Assuming premise y is directly related to x2, k must exist by which y = k * x2.
Y is directly a square of the square with X, yet what does this mean?Also, we wish to use the proportional variable, k, in a solution to describe each of these relationships. So, in the first, y changes in direct proportion to the square of x. This may now be expressed as y is directly related to x squared. In the above equation, y is equal to a certain integer multiplied by x squared.
When X and Y are connected directly, what does it mean?This implies that the proportion between both always maintains the same, meaning that if x improves, y rises, and as x drops, y decreases. The proportionality connection equation's graph is a line that passes directly through the origin.
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A food processor draws 8.47 A of current when connected to a potential difference of 110 V.
a. What is the power consumed by this appliance?
b. How much electrical energy is consumed by this food processor monthly (30 days) if it is used on average of 10.0 min every day?
c. Assume that the price of electrical energy is 7.00 $/kWh. What is the monthly cost of using this food processor?
2. The electric meter in a house indicates that the refrigerator consumes 70.0 kWh in a week.
a. What is the power consumption of the refrigerator?
b. Assuming it is connected to a potential difference of 120 V , how much current does the refrigerator draw?
3. The heating element of an electric broiler dissipates 2.8 kW of power when connected to a potential difference of 120 V.
a. What is the resistance of the element?
b. How much current does the broiler draw? Use two ways to find out, and verify your answer.
Answer:
i want the answer
Explanation:i want the answer
a. The power consumed by this appliance is 931.7W
b. The electrical energy is consumed by this food processor monthly (30 days) if it is used on average of 10.0 min every day is 4.65kWh
c. The monthly cost of using this food processor is 32.55 $
What is power?
The rate of consumption of energy is power. it is given by the product of potential difference(V) and current(I)
a. P = VI
here V = 110V . I = 8.47 A
P = 110 x 8.47 = 931.7W
hence power consumed is 931.7 W
b. electrical energy consumed by this food processor monthly (30 days) if it is used on average of 10.0 min every day is
E = P/t
Here, P = 931.7 W = 0.93kW
t = 10 x 30 = 300 min = 5 h
So, E =0.93 x 5 = 4.65 kWh
hence electrical energy consumed is 4.65kWh
c. The monthly cost of using the food processor is
given ,
Cost of one unit is 7.00$
Cost of 4.65 unit will be 7.0 x 4.65 = 32.55$
monthly cost of using the food processor is 32.55$
2.
a. Power consumption of refrigerator is 416 W
P = E/t
Here, E = 70 kwh . t = 1 week = 168 h
So, P= 70/168 = 0.416 kW = 416 W
b. Current drawn by the refrigerator is 3.46A
P = VI
Here, V = 120V, P = 416 W
So, I = P/V = 416/120 = 3.46 A
3.
a. The resistance of the element is 5.14 Ω
b. Current drawn by the boiler is 23,33A
What is resistance?Resistance is the hindrance caused in the flow of current
a. The resistance is given by \(R = v^{2} / P\)
here V = 120V , P = 2.8kW = 2800W
R = (120 x 120)/ 2800 = 5.14Ω
Hence Resistance of the boiler is 51.4Ω
b. V = IR so, I = V /R
Here, V = 120V , R = 5.14Ω
So, I = 120/51.4 = 23.33 A
Hence current drawn by the boiler is 23.33A
The alternate way to find the current is by using formula
P = VI
I = P/V
Since, P = 2800W, V = 120V
So, I = 2800/120 =23.33 A
Hence Current comes out to be the same from both the method which verifies the answer .
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What is the Big-Bang Theory?
The Big Bang theory is the prevailing cosmological model that explains the origins of the universe. According to the theory, the universe began as a singularity, a hot and infinitely dense point, approximately 13.8 billion years ago. From this singularity, the universe expanded and cooled, eventually leading to the formation of subatomic particles, atoms, stars, and galaxies. The theory also states that the universe is still expanding and it's getting cooler and larger.
The theory was first proposed by Belgian priest and physicist Georges Lemaître in 1927 and later developed by Edwin Hubble's observations of the redshifts of distant galaxies in the 1920s and 1930s. The theory has been extensively tested and supported by a wide range of observational evidence, including cosmic microwave background radiation and the large-scale structure of the universe.
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Answer:
The Big-Bang Theory is the prevailing cosmological model for the universe from the earliest known periods through its subsequent large-scale evolution. The model describes how the universe expanded from an initial state of high density and high temperature, and offers a comprehensive explanation for a broad range of phenomena, including the abundance of light elements, the cosmic microwave background, large scale structure and Hubble's law. According to the Big-Bang Theory, the universe was once in an extremely hot and dense state which expanded rapidly. As it cooled, the first subatomic particles formed and then simple atoms, eventually leading to the formation of stars and galaxies. The Big-Bang Theory is supported by a wide range of scientific observations and provides a comprehensive explanation for the structure and evolution of the universe.
how is potential energy a scalar quantity even though it can be negative?
Explanation:
Potential energy is a scalar quantity because it has only magnitude and no direction. Its ability to be negative does not affect its scalar nature.
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To a man running east at the rate of 3m/s vain appears to fall vertically with a speed of 4m/s. Find the actual speed and direction of rain...
Answer:
The actual speed of the rain is 5 m/s and its direction is -53.13°
Explanation:
The actual speed of the rain V = speed of man, v + speed of rain relative to man, v'.
V = v + v'
We add these vectorially.
Since the man's speed is 3 m/s east, in the positive x - direction, we have v = 3i and the rain's speed is falling vertically at 4 m/s, in the negative y- direction, we have v' = -4j
So, V = v + v'
V = 3i + (-4j)
V = 3i - 4j
So, the magnitude of V which is its speed is V = √(3² + (-4)²) = √(9 + 16) = √25 = 5 m/s
The direction of V, Ф = tan⁻¹(vertical component/horizontal component) = tan⁻¹(-4/3) = tan⁻¹(-4/3) = tan⁻¹(-1.333) = -53.13°
So, the actual speed of the rain is 5 m/s and its direction is -53.13°
A car accelerates from 20 m/s to 30m/s in 10s
,draw velocity time graph to show cars motion.find the distance its travels by calculating the area under the graphing?
Answer:
250 m
Explanation:
Refer to the attachment for the graph. Here, we are asked to calculate the distance travelled.
⇒ Area under the graph = Distance travelled by the body
Let the distance travelled by the body be S. Area under the graph will be the area of the trapezium ABCD.Area of trapezium = ½ × Sum of parallel sides × Height
\( \twoheadrightarrow \quad \sf {S = \dfrac{1}{2}\times (AD + BC) \times OC} \\ \)
\( \twoheadrightarrow \quad \sf {S = \dfrac{1}{\cancel{2}}\times (10+30) \times \cancel{10}} \\ \)
\( \twoheadrightarrow \quad \sf {S = 1\times 50 \times 5} \\ \)
\(\twoheadrightarrow \quad \boxed{\red{\sf{ S = 250 \; m}}}\\\)
❝ Therefore, distance travelled by the body is 250 m. ❞
3. Chrome planting is one method used to prevent corrosion. This process can be carried out by a. Zone refining b. Using secondary cells c. Using primary cells d. Electrolylic process
ItItItIt is carried out by using secondary cells .
What is chrome plating is made up of ?It is made up of by aluminium, nickel ,zinc, titanium,copper ,steal , stainless steel. There are two different types of chrome plating hard chromium and decorative chromium plating.
Chrome plating is used to prevent corrosion . Helps to minimize the wear and tear ,as well as increase the lifespan of the material. By adding the layer on another material it can remove the corrosion, reduce friction, enhance its appearance.
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Rhea is driving north in a straight line. After driving for 2.4 kilometers, she turns west, and drives for 3.1 km. At the end of her drive, what is the magnitude of her displacement vector? To find the magnitude of a resultant vector, use the Pythagorean theorem: a² + b² = c² A) 3.9 km B) 5.5 km (this one is incorrect) C) 2.8 km D) 2.3 km
Option A) 3.9 km is the correct answer. the magnitude of Rhea's displacement vector is approximately 3.92 km.
In order to find out the magnitude of Rhea's displacement vector, we have to add up all of the displacement vectors.
Then we can use the Pythagorean theorem to calculate the magnitude of the resultant vector.
Since Rhea is first driving north for 2.4 km and then west for 3.1 km, we can represent her displacement vectors as follows: Δx = 0 km and Δy = 2.4 km for the first vector, and Δx = -3.1 km and Δy = 0 km for the second vector.
We can then add these vectors together by adding their components: Δx = 0 km + (-3.1 km) = -3.1 km and Δy = 2.4 km + 0 km = 2.4 km.
This gives us a resultant vector of -3.1 km east and 2.4 km north.
Using the Pythagorean theorem, we can find the magnitude of this vector: \(\sqrt{(\(-3.1 km)^{2} + (2.4 km)^{2} ) } = \sqrt{(9.61 + 5.76) km^{2} } = \sqrt{15.37 km^{2} } \approx 3.92 km.\)
Therefore, the magnitude of Rhea's displacement vector is approximately 3.92 km.
Therefore, option A) 3.9 km is the correct answer.
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1.2 consider the following time periods: Ancient civilisation, 21th century. in each time period, based on you understanding of the differences between the time periods: a) write a paragraph of five lines in each time period b)locate the time period in your own context.
Answer: In contrast to the 21st century, which is a period of enormous technological advancement and globalization, ancient civilizations were agrarian communities with a high degree of social stratification.
Explanation: the differences between ancient civilizations and the 21st century, in two paragraphs of five lines each:
A)
Ancient civilizations:
Paragraph 1: Ancient societies were agrarian, focusing on commerce and agriculture, with a small elite ruling a large population of farmers, artisans, and laborers.
Paragraph 2:Ancient civilizations advanced art, architecture, mathematics, science, and social systems, creating religious beliefs and intricate social systems like Egyptian, Greek, Roman, and Chinese.
21st century:
Paragraph 1: Globalization and technological advancements in the 21st century have made us connected to the world, enabling us to stay connected through information and communication tools.
Paragraph 2: The 21st century faces challenges like economic inequality, political instability, and climate change, yet it also represents a hopeful generation dedicated to improving the world and overcoming these challenges.
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In ancient civilizations, major developments in human history took place, such as the invention of writing systems and the rise of empires. In the 21st century, advancements in technology and globalization have transformed the world. Ancient civilizations have exerted a lasting influence on our modern world, from written communication to political systems and architectural wonders.
Explanation:In ancient civilizations, major developments in human history took place, such as the invention of writing systems, the rise of empires, and the development of complex societies. For example, in ancient Egypt, pharaohs ruled over a hierarchical society and constructed impressive monuments like the pyramids. In the 21st century, advancements in technology and globalization have transformed the world. This period is characterized by rapid communication, scientific and technological breakthroughs, and interconnectedness through the internet and social media.
Locating ancient civilizations in our own context, we can observe their influence in our modern world. The writing systems developed by ancient civilizations laid the foundation for written communication, which is still vital today. The concept of empires and nation-states, which began in ancient times, is significant in understanding modern political systems. Additionally, the architectural wonders of ancient civilizations, like the Great Wall of China and the Colosseum, continue to be celebrated and preserved as cultural heritage.
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air is a gas and the particles can be pushed closer toegether which is called
Two masses m1m1 and m2m2 exert a gravitational force of 12 N onto each other when they are 6 m apart. What will the gravitational force be if the masses are moved closer to be 3 m apart?
Answer:
48N
Explanation:
because as the distance is halfed. the force on the two objects are quadrupled.
Darcy suffers from farsightedness equally severely in both eyes. The focal length of either of Darcy's eyes is 19.8 mm in its most accommodated state (i.e, when the eye is focusing on the closest object that it can clearly see) What lens strength (a.k.a., lens power) of contact lenses should be prescribed to correct the farsightedness in Darcy's eyes? (Assume the lens-to retina distance of Darcy's eyes is 2.00 cm, and the contact lenses are placed a negligibly small distance from the front of Darcy's eyes)
i. 1.64D
ii. 2.98 D
iii. 2.19 D
iv. 3.49 D
v. 1.37 D
Answer:
Explanation:
Power of defective eye = (1 / near point )+ (1 / lens-retina distance )
1 / .0198 m = (1 / near point )+ (1 / .02 m )
= 50.50 = (1 / near point )+ 50
0.50 = 1 / near point
near point = 1 / .5 = 2m
= 200 cm .
for near point at 25 cm , convex lens will be required.
u = - 25 cm , v = - 200 cm ,
1 / v - 1 / u = 1 /f for lens
- 1 / 200 + 1 / 25 = 1 / f
= .04 - .005 = 1 /f
.035 = 1 / f
f = 28.57 cm = 0.2857 m
power = 1 /f
= 1 / 0.2857
= 3.5 D .
i v ) option is correct .
"An egg is free-falling from a nest in a tree. Neglect air resistance."
A There are two forces acting on the egg and
the forces are balanced.
C There are three forces acting on the egg and
the forces are unbalanced.
B There is one force acting on the egg and the
force is unbalanced.
D
There are four forces acting on the egg and
the forces are balanced.
In a scenario where an egg is free-falling from a nest in a tree and neglecting air resistance, there is one force acting on the egg and the force is unbalanced which is denoted as option B.
What is a Force?This is referred to as an external agent which is capable of influencing the motion of an object or body. It is also capable of changing the state of rest of a body and the unit in Newton.
When an object is falling from a height and there is no air resistance then the only force acting on it is gravitational force which is unbalanced as there is no equal and opposite force to make it stable.
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A softball player swings a bat, accelerating it from rest to 2.2 rev/srev/s in a time of 0.20 ss . Approximate the bat as a 2.3-kgkg uniform rod of length 0.96 mm , and compute the torque the player applies to one end of it.
Answer:
83.168 Nm
Explanation:
I=mass of bat* ( length )^2 /3
Moment of inertia from one end = 2.2 * (0.96)^2 / 3.
Ang. acc. = 2.2×2 pi / 0.2 = 22pi
Torque = 2.3 * (0.96)^2 / 3 * 22 pi = 83.168 Nm SI units
Mars orbits the sun at less then 60% of the speed of earth. True or false?
Answer:
True im pretty sure
Explanation:
Answer:
False
Explanation:
The answer is false, I tested it on IXL
John drove a truck for one hour at a rate of 80 kilometers per hour (km/hr). The next hour, he drove at 100 km/hr. What was his average speed during those two hours?
km/hr
Please i have asked a.question please help.me
Explanation:
Please i have asked a question in math please help me
Force varies directly with pressure. A force of 22,000 newtons acts on an object, causing 110 N/m² of pressure. The
force decreases to 18,000 newtons. What is the new amount of pressure caused by the force?
○ 45 N/m²
90 N/m²
O 75 N/m²
60 N/m²
The final amount of pressure caused by the force is 90 N/m².
Initial amount of force, F₁ = 22 x 10³ N
Initial amount of pressure produced, P₁ = 110 N/m²
Final amount of force exerted, F₂ = 18 x 10³ N
Pressure is defined as the amount of force acting on an object per unit area of the object.
So, we can say that the force and pressure are directly proportional.
F ∝ P
So, F₁/P₁ = F₂/P₂
Therefore, the final amount of pressure caused by the force is,
P₂ = F₂P₁/F₁
P₂ = 18 x 10³x 110/22 x 10³
P₂ = 18/0.2
P₂ = 90 N/m²
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The coefficient of static friction between a rubber tire and dry pavement is about 0.800. Assume that a car’s engine only turns the two rear wheels and that the weight of the car is uniformly distributed over all four wheels.
What limit does the coefficient of static friction place on the time min required for a car to accelerate from rest to 60.0 mph (26.8 m/s)?
The coefficient of static friction places a limit of approximately 3.42 seconds on the minimum time required for the car to accelerate from rest to 60.0 mph (26.8 m/s).
To find the limit that the coefficient of static friction places on the minimum time required for a car to accelerate from rest to 60.0 mph (26.8 m/s), we need to consider the maximum acceleration the car can achieve due to the friction between the rear tires and the pavement.
The maximum acceleration can be determined using the formula:
a_max = μs * g
where μs is the coefficient of static friction and g is the acceleration due to gravity (approximately 9.8 m/s²).
In this case, since the car's engine only turns the two rear wheels, the maximum acceleration is limited by the friction force between the rear tires and the pavement.
Now, to calculate the minimum time required to accelerate to 60.0 mph (26.8 m/s), we can use the following kinematic equation:
v = u + a * t
where v is the final velocity (26.8 m/s), u is the initial velocity (0 m/s), a is the acceleration, and t is the time.
Rearranging the equation, we have:
t = (v - u) / a
Plugging in the values, we get:
t = (26.8 m/s - 0 m/s) / a_max
t = 26.8 m/s / (μs * g)
Substituting the given value for the coefficient of static friction (μs ≈ 0.800) and the acceleration due to gravity (g ≈ 9.8 m/s²), we can solve for the minimum time required:
t = 26.8 m/s / (0.800 * 9.8 m/s²)
t ≈ 3.42 seconds
Therefore, the coefficient of static friction places a limit of approximately 3.42 seconds on the minimum time required for the car to accelerate from rest to 60.0 mph (26.8 m/s).
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In a five paragraph essay, the ________ is the main idea you're trying to prove.
Which of the following statement is true of ATP? A. ATP stands for adenosine triphosphate
B. ATP consists of one adenosine atom and three phosphate atoms
C. ATP consists of one adPOenosine atom and two phosphate atoms
D. The breakdown of ATP provides the energy needed to fuel muscle contraction
The one that is accurate is that when the phosphate is broken down into ADP, ATP releases energy.
Does ATP save its energy in glucose form?The energy that cells need is produced through the breakdown of glucose. More energy cannot be stored by ATP molecules than is released by the cells. In actuality, ATP doesn't retain as much energy as a glucose molecule. See the equation in the question; roughly 38 ATP molecules are produced for every glucose molecule.
How does ATP store energy?The cell stores extra energy by reattaching a free phosphate molecule to ADP, converting it back into ATP. This extra energy can come from the breakdown of food that has been ingested or, in the case of plants, energy produced during photosynthesis.
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A ball is thrown directly downward with an initial speed of 8.30 m/s, from a height of 29.2 m. After what time interval does it strike the ground?
The ball's height \(y\) at time \(t\) is given by
\(y = 29.2\,\mathrm m - \left(8.30\dfrac{\rm m}{\rm s}\right) t - \dfrac12 gt^2\)
where \(g=9.80\frac{\rm m}{\mathrm s^2}\).
Solve for \(t\) when \(y=0\). Omitting the units, we have
\(29.2 - 8.30t - \dfrac g2 t^2 = 0\)
I'll solve by completing the square.
\(29.2 - \dfrac g2 \left(t^2 + \dfrac{16.6}g t\right) = 0\)
\(29.2 - \dfrac g2 \left(t^2 + \dfrac{16.6}g t + \dfrac{8.3^2}{g^2}\right) = -\dfracg2 \times \dfrac{8.3^2}{g^2}\)
\(29.2 - \dfrac g2 \left(t + \dfrac{8.3}g\right)^2 = -\dfrac{8.3^2}{2g}\)
\(\dfrac g2 \left(t + \dfrac{8.3}g\right)^2 = 29.2 + \dfrac{8.3^2}{2g}\)
\(\left(t + \dfrac{8.3}g\right)^2 = \dfrac{58.4}g + \dfrac{8.3^2}{g^2}\)
\(t + \dfrac{8.3}g = \pm \sqrt{\dfrac{58.4}g + \dfrac{8.3^2}{g^2}}\)
\(t = -\dfrac{8.3}g \pm \sqrt{\dfrac{58.4}g + \dfrac{8.3^2}{g^2}}\)
\(\implies t \approx -3.43 \text{ or } t \approx 1.74\)
Ignore the negative solution; the ball hits the ground about 1.74 s after being thrown.
Question 2 of 10
What is the current in the 10.0 2 resistor?
10.00
w
120.0 V
20.00
w
30.00
A. 10.0 A
B. 12.0 A
C. 0.0833 A
O D. 2.00 A
Answer:
2.00 A
Explanation:
Total resistance = 10 + 20 + 30 = 60 ohms
Potential difference (V) = 120volts
Current (I) =?
from Ohms law V = IR
==> I = V/R = 120/60 = 2 A
Note: for resistors in series equal amount of electric current flows through the circuit
in this experiment you need to examine the idea of thermal energy transfer. Using a controlled experiment what might a good question about the variables that affect thermal energy transfer be? Therapist energy transfer depends on many properties, but limit your question to only two
The thermal conductivity of a material and the temperature differential between two objects affect the rate of thermal energy transfer between them would be an excellent question on the factors that influence thermal energy transfer.
What is an example of regulating the passage of thermal energy?The amount of radiant energy that enters a residence in the winter is maximised by large windows that face south. Tiny windows that face north help keep heat in. Triple-paned windows minimise thermal energy loss.
What elements influence the transfer of thermal energy?The surface area, volume, material, and kind of the surface the object is in touch with are all factors that affect how quickly an object transfers energy by heating.
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The eight plants of the Solar System orbit the Sun in a chaotic random way.
True
False
Answer:
The Solar System has plants? I assume you meant planets. If so, that is false
Explanation:
The way in which one atom interacts with another atom is mostly influenced by the configuration of the
A. electrons farthest from the nucleus.
B. protons in the center of the nucleus.
C. electrons closest to the nucleus.
D. protons on the outer edge of the nucleus.
The way in which one atom interacts with another atom is mostly influenced by the configuration of the electrons farthest from the nucleus.
Option A.
What is atom?An atom can be defined as the smallest part of a substance that cannot be broken down chemically. Each atom has a nucleus (center) made up of protons (positive particles) and neutrons (particles with no charge).
The arrangement of electrons in orbitals and shells around the nucleus is referred to as the electronic configuration of the atom.
Thus, we can conclude that the way in which one atom interacts with another atom is mostly influenced by the configuration of the electrons farthest from the nucleus.
The remaining options do not fit the empty space properly, and they include;
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1.How do we define electric potential at any point in space ?
2.How does the electric potential change along the direction of the net electric field?Explain them in details.
Answer:
1. The electric potential at any point in space, is the work done in moving a unit charge from infinity to that point.
2.The electric potential varies radially by decreasing as the distance from the electric field increases.
Explanation:
1. The electric potential at any point in space, is the work done in moving a unit charge from infinity to that point. It is defined mathematically as, V = W/q where V = electric potential, W = work done in moving charge q into electric field and q = charge. For the work done of moving a charge q into an electric field of charge q' at a distance r between them, W = kqq'/r and work done per unit charge in moving q in electric field is V = W/q = kqq'/r ÷q = kq'/r, Also, for an electric field, E, V = ∫E.dr where r is the direction moved by the charge in the electric field.
2. Since the electric potential V = kq'/r, V ∝ 1/r since k and q' are constant. So, the electric potential varies radially by decreasing as the distance from the electric field increases.
4. A car travels at a speed of v = 54 km/h. During emergency braking, the wagon decelerates (brakes) with a deceleration (braking) of 3m/s per second. a) Convert the speed into the unit m/ s.b) Calculate how long the braking lasts. c) Sketch the v-t diagram and calculate the braking distance!
The given velocity is 54km/hr, which, when converted to m/s using 1km = 1000m and 1 hour = 3600 seconds, equals 15m/s.
How to calculate distance?Now substitute the initial speed u = 15m/s values.
v = 0m/s as the final velocity
Time is 6 seconds.
In the a= -3 m/ s2 equation,
s= ut + 1/2at2 s= 15 6+ 1/2(-3)(6)2 s= 90-45 s = 45m
As a result, after using the brakes, the car will halt for up to 45 meters.
The inverse of acceleration is deceleration. The deceleration will be calculated by dividing the final velocity minus the initial velocity by the time required for the velocity drop.
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IM BEGGING ILL GIVE BRAINLEST PLEASEEEEEEE HELP ME Distance and amount of charge are factors that determine which of the
following quantities?
A. Electrostatic force
B. Electric potential
C. Electric potential energy
D. All of the above
Explanation:
Distance and amount of charge are factors that determine which of the
following quantities?
D. All of the above
One end of a spring is attached to a wall. A 26 N pull on the other end causes the spring to stretch by 3.0 cm . What is the spring constant?
The force constant of the spring is 866.7 N/m.
What is the Hooke's law?In order to fix the question that we have here we have to look at the Hooke's law. From the Hooke's law we have to note that the force that is causing the string to become expanded is proportional to the extension of the spring as long as the elastic limit has not been exceeded.
Now we know that the Hooke's law would refer to the force and the extension and that is what we would need to be able to solve in order to get the force constant as we have been asked in the problem that we have here.
Thus;
F = Ke
F = force
K = force constant
e = extension
Then;
K = F/e
K = 26 N/3 * 10^-2 m
K = 866.7 N/m
From the calculation that we have done in the lines above, we have obtained the force constant to be about 866.7 N/m.
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2×3.14√(1.0m/(9.8〖ms〗^(-1) )=)
This is the period in a simple harmonic motion which is 2 seconds in this question.
What is Period ?The period of an oscillatory object can be defined as the total time taken by a vibrating body to make one complete revolution about a reference point.
We are given the below question
2×3.14√(1.0m/(9.8〖ms〗^(2) )= T
This question can as well be expressed as
2π√(L/g) which is equal to period T.
In a nut shell, Period T = 2×3.14√(1.0m/9.8)
T = 6.28√0.102
T = 6.28 × 0.32
T = 2.006 s
Therefore, the period T of the oscillation is 2 seconds approximately.
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A spring is attached to an inclined plane as shown in the figure. A block of mass m = 2.27 kg is placed on the incline at a distance d = 0.327 m along the incline from the end of the spring. The block is given a quick shove and moves down the incline with an initial speed v = 0.750 m/s. The incline angle is = 20.0°, the spring constant is k = 455 N/m, and we can assume the surface is frictionless. By what distance (in m) is the spring compressed when the block momentarily comes to rest?
Answer:
0.1351 m
Explanation:
*my number calculations may be wrong, but the process is correct*
W = Wg - Ws = mgh - \(\frac{1}{2}\)kx^2 = mg(d + x)sinθ - \(\frac{1}{2}\)kx^2
Δk = 0 - \(\frac{1}{2\\}\)mv\(_{i}\)^2
W = Δk
-\(\frac{1}{2}\)mv\(_{i}\)^2 = mg(d + x)sinθ - \(\frac{1}{2}\)kx^2
Now plug in your given values:
m=2.27, g=9.8, d=0.327, θ=20, k=455, v=0.750
Now rearrange the equation so it is in the form ax^2 + bx + c = 0 where x is the unknown distance you are looking for.
~if my math is correct it should be:~
0 = -227.5x^2 + 7.608580108x + 3.126443195
Now plug your numbers into the quadratic formula and the positive x value you get is the answer.
~if my math is correct it should be:~
x = 0.1351376847 m = 0.1351 m