
(b) Tension in the string:
The tension in the string can be determined by considering the forces acting on m₂. The net force on m₂ is equal to its mass multiplied by its acceleration:
Net force = m₂a
Substituting the given values, m₂ = 4.00 kg and a = -3.27 m/s², we can calculate the tension:
Tension = (4.00 kg)(-3.27 m/s²)
Tension = -13.08 N
Therefore, the tension in the string is approximately -13.08 N. The negative sign indicates that the tension acts in the opposite direction of the weight of m₂.
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Calculating percentage using Bernoulli's equation on an aeroplane wing
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Bernoulli's equation can be used to calculate the pressure difference and hence the lift generated by an aeroplane wing.
How is Bernoulli's equation used?The equation is: P + 1/2 × ρ × v² + ρ × g × h = constant
Where P is the pressure, ρ is the density of the fluid (air), v is the velocity of the fluid, g is the acceleration due to gravity, and h is the height.
To calculate the lift generated by an aeroplane wing, we can use the Bernoulli's equation to find the pressure difference between the top and bottom of the wing. The pressure difference creates an upward force, which is the lift.
To find the percentage of the lift generated by an aeroplane wing, use the total weight of the aeroplane and divide the lift by the weight, and then multiply by 100 to get the percentage.
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The complete question is:
Calculating percentage using Bernoulli's equation on an aeroplane wing. Explain!
An object is pushed at an angle of 42˚ by a force of 135 N through a distance of 829 cm. Find the work done by the object.
Answers
The work done by the object is 831.69 J.
What is work?Work can be defined as the product of mass and distance.
To calculate the work done by the object, we use the formula below
Formula:
W = Fdcos∅............ Equation 1Where:
W = Work done by the objectF = Force on the object∅ = Angle.From the question,
Given:
F = 135 Nd = 829 cm = 8.29 m∅ = 42°Substitute these values into equation 1
W = 135×8.29×cos42°W = 831.69 J.Hence, The work done by the object is 831.69 J.
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