The energy source of quasars or active galaxies is currently thought to be matter falling toward a massive black hole in the center of a galaxy, according to persuasive evidence discovered by astronomers.
How does science define energy?The definition of energy is "capacity to do activity, which is ability to apply force causing motion of an object." Energy is simply the force that moves objects, despite this definition's seeming complexity. Both potential and kinetic energy fall under this category.
what is The importance of energyDue to the fact that it is a fundamental human requirement, energy is crucial to our daily existence. Our constructions, which are constructed by humans, are heated and cooled by energy. Even the simplest tasks like lifting your finger or getting out of bed require energy.
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HEYYYY! PLEASE HELP ME!!
Turn this Algebraic expression into a verbal expression.
2(3j+5+8j)
I need this today! The rest of it is due today too! Thank you!! <33
Answer:
22j+10
Explanation:
that is it in a verbal expression
what is measurement? why is it important to have regular supervision of the weights and measurement in the market?
Answer:
The comparison of unknown quantity with known quantity is called measurement.
If the total momentum of a system of an old woman pushing a shopping cart is 450 kg×m/s, both with a velocity of 3 m/s, and the woman has a mass of 50 kg, what is the mass of the cart?
Answer:
100kg
Explanation:
Momentum is defined as the product of mass times velocity:
\(p=mv\)
The total momentum M must be equal to the sum of momentums of the system components, in this case the momentum of the lady plus the momentum of the cart:
\(M=m_{woman}v_{woman}+m_{cart}v_{cart}\)
since both the woman and the shopping cart have the same velocity:
\(v_{woman}=v_{cart}=v\)
the equation becomes:
\(M=m_{woman}v+m_{cart}v\\M=v(m_{woman}+m_{cart})\)
and since we need the mass of the cart we solve for \(m{cart}\):
\(m_{woman}+m_{cart}=\frac{M}{v} \\\\m_{cart}=\frac{M}{v} -m_{woman}\)
the values given by the problem are the following:
total momentum: \(M=450kgm/s\)
mass of the woman: \(m_{woman}=50kg\)
velocity: \(v=3m/s\)
we substitute all of them in the equation to find the mass of the shopping cart:
\(m_{cart}=\frac{450kgm/s}{3m/s} -50kg\\\\m_{cart}=150kg-50kg\\\\m_{cart}=100kg\)
the mass of the cart is 100kg.
under which conditions do both convex and concave mirrors form virtual images state whether or not each can form a real image if the mirror can form a real image describe how this occurs
Answer:
Explanation:Concave mirrors can make a real image.when the object is away from the mirror it is called real image and when the object is closer to the mirror it is called virtual mirror.
A ball is thrown in the air with an initial velocity of 10m/s. If it reaches a maximum height of 3.0 m, what angle would it have been thrown at?
To determine the angle at which the ball was thrown, we can use the equations of projectile motion.
Vertical component: v_y = v * sin(θ)
Horizontal component: v_x = v * cos(θ)
Δy = v_y * t + (1/2) * g * t^2
Since the ball reaches a maximum height, Δy = 3.0 m, and the acceleration due to gravity is approximately 9.8 m/s^2, we can rearrange the equation to solve for time (t):
3.0 = 0 * t + (1/2) * 9.8 * t^2
t ≈ √0.6122
t ≈ 0.7837 s
Now that we have the time taken to reach the maximum height, we can calculate the vertical component of the initial velocity:
v_y = v * sin(θ)
0 = 10 * sin(θ)
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A boy wishes to make a catapult out of a rubber band of width 9mm and thickness 1.55mm. Determine the length of the band that must use so that when he stretches it by 0.25 of its natural length and releases it the velocity of a pebble of mass 0.006kg will be 30m\s. take the young modulus of the rubber to be 4×10^7 N\m^2
Answer:
To solve this problem, we can use the formula for the potential energy stored in a stretched spring or rubber band: U = (1/2) k x^2
where U is the potential energy, k is the spring constant, and x is the amount of stretch.
We can rearrange this formula to solve for k: k = 2 U / x^2
The velocity of the pebble can be found using conservation of energy:
(1/2) m v^2 = U
where m is the mass of the pebble and v is its velocity.
Rearranging this formula, we get: v = sqrt(2 U / m)
We can combine these formulas to solve for the length of the rubber band:
k = (4 U) / (0.25 L^2)
v = sqrt((8 U) / (0.006))
where L is the original length of the rubber band.
Since the width and thickness of the rubber band are given, we can calculate its cross-sectional area:
A = (9 mm) x (1.55 mm) = 13.95 mm^2 = 1.395 x 10^-5 m^2
Using the Young's modulus given in the problem, we can calculate the spring constant: k = (A / L) x (Y / 4)
where Y is the Young's modulus.
The formula for k above, we get: (4 A Y / L^3) x (U / 0.25) = 0.006 v^2
Solving for L, we get: L = (4 A Y U / 0.006 v^2)^1/3
Substituting the given values and solving, we get: L = 34.86 cm
Therefore, the length of the rubber band should be approximately 34.86 cm to achieve the desired velocity of the pebble
when a blinking light source moves relative to you, the speed of the light group of answer choices remains constant but the frequency of blinks can change. stays the same, as does the blinking frequency. changes but the frequency of blinks remains constant.
When the blinking light sources moves relative to us, the speed of light remains constant but frequency of blinks can change.
What is frequency?Frequency of a light wave is the number of wave cycles obtained per unit time. Thus it is inverse of the time and has the unit of s⁻¹ which is equivalent to 1 hertz, Hz.
The speed of light is constant at any direction or for any distance and it is equal to the value 3 × 10⁸. This constancy of light is introduced from the theory of special relativity.
When the light source moves closer to the observer, the number of wave cycles catches by the observer increases thereby the frequency. Therefore when the blinking light moves closer to us, its frequency changes but speed remains constant.
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1) both lights will blink at the same time every 20 seconds
2)Both lights will blink at the same time every 36 seconds
3) 2 lights will blink together is that you must find the least common factor (LCM) of both numbers and when both hit the same number then that is when both lights blink at the same time.
When speed of light remains constant?When a blinking light source moves relative to you, the speed of the light remains constant but the frequency of blinks can change. stays the same, as does the blinking frequency. changes but the frequency of blinks remains constant.
For example, for number 1 we have 4 and 5 seconds when the lights blink
4: 4, 8, 12, 16, 20...
5: 5, 10, 15, 20...
we see that the LCM factor is 20 and that is when both lights will hit at the same time.
Therefore, 1) both lights will blink at the same time every 20 seconds
2)Both lights will blink at the same time every 36 seconds
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Our solar system is 4.6 billion years old. Based on the age of the solar system, how many galatic years has planet Earth been around?
Therefore, based on the estimated duration of a galactic year, Earth has been around for approximately 18.4 to 20.4 galactic ye
A "galactic year" refers to the time it takes for our solar system to complete one orbit around the Milky Way galaxy. The exact duration of a galactic year is not precisely determined due to various factors, such as the varying speeds of stars within the galaxy. However, it is estimated to be roughly 225-250 million years.
To calculate the number of galactic years Earth has been around based on the age of the solar system (4.6 billion years), we can divide the age of the solar system by the estimated duration of a galactic year:
Number of Galactic Years = Age of the Solar System ÷ Duration of a Galactic Year
Number of Galactic Years = 4.6 billion years ÷ 225-250 million years
Number of Galactic Years ≈ 18.4 to 20.4 galactic years
Therefore, based on the estimated duration of a galactic year, Earth has been around for approximately 18.4 to 20.4 galactic years.
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Global climate and weather patterns are driven by differences in the amount of heat energy in different areas of the Earth. Which statement best explains why different areas of the Earth have different amounts of heat energy?
The Earth receives different amounts of solar energy in different regions.
ocean currents and global wind patterns, which are caused by convection currents, most strongly affect a region's
climate
An area with an average annual temperature of more than 64°F and greater than 59 inches of annual rainfall would be an example of which type of climate?
tropical
Which of the following factors would affect the weather patterns of a region?
all of these
Water cycles from the atmosphere into the hydrosphere through precipitation. Water cycles from the hydrosphere back to the atmosphere through evaporation.
Which of the following is one way that these patterns can effect climate?
Areas located near a large body of water typically receive more precipitation than areas that are not located near water.
Convection currents, which affect weather and climate, are created by
the uneven heating of the Earth.
Which of the following statements best describes global temperature patterns?
The temperature of a specific region tends to change in fairly predictable patterns throughout a day and during the course of a year.
Seasonal changes in water temperature tend to remain within a narrow range. This is opposed to air temperature, which tends to fluctuate across a wide range. The relative stability of ocean temperatures helps to regulate the temperatures of coastal regions. Why can water remain within a narrow range of temperatures?
It has a high heat capacity.
The Sun's energy is critical to the Earth's climate and weather patterns because it drives the water cycle. Which stage of the water cycle is the Sun's energy most critical to?
evaporation
he polar climate zone is the coldest of the three zones. Why is this?
The polar climate zone is located between about 67°N latitude and the North Pole—this latitude zone receives less sunlight than the other two latitude zones.
Weather is a condition of the atmosphere at a particular time and place. Wind, rain, and cloud formations are all forms of weather phenomena. What is the primary source of energy for weather phenomena?
solar radiation
The equator tends to contain regions with hot climates. However, the Rwenzori Mountains, which are located close to the equator, are covered in ice caps. Why is the climate of the Rwenzori Mountains not hot?
Temperatures decrease with elevation
A number of factors work together to create climate. What are the two main factors to consider in determining the climate of an area?
temperature and precipitation
The best statement that explains why different areas of the Earth have different amounts of heat energy is that "Earth receives different amount of solar energy in different regions " .
In the question ,
it is given that ,
Global climate & weather patterns are driven by differences in amount of heat energy in different areas of Earth .
we have to find the true statement for the given cause .
we know that ;
Different parts in the Earth surface receive different amounts of sunlight . The Sun rays strike the Earth surface most directly at Equator.
that means Near the poles, the Sun rays strike surface at a slant due to which the rays spread over wide area.
The more focused rays are, more energy the area receives, and it will be more warmer .
Therefore , the correct statement to explain given reason is "Earth receives different amount of solar energy in different regions " .
The given question is incomplete , the complete question is
Global climate and weather patterns are driven by differences in the amount of heat energy in different areas of the Earth. Which statement best explains why different areas of the Earth have different amounts of heat energy ?
(a) The solar radiation from the Sun is equally distributed across the Earth at all times.
(b) The gravitational energy from the Sun varies greatly in different regions of the Earth.
(c) The Earth spins at different rates so the rotational energy of the Earth varies.
(d) The Earth receives different amounts of solar energy in different regions
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What is the net work required to slow down a 5,020kg car from 41.0m/s to 21.0m/s?
a. Wnet = 6.22 · 106J
b. Wnet = 5.02 · 104J
c. Wnet = -3.11· 106J
d. Wnet =-9.85 · 105J
The net work that has been done is obtained as 5.02 * 10^4J. Option B
What is the net work that is required?We have to note that the work that is done is defined as the product of the force that has been applied and the acceleration of the object. In this case ,we can see that there is work that has been done as the velolcity of the object is changed.
Hence;
Work done = 1/2mΔv^2
m = mass of the object
v = velocity of the object
Thus;
Work done = 0.5 * 5020 * (21 - 41)^2
Work done = 5.02 * 10^4J
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What is the power of a crane that does 5.60 kJ of work in 2.80 s?
Answer:
2000 WExplanation:
The power of the crane can be found by using the formula
\( p = \frac{ \orange{w}}{ \orange{t}} \\ \)
w is the workdone
t is the time taken
From the question we have
\(p = \frac{5600}{2.8} \\ \)
We have the final answer as
2000 WHope this helps you
Which one is greater 2.62 , 2 2/5 , 26.8 , 2.26 , 271%.
In order to compare the numbers, let's put all of them into the decimal form:
\(\begin{gathered} 2.62 \\ \\ 2\frac{2}{5}=2+\frac{2}{5}=\frac{10}{5}+\frac{2}{5}=\frac{12}{5}=2.4 \\ \\ 26.8 \\ \\ 2.26 \\ \\ 271\text{\%}=\frac{271}{100}=2.71 \end{gathered}\)We can see that the greater one is 26.8 (all other numbers are close to 2, and this one is close to 27).
The numbers in decrescent order are:
26.8, 271%, 2.62, 2 2/5, 2.26.
Answer:
26.8
Explanation:
2.26 < 2.4 < 2.62 < 271/100 = 2.71 < 26.8
Three lamps with wattages of 100 watts, 250 watts, and 60 watts, are connected on a circuit. What is the total power consumed by the circuit when all lamps are operating at the rated voltage
The total power consumed by the circuit is 410 watts
Power can be described as the rate at which work is carried out in a body. It can also be described as the movement or transfer of energy from one form to another.
From the question stated above, the total power can be calculated as follows:
P1 + P2 + P3
= 100 + 250 + 60
= 410
Hence the total power in the circuit is 410 watts
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energy is transmitted only in indivisible discrete quantities
Answer:
Planck postulates that the energy exchanges between matter and radiation do not take place in continuous manner but by discrete and indivisible quantities or quanta of energy. He then shows that the quantum of energy must be proportional to the frequency ν of the radiation. (1.1) where h is known as the Planck’s constant.
Explanation:
what is technology?
Answer:
Technology is the application of scientific knowledge to the practical aims of human life or, as it is sometimes phrased, to the change and manipulation of the human environment.
Please Mark it as brainlist answer.
Different forces were applied to five balls, and each force was applied for the same amount of time. The data is in the table. A 4 column table with 3 rows. The first column is labeled Object with entries Ball A, Ball B, Ball C, Ball D. The second column is labeled Force in Newtons with entries 50 N, 60 N, 70 N, 80 N. The third column is labeled Time in seconds with entries 1. 25, 1. 25, 1. 25, 1. 25. The fourth column is labeled Impulse in Newtons times seconds with entries 62. 5, 75, 87. 5, 100. If the force on ball A doubles while the time remains the same, what happens to the impulse? It divides in half. It does not change. It doubles. It quadruples.
The magnitude of impulse on Ball A will become twice (doubles). Hence, option (c) is correct.
Impulse:
The effect of applied force acting for a very small interval of time is known as Impulse.
Given data:
The initial magnitude of the force on Ball A is, F = 50 N.
The time interval for the applied force on Ball A is, t = 1.25 s.
And the impulse at initial on ball A is, I = 62.5 N-s.
Now, if force on ball A doubles, which means new magnitude of force is,
F' = 2F
F' = 2 × 50
F' = 100 N
For same time interval, the new impulse on Ball A is given as,
I' = F' × t
Solving as,
I' = 100 × 1.25
I' = 125 N-s
Taking the ratio of both the impulses as,
I' / I = 125/62.5
I' = 2 I
Thus, we can conclude that the magnitude of impulse on Ball A will become twice (doubles). Hence, option (c) is correct.
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Answer:
C. It doubles.
Explanation:
hope this helps:)
Please help with the following image!
The kinetic energy of the ball is 450 J.
What is the kinetic energy of the ball?We have to note that the kinetic energy that the body has is the energy that the body has due to the fact that the body is in motion. This is why the object that undergoing kinetic energy must have a velocity of the object.
We have to note that the kinetic energy can be given using the formula;
KE = 0.5mv^2
KE = kinetic energy
m = mass of the object
v = velocity of the object'
Then we have;
KE = 0.5 * 4 * 15^2
KE = 450 J
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In freefall, heavier objects fall with a greater acceleration than lighter objects.
Answer:
That is not true all objects fall at the same speed excepts things like feathers or paper.
Answer: false
Explanation: apex
Place a +3q point charge at the origin, and a -q point charge on the x-axis at D = 0.500 m. At what point on the x-axis will the net forces from the other two charges acting on a third charge, q°, be equal to zero?
The Point on the x-axis that the net forces from the other two charges acting on a third charge, q°, will be equal to zero is
x=1.72units
This is further explained below.
What are forces?Generally, The total amount of forces exerted on an item is referred to as its net force. The total of N forces exerted on an item is given in the equation below.
The total force operating on an item, which may include a number of different forces, is known as the net force acting on the object.
The n forces operating on an item are added up in this equation. According to this formula, the amount of net force exerted on an item is equal to the mass times the acceleration of the object.
+3q <------>+11q
\(&\frac{1}{4 \pi E v}\left(\frac{3 q}{x^2}-\frac{11 q}{(5-x)^2}\right)=0 \\\\&\frac{3}{x^2}=\frac{11 q}{(5-x)^2} \\&\frac{5-x}{x}=\sqrt{\frac{11}{3}}=1.91 \\\\\)
5-x=1.91 x
=1.715
=1.72units
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que tienen en común la materia y el sistema?
Answer:
La materia es la sustancia de la que está hecho todo material. En física, el sistema es una de las propiedades de la materia. Se puede transferir entre objetos y convertir en forma. No se puede crear ni destruir.
espero que te ayude!
A dolphin's tops speed is 17 m/s. If a dolphin swam at this constant velocity for one hour
(3600 s), how far would she go?
Answer:
The answer is 61,200 mExplanation:
To find the distance covered by the dolphin , we use the formula
distance = velocity × timeFrom the question
velocity = 17 m/s
time = 3600 s
We have
distance = 17 × 3600
We have the final answer as
61,200 mHope this helps you
Approximately where is the Sun in terms of its total lifetime?
A. It is about halfway through its life.
B. It is only 1/10 of the way through its life.
C. It is about 3/4 of the way through its life.
D. It is about 1/4 of the way through its life.
The Sun is approximately 3/4 of the way through its lifetime.
The Sun is a main-sequence star, meaning it is in the middle stage of its life cycle. Stars like the Sun undergo nuclear fusion, where hydrogen atoms fuse to form helium and release energy. This fusion process provides the Sun with the energy to shine.
Based on current scientific understanding, the Sun is estimated to have a total lifetime of about 10 billion years. It is currently around 4.6 billion years old, which means it has already passed the quarter mark of its lifetime.
As the Sun continues to burn hydrogen in its core, it will gradually undergo changes. Over time, it will exhaust its hydrogen fuel and start to expand into a red giant, eventually shedding its outer layers and forming a white dwarf.
Therefore, considering the Sun's age and estimated total lifetime, it is believed to be approximately 3/4 of the way through its life. However, it's important to note that estimating the exact lifespan of a star is complex, and our understanding may evolve with further research.
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The Sun is approximately 3/4 of the way through its lifetime.The Sun is a main-sequence star, meaning it is in the middle stage of its life cycle. Stars like the Sun undergo nuclear fusion, where hydrogen atoms fuse to form helium and release energy. This fusion process provides the Sun with the energy to shine.
Based on current scientific understanding, the Sun is estimated to have a total lifetime of about 10 billion years. It is currently around 4.6 billion years old, which means it has already passed the quarter mark of its lifetime.
As the Sun continues to burn hydrogen in its core, it will gradually undergo changes. Over time, it will exhaust its hydrogen fuel and start to expand into a red giant, eventually shedding its outer layers and forming a white dwarf.
Therefore, considering the Sun's age and estimated total lifetime, it is believed to be approximately 3/4 of the way through its life. However, it's important to note that estimating the exact lifespan of a star is complex, and our understanding may evolve with further research.
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which of the following travels the slowest? radio waves visible light x-rays infrared light the (radio waves, visible light, x-rays and infrared light) all travel at the same speed
All of the following (radio waves, visible light, x-rays, and infrared light) travel at the speed of light, which is 299,792,458 meters per second. Therefore, none of them travel at the same speed.
Electromagnetic waves are a type of energy wave that consists of oscillating electric and magnetic fields, which propagate through space at the speed of light. They are created by the motion of charged particles, and they can travel through a vacuum or through various materials.
All of the options listed, including radio waves, visible light, X-rays, and infrared light, travel at the same speed, which is the speed of light in a vacuum and all of them are electromagnetic waves. This speed is approximately 299,792,458 meters per second (or about 186,282 miles per second).
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in what state of matter can conduction occur.
Answer: Conduction occurs more readily in solids and liquids, where the particles are closer to together, than in gases, where particles are further apart.
Answer:
conduction occurs when gas becomes liquid.
What is the height of the cannon before it is launched, at t=0? Remember to include units.
The height of the cannon before it is launched, at t=0, is 58 m.
Model for the motion of the cannon ball
The equation of motion of the cannon ball is given as;
h(t) = -4.9t² + 19.8t + 58
Height of the cannon at time, t = 0The initial height of the cannon before it was launched is calculated as follows;
h(0) = -4.9(0) + 19.8(0) + 58
h(0) = 58 m
Thus, the height of the cannon before it is launched, at t=0, is 58 m.
Complete question is below:
The equation that models the path of a cannon ball is h(t) = -4.9t² + 19.8t + 58. What is the height of the cannon before it is launched, at t=0? Remember to include units.
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Susie Small finds she weighs 300 N.
Calculate her mass.
Answer:
30Kg
Explanation:
Weight = mass x gravitational field strength
300 = mass x 10
mass = 30kg
gravitational field strength is 9.8 on earth but normally we take it to be 10 for easy reference and calculations
The mass will be "30 kg". A further solution is provided below.
According to the question,
Weight,
300 NWe know that,
Gravitational field strength,
10The mass will be:
→ \(Weight = Mass\times Gravitational \ field \ strength\)
or,
→ \(Mass = \frac{Weight}{Gravitational \ field \ strength}\)
By putting the values, we get
→ \(= \frac{300}{10}\)
→ \(= 30 \ kg\)
Thus the above solution is right.
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if a 1.11 n⋅mn⋅m torque is required to pull a given weed, what force did the weed exert on the tool?
Therefore, the force exerted by the weed on the tool is 5 Newtons.
When an engine exerts itself, torque, which is a twisting force, speaks to the rotational force of the engine and quantifies how much of that twisting force is accessible. Everyday activities like turning a doorknob, opening a drink bottle, using a tool, or peddling a bicycle all involve torque.
To find the force exerted by the weed on the tool, we can use the formula:
Torque = Force × Lever Arm
Given that the torque is 1.11 nm and the lever arm is 0.22 m, we can rearrange the formula to solve for the force:
Force = Torque / Lever Arm
Converting the lever arm from centimeters to meters, we have:
Force = 1.11 nm / 0.22 m
= 5 N
Therefore, the force exerted by the weed on the tool is 5 Newtons.
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Find the net force acting on a box that has a force of 50 newtons pulling at an angle of 30 degrees and a force of 90 newtons pulling at a 160 degree angle
Answer:
Approximately \(69\; {\rm N}\) at approximately \(126^{\circ}\).
Explanation:
Assume that both angles in the question are relative to the positive \(x\)-axis (towards the positive horizontal direction.)
Horizontal component (\(x\)-component) of the two forces would be:
\((50\; {\rm N}) \, \cos(30^{\circ}) = \left(25\, \sqrt{3}\right)\; {\rm N} \approx 43.3\; {\rm N}\).\((90\; {\rm N}) \, \cos(160^{\circ}) \approx (-84.6) \; {\rm N}\).Note that the \(x\)-component of the \(90\; {\rm N}\) force is negative since this components points away from the positive \(x\!\)-direction.
Hence, the net force in the \(x\)-component would be:
\((50\; {\rm N}) \, \cos(30^{\circ}) + (90\; {\rm N}) \, \cos(160^{\circ}) \approx (-41.3) \; {\rm N}\).
(Again, this component is negative since it points away from the positive \(x\)-axis.)
Similarly, the vertical component (\(y\)-component) of the two forces would be:
\((50\; {\rm N}) \, \sin(30^{\circ}) = 25\; {\rm N}\).\((90\; {\rm N}) \, \sin(160^{\circ}) \approx 30.8 \; {\rm N}\).Hence, the net force in the \(y\)-component would be:
\((50\; {\rm N}) \, \sin(30^{\circ}) + (90\; {\rm N}) \, \sin(160^{\circ}) \approx 55.8\; {\rm N}\).
Refer to the diagram attached. The resultant net force is the vector sum of the components. Apply the Pythagorean Theorem to find this net force:
\(\begin{aligned}(\text{net force}) &= \sqrt{(\text{$x$-component})^{2} + (\text{$y$-component})^{2}} \\ &\approx \sqrt{(-41.3)^{2} + (55.8)^{2})}\; {\rm N} \\ &\approx 69\; {\rm N}\end{aligned}\).
Find the angle of this net force relative to the positive \(x\)-axis using the inverse cosine function \(\arccos\):
\(\begin{aligned}\arccos\left(\frac{(\text{$y$-component})}{(\text{net force})}\right) &\approx \arccos\left(\frac{55.8\; {\rm N}}{69\; {\rm N}}\right) \\ &\approx 126^{\circ}\end{aligned}\).
(The units might need to be converted into degrees.)
What is energy and what is the formula of energy
Answer:
Energy is: the ability to do work
The formula for energy is: power x time = energy
Explanation:
Hope this helps (there isn't really an explanation)
If a runner exerts 457 j of work to make 321 w of power then how long did it take the runner to do the work
The time taken by the runner to do the work is 1.42 seconds.
Given the data in the question;
Work done; \(W = 457J\)Power; \(P = 321W\)Time elapsed; \(t = \ ?\)PowerPower can be simply referred to as the quantity of energy transferred per unit time.
It is expressed as;
\(P = \frac{W}{t}\)
Where W is work done and t is time elapsed.
To determine the time it took the runner to do the work, we substitute our given values into the expression above.
\(P = \frac{W}{t} \\\\t = \frac{W}{P} \\\\t = \frac{457J}{321W} \\\\t = \frac{457 kgm^2/s^2}{321 kgm^2/s^3}\\\\t = 1.42s\)
Therefore, the time taken by the runner to do the work is 1.42 seconds.
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