Answer:
80%
Explanation:
efficiency = (useful work out / total energy in) x 100
= \(\frac{80}{100}\) x 100
= 80%
A thin half ring with a radius of R = 10 cm is uniformly charged with a linear density of = 1 Mikrokulon/m and located in a vacuum. Determine the force F of interaction between the half ring and a point charge q = 20 nC located at the center of curvature. (don't use chatgpt please)
Answer:
Explanation:
F = k * q * lambda * R * π * (1 - √2/2)
Substituting the given values of q, lambda, R, and k, we get:
F = (9 x 10^9 N*m^2/C^2) * (20 x 10^-9 C) * (1 x 10^-6 C/m) * (0.1 m) * π * (1 - √2/2)
F ≈ 8.58 x 10^-4 N
Therefore, the force of interaction between the half ring and the point charge is approximately 8.58 x 10^-4 N.
plzzz help will give brainlist
Below are views related to education.
---------------------------
Civics should be taught in public schools.
Good citizenship is learned in communities.
---------------------------
Which conclusion can be drawn from these views?
A. Civic involvement is important to building strong societies.
B. Civic participation should be learned at home.
C. Political conflict is a threat to strong societies.
D. Political conflict should be reduced through legislation.
Answer:
A.
Explanation:
this would make sense but it seems to be more like they both sound different
Electromagnetic radiation of a specific wavelength or energy is called
A. a photon
B. a speed
C. a threshold
D an optimal length
Electromagnetic radiation of a specific wavelength or energy is called a photon.
Electromagnetic radiation of a specific wavelength or energy is called a photon. A photon is a fundamental particle of light and is the smallest unit of electromagnetic radiation. It has no mass, but carries energy and momentum. Photons travel through space at the speed of light and can exhibit both wave-like and particle-like behaviors.The energy of a photon is directly proportional to its frequency or inversely proportional to its wavelength. This relationship is known as the Planck-Einstein equation and can be expressed as E = hf, where E is the energy of the photon, h is Planck's constant, and f is the frequency of the radiation.When a photon interacts with matter, it can be absorbed, reflected, or scattered. The energy of the photon is transferred to the absorbing material, causing an excitation or ionization of the atoms or molecules. This process is the basis for many scientific techniques, such as spectroscopy, where the absorption or emission of photons by a material is used to identify its chemical composition and structure. Understanding the properties of photons and their interactions with matter is essential for many fields of science, including optics, physics, and chemistry.
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convert 750W into kilowatts
Ans. 0.75
To convert watts into kilowatts we must divide it by 1000
so dividing 750W by 1000
we get,
750/1000 = 0.75
hence 750W in kilowatts equals to 0.75
when an object is thrown, the thrower pushes the object. that causes the object to move in a what motion?
Answer:
When an object is thrown, the thrower pushes the object. This causes the object to move in a
Explanation:
A car travels 24 m East in 3 s. what is the velocity of the car?
Well, since you noted the direction of travel is “due east”, that clearly means the question is asking about a frame of reference that included planetary rotation into the mix. At the equator, that’s about 460m/s in the eastward direction. Clearly, at the north pole, that’s zero—you’re effectively stationary. So, let’s assume you’re somewhere between the equator and the pole, so we’ll take the average of the two, and say the earth is contributing 230m/sec of eastward velocity. So, at time t=0s, your velocity is 230m/sec; at time t=30s, your velocity is 254m/sec. Thus, you plug those into the formula, and you get (254–230)/(30–0), or 0.8m/sec^2.
Now, if the question was to consider this from a larger frame of reference, we’d also have to take the rotation of the earth around the sun into consideration, which is about 107,000km/hr, or about 29,722m/sec. The problem is that we don’t know if we need to *add* that to the rotational velocity of the earth, and motion of the car, or *subtract* it; that all depends on whether the side of the earth that the car is on is facing the sun, or away from the sun. If we assume that sane people do math experiments on their cars only when the sun is shining, then we need to add the velocity in as well; so we get 29,722+230+24, or (29,976–29,952)(30–0). However, that only works if you do your vehicular calculations in the daytime. If, on the other hand, you’re a dark, brooding vigilante who only comes out after darkness falls to drive around, then we need to adjust our calculations to account for the fact that you’re now going retrograde with respect to the sun. Thus, the calculation would become 29,722–230–24, or (29468–29492)/(30–0), or -0.8m/sec^2.
HOPE THIS HELPS :)
Answer:
average speed: 6.6 m/s
average velocity: 1.8 m/s South
YOUR WELCOME
Una anciana camina 0.30 km en 10 minutos dando la vuelta un centro comercial calcule su rapidez media 
The average speed of the elderly woman walking around the shopping center is 1.80 km/h.
To calculate the average speed of the elderly woman, we can use the formula for velocity, which is equal to the distance traveled divided by the time taken. In this case, the distance traveled is 0.30 km and the time taken is 10 minutes. However, average speed is generally expressed in units of distance per unit of time, so we need to convert minutes to hours.
There are 60 minutes in one hour, so 10 minutes is equal to 10/60 = 1/6 hours.
Now we can calculate the average speed by dividing the distance traveled (0.30 km) by the time taken (1/6 hours):
Average speed = 0.30 km / (1/6 h)
= 0.30 km * (6/1 h)
= 1.80 km/h
Therefore, the average speed of the elderly woman walking around the shopping center is 1.80 km/h.
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2(a)Find the density of air filled in polythene container with mass of 0.419kg when it is empty. When filled with extra air its mass increased to 0.428kg also the top of polythene container mass connected to the perplex box of volume 1000cm³ and the number of times of air inside was 7.2 times
When filled with extra air its mass increased to 0.428kg also the top of polythene container mass connected to the perplex box of volume 1000cm³ and the number of times of air inside was 7.2 times. The density of the air filled in the polythene container is approximately 1.25 kg/m³.
The density of air filled in the polythene container can be determined by considering the change in mass and volume of the container before and after filling it with air. Given that the mass of the empty container is 0.419 kg and the mass of the container when filled with extra air is 0.428 kg, and the volume of the perplex box is 1000 cm³.
Calculate the mass of the air inside the container by subtracting the mass of the empty container from the mass of the container when filled with air:
Mass of air = Mass of filled container - Mass of empty container
= 0.428 kg - 0.419 kg
= 0.009 kg
Calculate the volume of the air inside the container using the given number of times the air inside is 7.2:
Volume of air = Volume of perplex box * Number of times air inside
= 1000 cm³ * 7.2
= 7200 cm³
Convert the volume of air to cubic meters (m³) by dividing by 1000000:
Volume of air = 7200 cm³ / 1000000
= 0.0072 m³
Calculate the density of air using the formula:
Density = Mass / Volume
Density = 0.009 kg / 0.0072 m³
≈ 1.25 kg/m³
Therefore, the density of the air filled in the polythene container is approximately 1.25 kg/m³.
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assignment questions
Answer:
which on a is the question
How is cold front formation different from stationary front formation?
Stationary fronts form between warm and cold air masses, while cold fronts form when a cold air mass advances against a warm air mass.
Cold fronts form between two air masses that barely move, while stationary fronts form when a warm air mass is trapped between two cold air masses.
Cold fronts form when a warm air mass moves over a cold air mass, while stationary air fronts form when a cold air mass moves over a warm air mass.
Stationary fronts form when a warm air mass is trapped between two cold air masses, while cold fronts form when a warm air mass moves over a cold air mass.
Mark this and return
Answer:
A
Explanation:
An object starts from rest at the origin and moves along the x axis subject to the force shown in the figure below. If the mass of
the object is 38.0 kg, determine the speed of the object at the following positions. Each unit along the position axis is 2.00 m and
each unit along the force axis is 3.00 N.
The speeds of the object at the various positions are :
At x = A; speed = 2.06 m/sAt x = B; speed = 2.38 m/sAt x = speed = 0 m/sWhat is the formula to determine the velocity or speed?The formula to determine the velocity or speed is given below:
velocity or speed = √(2s * F/m)
where:
s the position or displacementF is the forcem is the massThe speeds of the object at the various points are given below:
At x = A: force = 9 N; s = 6 m
speed = √(2 * 6 * 9 / 38)
speed = 2.06 m/s
At x = B; Force = 9 N; s = 12 m
speed = √(2 * 12 * 9 / 38)
speed = 2.38 m/s
At x = C; Force = 0 N; s = 18 m
speed = √(2 * 12 * 0 / 38)
speed = 0 m/s
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A crate with a mass of 35.0 kg is pushed with a horizontal force of 150 N. The crate moves at a constant speed across a level, rough surface a distance of 5.85 m
(a) The work done by the 150 N force is 877.5 Joules.
(b) The coefficient of kinetic friction between the crate and the surface is approximately 0.437.
To answer this problem, we must take into account the work done by the applied force as well as the work done by friction.
(a) The applied force's work may be estimated using the following formula:
Work = Force * Distance * cos(theta)
where the force is 150 N and the distance is 5.85 m. Since the force is applied horizontally and the displacement is also horizontal, the angle theta between them is 0 degrees, and the cosine of 0 degrees is 1.
As a result, the applied force's work is:
Work = 150 N * 5.85 m * cos(0) = 877.5 J
So, the work done by the 150 N force is 877.5 Joules.
(b) Frictional work is equal to the force of friction multiplied by the distance. The work done by friction is identical in amount but opposite in direction to the work done by the applied force since the crate travels at a constant speed.
The frictional work may be estimated using the following formula:
Work = Force of Friction * Distance * cos(theta)
The net force applied on the crate is zero since it is travelling at a constant pace. As a result, the friction force must be equal to the applied force, which is 150 N.
Thus, the work done by friction is:
Work = 150 N * 5.85 m * cos(180) = -877.5 J
Since the work done by friction is negative, it indicates that the direction of the frictional force is opposite to the direction of motion.
The coefficient of kinetic friction may be calculated using the following equation:
Friction Force = Kinetic Friction Coefficient * Normal Force
The normal force equals the crate's weight, which may be computed as:
Normal Force = mass * gravity
where the mass is 35.0 kg and the acceleration due to gravity is approximately 9.8 m/s^2.
Normal Force = 35.0 kg * 9.8 m/s^2 = 343 N
Now, we can rearrange the equation for the force of friction to solve for the coefficient of kinetic friction:
Force of Friction = coefficient of kinetic friction * Normal Force
150 N = coefficient of kinetic friction * 343 N
coefficient of kinetic friction = 150 N / 343 N ≈ 0.437
As a result, the kinetic friction coefficient between the container and the surface is roughly 0.437.
In summary, the work done by the 150 N force is 877.5 Joules, and the coefficient of kinetic friction between the crate and the surface is approximately 0.437.
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For the complete combustion of 47 g of gasoline (octane, C8H18), the mass of oxygen consumed is:
The rms speed (in m/s) of oxygen molecules of the gas at tempreture 300K, is 483.
What is tempreture?
tempretures s the physical quantity that expresses quantitatively perception of hotness and coldness .
Sol-The rms speed of a gas molecules at absolute temperature T is given by:
Vrms= √ 3RT/M
where, R=8.31JmolK^-1
universal gas constant
M= molar mass of gas in kg
For Oxygen, M=0.032kg/mol T=300K (given)
Therefore, Vrms
of Oxygen molecules will be:
=
0.032
3×8.31×300
=483 m/s
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Activity
Many characters portrayed in the media suffer from psychological disorders. For example, piglet from Winnie the Pooh has generalized anxiety
disorder and Elsa from the movie Frozen has agoraphobla. Similarly, Identify at least four characters from movies or television shows and
describe the disorders the characters suffer from in the stories.
Answer:
Explanation:
Belle from beauty and the beast has what they call Stockholm syndrome.
Spongebob from Spongebob square pants has what is called Williams-Beuren syndrome
Ariel from the Little Mermaid has what they call Disposophobia.
Alice from Alice in the wonderland has what is called schizophrenia
Scar from the Lion King has what is known as anti social personality disorder.
Like the question suggested, many characters suffer different types of disorder, and I've just listed out a few
A metallic spoon is placed in a hot cup of coffee. If the coffee gives away 190 calories to the spoon to cool down by 0.75°C, what is the mass of the coffee? (Assume that ccoffee = 1.0 cal/gC°.)
Taking into account the definition of calorimetry, the mass of the coffee is 253.33 g.
CalorimetryCalorimetry is the measurement and calculation of the amounts of heat exchanged by a body or a system.
Sensible heat is defined as the amount of heat that a body absorbs or releases without any changes in its physical state (phase change).
So, the equation that allows to calculate heat exchanges is:
Q = c× m× ΔT
where:
Q is the heat exchanged by a body of mass m.c is the specific heat sudstance.ΔT is the temperature variation.Mass of coffeeIn this case, you know:
Q= 190 caloriesc= 1 \(\frac{cal}{gC}\)m= ?ΔT= 0.75 CReplacing in the equation that allows to calculate heat exchanges is:
190 cal = 1 \(\frac{cal}{gC}\)× m× 0.75 C
Solving:
m= 190 cal÷ (1 \(\frac{cal}{gC}\)× 0.75 C)
m=253.33 g
Finally, the mass of the coffee is 253.33 g.
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According to the kinetic theory, what happens when the temperature of water
increases?
The water molecules increase their speed.
The water molecules do not change speed.
The water molecules decrease their speed.
An aeroplane is circling above an airport in a horizontal circle at a speed of 400 kmh-1.The banking angle of the wings is 20.What is the radius of the circular path?
Answer: the radius of the circular path is approximately 1637.58 meters.
Explanation:
The centripetal force acting on the airplane is provided by the component of the gravitational force that acts towards the center of the circular path. This component is given by:
F_c = m * g * tan(banking angle)
Where:
F_c is the centripetal force
m is the mass of the airplane
g is the acceleration due to gravity
tan(banking angle) is the tangent of the banking angle
Now, the centripetal force is also given by the formula:
F_c = (m * v^2) / r
Where:
v is the speed of the airplane
r is the radius of the circular path
Equating the two expressions for F_c, we get:
(m * g * tan(banking angle)) = (m * v^2) / r
Canceling out the mass (m) on both sides of the equation, we have:
g * tan(banking angle) = v^2 / r
Solving for r, we get:
r = (v^2) / (g * tan(banking angle))
Substituting the given values:
v = 400 km/h = 400,000 m/h
g = 9.8 m/s^2
banking angle = 20°
Converting the speed to m/s:
v = 400,000 m/h * (1/3600) h/s = 111.11 m/s
Converting the banking angle to radians:
banking angle = 20° * (π/180) rad/° = 0.3491 rad
Now, substituting the values into the formula:
r = (111.11^2) / (9.8 * tan(0.3491))
r ≈ 1637.58 meters
Therefore, the radius of the circular path is approximately 1637.58 meters.
The
principle which allows a rainbow to form is
Explanation:
A rainbow is a meteorological phenomenon that is caused by reflection, refraction and dispersion of light in water droplets resulting in a spectrum of light appearing in the sky. It takes the form of a multicoloured circular arc. Rainbows caused by sunlight always appear in the section of sky directly opposite the sun.
Hope it helps You °_°
A string that is under 55.0 N of tension has linear density 4.20 g/m . A sinusoidal wave with amplitude 3.10 cm and wavelength 1.70 m travels along the string.
What is the maximum velocity of a particle on the string?
A string that is under 55.0 N of tension has linear density 4.20 g/m. The maximum velocity of a particle on the string is 114.4 m/s
The speed of a transverse wave on a string under tension is given by:
v = sqrt (T/μ)
Where:
v = speed or velocity of the wave
T = tension on the string
μ = density per unit length
In the given problem:
T = 55 N
μ = = 4.2 g/m = 4.2 x 10⁻³ kg/m
Plug these parameters into the formula:
v = sqrt (T/μ)
= sqrt (55 / 4.2 x 10⁻³ ) = 114.4 m/s
The maximum velocity of a particle on the string is equal to the velocity of the transverse wave, that is 114.4 m/s
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Please help me on this
Answer:
Explanation:
read the assignment and use this
Topic sentence
Evidence from the text
Thoughts in your own words
Opinion
Wrap up sentence
T
E
T
O
W
and 2 of those make 2 paragraphs
A Motorcycle Jump. You are planning to make a jump with your motorcycle by driving over a ramp that will launch you at an angle of 30.0° with respect to the horizontal. The front edge of the ramp on which you are supposed to land, however, is 25.0 ft lower than the edge of the launch ramp (i.e., your launch height).
(a) Assuming a launch speed of 55.0 mph, at what horizontal distance from your launch point should the landing ramp be placed?
(b) In order to land smoothly, the angle of the landing ramp should match the direction of your velocity vector when you touch down. What should be the angle of the landing ramp?
a. the landing ramp should be placed at 276.298 ft horizontally from the launch point.
(b) the angle of the landing ramp is 30°.
How do we calculate?(a)
Launch speed = 55.0 mph * (1.467 ft/s)
= 80.685 ft/s
Horizontal distance = Launch speed * Time of flight
Vertical velocity = Launch speed * sin(30.0°)
Time to reach maximum height = Vertical velocity / g
Vertical distance = (1/2) *g * t²
and Time = √(2 * Vertical distance / g)
Total time of flight = 2 * Time to reach maximum height + Time for descent
Horizontal distance = Launch speed * Total time of flight
The Vertical velocity = 80.685 ft/s * sin(30.0°)
= 40.3425 ft/s
Time to reach maximum height = 40.3425 ft/s / 32.2 ft/s²
Time to reach maximum height = 1.253 s
Time of descent = √(2 * 25.0 ft / 32.2 ft/s²)
Time of descent = 0.913 s
Total time of flight = 2 * 1.253 s + 0.913 s
Total time of flight = 3.419 s
In conclusion, the horizontal distance = 80.685 ft/s * 3.419 s
horizontal distance = 276.298 ft
b.
the angle of the landing ramp is 30.0 be the same as the launch angle.
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Brainlist!! Help!! Atom A consists of 10 protons, 12 neutrons, and 10 electrons.
Atom B consists of 10 protons, 10 neutrons, and 12 electrons.
The atoms are isotopes of each other.
The atoms are not isotopes of each other.
Atom A has 10 protons, 12 neutrons, and 10 electrons, while Atom B has 10 protons, 10 neutrons, and 12 electrons.
Atom A and Atom B are not isotopes of each other. Isotopes are atoms of the same element that differ in the number of neutrons but have the same number of protons. In this case, Atom A and Atom B have different numbers of protons, which means they are not isotopes of each other.
The number of protons determines the element, and since Atom A and Atom B have different numbers of protons, they belong to different elements.
Isotopes, on the other hand, have the same number of protons but differ in the number of neutrons.
This variation in the number of neutrons gives isotopes different atomic masses while retaining the same chemical properties.
However, Atom A and Atom B do not fulfill this criterion, so they cannot be considered isotopes of each other.
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when the mass of an object increases, the forcé of gravity
Answer:
increace
Explanation:
they are both going up
12.
A hiker walks for 5km on a bearing of 053" true (North 53° East). She then turns and
walks for another 3km on a bearing of 107° true (East 17° South).
(a)
Find the distance that the hiker travels North/South and the distance that she travels
East/West on the first part of her hike.
The hiker travelled 4.02 km North/South and 4.74 km East/West during her hike.
This question involves vector addition, the resolution of vectors, the use of bearings, and trigonometry in the calculation of the hiker's movement.
This may appear to be a difficult problem, but with some visual aid and the proper use of mathematical formulas, the issue can be addressed correctly.
Resolution of VectorThe resolution of a vector is the process of dividing it into two or more components.
The angle between the resultant and the given vector is equal to the inverse tangent of the two rectangular components.
Angles will always be expressed in degrees in the solution.
The sine, cosine, and tangent functions in trigonometry are denoted by sin, cos, and tan.
The tangent function can be calculated using the sine and cosine functions as tan x = sin x/cos x. Also, in right-angled triangles, Pythagoras’ theorem is used to find the hypotenuse or one of the legs.
Distance Travelled North/SouthThe hiker traveled North for the first part of the hike and South for the second.
The angles that the hiker traveled in the first part and second parts are 53 degrees and 17 degrees, respectively.
The angle between the two is (180 - 53 - 17) = 110 degrees.
The angle between the resultant and the Northern direction is 110 - 53 = 57 degrees.
Using sine and cosine, we can calculate the north/south distance traveled to be 5 sin 57 = 4.02 km, and the east/west distance to be 5 cos 57 = 2.93 km.
Distance Travelled East/WestThe hiker walked East for the second part of the hike.
To calculate the distance travelled East/West, we must first calculate the component of the first part that was East/West.
The angle between the vector and the Eastern direction is 90 - 53 = 37 degrees.
Using sine and cosine, we can calculate that the distance travelled East/West for the first part of the hike is 5 cos 37 = 3.88 km.
To determine the net distance travelled East/West, we must combine this component with the distance travelled East/West in the second part of the hike.
The angle between the second vector and the Eastern direction is 17 degrees.
Using sine and cosine, we can calculate the distance traveled East/West to be 3 sin 17 = 0.86 km.
The net distance traveled East/West is 3.88 + 0.86 = 4.74 km.
Therefore, the hiker travelled 4.02 km North/South and 4.74 km East/West during her hike.
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If the average kinetic energy of the molecules in an ideal gas initially at 18°C doubles, what is the final temperature of the gas?a.)9°Cb.)504°C c.)309°Cd.)36°C
ANSWER
c. 309°C
EXPLANATION
The average kinetic energy of the molecules in an ideal gas is proportional to the temperature of the gas,
\(KE=k\cdot T\)Where the temperature is measured in Kelvin.
For this problem it is not necessary to specify what is the value of k, we just need to know that it is a constant.
So, if the kinetic energy doubles, so does the temperature (in Kelvin).
The initial temperature of the gas is,
\(T_i=18\degree C+273=291\text{ }K\)If the temperature doubles,
\(T_f=2T_i=2\cdot291K=582K\)In degrees Celsius this is,
\(T_f=582K-273=309\degree C\)Hence, the final temperature of the gas is 309°C.
When a baseball curves to the right (a curveball) , air is flowing faster over the right side than over the left side. at the same speed all around the baseball, but the ball curves as a result of the way the wind is blowing on the field. faster over the left side than over the right side. faster over the top than underneath.
Answer:
faster over the left side than over the right side.
Explanation:
due to ball rotation, the right side is more closely matched to the speed of the air passing by as the ball progresses. This causes the air to stick more closely to the right side of the ball and that air stays with the ball surface as the spin moves it to the back of the ball and therefore leftward. As every action has an equal and opposite reaction the leftward force moving air causes the ball to experience an equal rightward force.
When the baseball curves to the right (a curveball), then the ball moves faster over the left side than over the right side.
What direction does a curveball move?The ball, which is thrown with a spin, is curve in the direction in which the front of the ball turns.
When a baseball curves to the right (a curveball),
For this condition, the pressure of air should be high on the left side than the pressure on right side.Molecules of the air on right side pushed backward by this spinning ball.The left side with high pressure push the ball towards right side where the pressure is low.Due to higher pressure, the ball move faster on the left side than the right side.Hence, when the baseball curves to the right (a curveball), then the ball moves faster over the left side than over the right side.
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Which factors affect the gravitational force between two objects?
-
distance and velocity
O mass and distance
O mass and weight
acceleration and weight
TELE
Answer:
mass and distance
Explanation:
mass, and distance. The force of gravity depends directly upon the masses of the two objects, and inversely on the square of the distance between them.
13 Which of these fitness events happened LAST? OA. PE becomes part of American school curriculum. OB. Title IX forbids gender discrimination in sports. O C. The YMCA opens a gym in America. O D. The adjustable plate-loaded barbell is invented.
The answer is A. PE becomes part of American school curriculum.
Title IX, which forbids gender discrimination in sports, was enacted in 1972.
The YMCA opened its first gym in America in Boston in 1851.
The adjustable plate-loaded barbell was invented in the late 1940s by a man named George Snyder.
Physical Education (PE) has been a part of American school curriculums for well over a century, with the first school gymnasiums being built in the 1800s.
What is an american school curriculum?
The American school curriculum is the set of educational standards and guidelines used by schools in the United States to structure their academic programs. The curriculum typically includes courses in core academic subjects such as English, math, science, and social studies, as well as elective courses in areas such as the arts, foreign languages, and physical education.
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A table tennis ball has a mass of about 2.45 g. Suppose the ball is hit across the table with a speed of 4.0 m/s. What is it’s kinetic energy?
Answer:
0.0196 j
Explanation:
i) The formula for kinetic energy is as follows: 0.5*m*v^2
ii) Since we have all the values all that's left is to plug them into the equation
iii) First, WE MUST, Convert grams into kgs as this is the SI unit of mass so 2.45/1000
iv) All that's left now is to plug it into the equation so:
0.5* (s.45/1000)*(4^2)
v) Lastly we add the unit joules at the end as we're talking about energy
Hope this was useful! :)
19. Assume this process is 10% efficient, how much work is done by the gas expanding into the atmosphere?
The amount of work done by the gas is proportional to the pressure and the change in volume, as well as the efficiency of the process. If the pressure and volume are known, the work done by the gas can be calculated by multiplying these values by the efficiency of the process.
The amount of work done by a gas when it expands is proportional to the change in volume, pressure, and temperature. According to the first law of thermodynamics, the energy of a closed system is conserved, so the work done by the expanding gas is equal to the energy transferred from the gas to the environment in the form of work. Therefore, the work done by the gas is equal to the change in energy of the system. Assume that the process is 10% efficient. Then, only 10% of the energy available to the system is converted into work. This means that the remaining 90% of the energy is lost to the environment in the form of heat. As a result, the amount of work done by the gas expanding into the atmosphere is given by the formula
W = E x η, where W is the work done by the gas, E is the energy available to the system, and η is the efficiency of the process. The energy available to the system is determined by the difference between the internal energy of the gas before and after the expansion. The internal energy of a gas is determined by its temperature, pressure, and volume.
Assuming that the temperature and pressure are constant, the change in internal energy is proportional to the change in volume. Therefore, the energy available to the system is equal to the product of the pressure and the change in volume: E = P x ΔV, where P is the pressure of the gas and ΔV is the change in volume during the expansion. Substituting this equation into the formula for work, we get W = P x ΔV x η.
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