The correct answer is 441 N.
The force that pulls objects toward the centre of the Earth is known as earth gravity. The acceleration of all the bodies that are affected by gravity is almost equal to the strength of the gravitational field.
The force exerted on an object by gravity is known as the weight of a body.
As a result, we can state that weight is only a force.
Given that the mass of a person on earth is = 45 kg
and that gravity's acceleration on earth is = 9.8 ms^2.
Weight, then, is defined as mass multiplied by the gravitational acceleration, or W = m × g.
W = 45 × 9.8
W = 441 N
Hence, the total weight on Earth will be 441 Newton.
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three equal point charges, each with charge 1.95 μc , are placed at the vertices of an equilateral triangle whose sides are of length 0.450 m . what is the electric potential energy u of the system? (take as zero the potential energy of the three charges when they are infinitely far apart.)
The electric potential energy U of the system is 11.39 * [tex]10^{-2}[/tex] J
We know that,
U = [tex]q^{2}[/tex] / 4 π ε₀ d
where,
U = Electric potential energy
q = Point charge
ε₀ = Permittivity of free space
d = Length
Given that,
q = 1.95 * [tex]10^{-6}[/tex] C
d = 0.45 m
ε₀ = 8.85 * [tex]10^{-12}[/tex] [tex]C^{2}[/tex] N [tex]m^{2}[/tex]
U = [tex]U_{1}[/tex] + [tex]U_{2}[/tex] + [tex]U_{3}[/tex]
U = 3 [tex]q^{2}[/tex] / 4 π ε₀ d
U = 8.99 * [tex]10^{9}[/tex] * 3 * ( 1.3 * [tex]10^{-6})^{2}[/tex] / 0.45
U = 11.39 * [tex]10^{-2}[/tex] J
Electric potential energy is the amount of energy that is needed to move a charge against an electric field.
Therefore, the electric potential energy U of the system is 11.39 * [tex]10^{-2}[/tex] J
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How many valence electrons does the ground-state electron configuration of nitrogen have?.
Answer:
it has 5 valence electrons
Explanation:
nitrogen has a total of 5 valence so doubling that we would have a total of 10 valence electrons with 2 nitrogen atoms
Which statement best describes an isolated system?
Energy flows into and out of the system but matter is contained.
There is no energy or matter that exists inside an isolated system.
Energy is contained within the system and matter is exchanged.
Neither energy nor matter are exchanged with the surroundings.
The statement best describes an isolated system is,
(C) Neither energy nor matter are exchanged with the surroundings.
What is Isolated system?Isolated system is a thermodynamic term which we are used to understand the characteristics of the system. An isolated system means that cannot exchange neither energy nor mass outside the boundaries of the system.
How can we conclude that nothing are exchanged with surroundings in isolated system?According to the definition of the isolated system, we know that, Isolated system is a system that is completely bound to its boundary. That means it is closed within its boundary.
But it is not closed system. Because in closed system mass is conserved but energy can be exchanged outside the boundaries of the system.
In the characteristics of isolated system, we know it cannot exchange neither energy nor mass outside the boundaries of the system.
So, from the above discussion we can easily state that, the statement best describes an isolated system is, (C) Neither energy nor matter are exchanged with the surroundings.
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Suppose a man is sitting on a chair and exerting 100 N of force downward, while a spring beneath the chair exerts 150 N of force upward. If you assign a negative value to the downward force, what is the net force of this system?
A man is sitting on a chair and exerting 100 N of force downward, while a spring beneath the chair exerts 150 N of force upward. The net force acting on the system is in the upward direction with a magnitude of 50N.
Force is the product of mass and acceleration which is dependent on the rate of change of momentum.
According to the given question,
Magnitude of force in the downward direction = 100N
Downward force = 100N
Magnitude of force in the upward direction = 150N
Upward force = -150N
Net force on the system = Upward force + Downward force
Net force on the system = -150N + 100N
Net force on the system = -50N
Hence, the net force acting on the system is in the upward direction with a magnitude of 50N.
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Answer:
(Question) Which of the following best describes the sum of all forces acting on an object?
(Answer) net force, which is a vector sum
(Question) Suppose a man is sitting on a chair and exerting 100 N of force downward, while a spring beneath the chair exerts 150 N of force upward. If you assign a negative value to the downward force, what is the net force of this system?
(Answer) 50 N
(Question) During a game of pool, a cue ball travels to the left with 70 N of force and collides with the four ball moving with a force of 50 N to the right. If you assign a negative value to the force moving to the right, what is the net force of this system?
(Answer) 20 N
(Question) Recall that the formula for momentum is: P=mv Which of the following correctly shows momentum being calculated?
(Answer) 45 kg*m/s=(9 kg) (5 m/s)
(Question) A hockey puck with a mass of 0.12 kg is traveling across the ice at a velocity of 150 m/s downfield. What is the momentum of the hockey puck?
(Answer) P=18 kg*m/s
Explanation:
I just finished the quick check UwU
you are speeding down the highway at a constant velocity of 50 m/s. a highway patrol officer at rest on the side of the road notices you are speeding and begins to chase after you at the exact moment you pass them. if the highway patrol car has a constant acceleration of 0.8 m/s2 , how long (in seconds) will it be before they catch up to you?
The highway patrol car catches you after 125 sec
We know that,
s = ut + 1/2 at²
v = s / t
where,
s = Distance
u = Initial velocity
t = Time
a = Acceleration
Given that,
The patrol car has with a constant acceleration of 0.8 m / s²
Initial velocity of car = 0
Velocity of your vehicle = 50 m / s
After the traffic signal distance travelled by your vehicle and patrol car is equal and time taken is also equal.
For your vehicle,
s = v * t
For the patrol car,
s = ut + 1/2 at²
vt = ut + 1/2 at²
50 t = 0 + 1 / 2 * 0.8 * t²
t = 125 sec
Velocity is the distance travelled by an object with respect to time. Its unit is m / s
Therefore, the highway patrol car will catchup to you after 125 sec
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Lamar Jackson and tavon young are standing 5m away from each other. Lamar throws a football to tavon and tavon throws the football to Lamar.
What is the displacement of the football after the two throws describe above.
The Displacement of the football after the two throws is 0m.
The Displacement of the football is dependent on the Initial and final position of the body. It is calculated as:
Displacement = Final position - Initial position
Since, the Initial position of the football is at Lamar Jackson and the Final position of the football is at Tavon Young after the first throw.
Now, After the second throw, the Initial position of the football is at Tavon Young and the Final position of the football is at Lamar Jackson.
So, after the Two throws, The Initial position of the football is at Lamar Jackson and Final position of the football is at Lamar Jackson.
Since, the Initial position and Final position is same. Hence the Displacement of the football is 0m.
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9. How did you come up with your answer for #8?
10. If the falling time of an object is doubled, by what factor does the distance increase? Use
the times 2 seconds and 4 seconds to prove your answer. (Hint: x-v4+1/2af²)
a.
b.
To win the game, a place kicker must kick
a football from a point 35 m (38.276 yd) from
the goal, and the ball must clear the crossbar,
which is 3.05 m high. When kicked, the ball
leaves the ground with a speed of 20 m/s at
an angle of 43.6° from the horizontal.
The acceleration of gravity is 9.8 m/s².
By how much vertical distance does the ball
clear the crossbar?
Answer in units of m.
The vertical distance by which the ball clear the crossbar is
As given in the question,
To win the game, a place kicker must kick a football from a point 35 m (38.276 yd) from the goal,The ball must clear the crossbar, which is 3.05 m high.the ball leaves the ground with a speed of 20 m/s at an angle of 43.6◦.The acceleration of gravity is 9.8 m/s.The distance between two vertical places is known as the vertical separation or vertical distance. There are numerous ways to express vertical position using vertical coordinates, including depth, height, altitude, elevation, etc.
By how much vertical distance does the ball clear the crossbar?
The vertical clearance distance between the crossbar and the ball as stated in the query,
A place kicker must make a football kick from a point 35 meters (38.276 yards) from the goal to win the game.
The 3.05 m-high crossbar must be passed by the ball.
The ball leaves the ground at an angle of 43.6 degrees and a speed of 20 meters per second.
9.8 m/s is the acceleration of gravity.
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James has an old kettle with a power rating of 1.4 kW. He buys a new kettle with a power rating of 2.0 kW. How does this affect the time it takes to boil a fixed volume of water?
The old kettle with a power rating of 1.4 kW and the new kettle with a power rating of 2.0 kW, due to this the time it takes to boil a fixed volume of water will decrease.
What is Power?The amount of work finished in a specific length of time is a definition of power. Watt (W), which is derived from joules per second (J/s), is the SI unit of power. Horsepower (hp), which is roughly equivalent to 745.7 watts, is a unit of measurement sometimes used to describe the power of motor vehicles and other devices.
A person's power is always based on the amount of labor they put in, thus if they work differently at different times, their power will likewise vary. Here is when the idea of average power enters the picture.
According to the question,
Power=Work done/time
Hence, as the power will increase, the time will automatically decrease because both are inversely proportional to each other.
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Answer:
The water will boil in less time.
What are the advantages of using unlicensed frequency bands for rf transmissions? (choose all that apply.)
B and C. An unlicensed frequency has the main benefits of being open to use by anyone and not requiring a license to transmit on it.
You are still subject to transmission rules and other limitations even though there are no additional expenses. Due to congestion, the fact that anyone can utilize the frequency spectrum is also a drawback.
What group defines the unlicensed frequencies utilized by Wi-Fi?The Wi-Fi Alliance fights for unlicensed spectrum and for preserving the advantages that Wi-Fi offers.
What kind of transmission and reception methods do 802.11 radios employ?802.11ax radios may broadcast and receive data in either the 2.4 GHz or 5 GHz frequency bands, in contrast to 802.11ac, only runs at 5 GHz. 802.11ax technology.
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Complete question:
What are the advantages of using unlicensed frequency bands for rf transmissions? (Choose all that apply.)
A. There are no government regulations.
B. There is no additional financial cost.
C. Anyone can use the frequency band.
D. There are no rules.
The area of a 120-turn coil / loop oriented its plane
perpendicular to a 0.20-T magnetic field is 0.050 m². Find the
average induced emf in this coil, if the magnetic field reverses
its direction in 0.34 s.
The average induced emf in this coil is 3.52 volts.
When a coil is kept inside a changing magnetic field, an emf/voltage is produced inside it which is given by the following formula:
EMF = NBA/t
Here N is the number of turns in the coil
B is the magnetic field in which the coil is kept
A is the area of the coil
T is the time during which the magnetic field reverses its direction
Putting the given values in the above equation,
E = 120 x 0.20 x 0.050/0.34
E = 3.52 volts
Thus, the average induced emf in this coil is 3.52 volts.
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The pieces of ice float on water ? give reason
Ice has less density ( i.e. 0.9 g/cm^3 ) than water ( i.e. 1.0 g/cm^3) . So , an ice cube floats in water...
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A car travels 20 km north. It then turns around and travels 30 km south. What is the car's displacement? 50 km south 10 km south 10 km north 50 km north
Answer:
Gehwywtwhay4wjwjgw6y 26526wisgeu3bjzx
I’m having difficulty answering this question. I don’t know how I should draw the graphs.
The correct answer is dependence of graph remain same. The Speed decreases,
We must first comprehend the difference between distance and displacement in order to understand average speed and average velocity. Distance is a scalar quantity that describes how much space an object has traveled. Displacement, which is a vector quantity, represents the smallest distance between two points. For instance, if a particle moves around a circle, its displacement is 0 but its distance traveled after one rotation is equal to the circle's circumference.
Any object's average speed is calculated by dividing its entire distance traveled by the total amount of time it took to complete that distance. An object's average speed indicates the average speed at which it will travel a given distance.
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If the magnified cell had a diameter of 40mm on the computer screen using the 10x ocular lens with the 40x objective lens, what would be the actual diameter of the cell in millimeters?.
The actual diameter of the cell would be 0.1 mm.
We are given that, the magnification due to the ocular lens is 10x and the magnification due to the objective lens is 40x.
Therefore, the total magnification of the whole setup will be 400x.
This means that an object with a diameter of x m will have a magnified diameter of 400x.
In the above situation, the magnified cell has a diameter of 40 mm.
When the actual diameter is x, the magnified diameter is 400x.
Hence 400x = 40 mm
x = 40 mm/400
x = 0.1 mm
Hence, the actual diameter of the cell would be 0.1 mm.
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The actual diameter of the cell would be 0.1 mm.
We are given that, the magnification due to the ocular lens is 10x and the magnification due to the objective lens is 40x.
Therefore, the total magnification of the whole setup will be 400x.
This means that an object with a diameter of x m will have a magnified diameter of 400x.
In the above situation, the magnified cell has a diameter of 40 mm.
When the actual diameter is x, the magnified diameter is 400x.
Hence 400x = 40 mm
x = 40 mm/400
x = 0.1 mm
Hence, the actual diameter of the cell would be 0.1 mm.
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Describe how the density of aluminium may be determined using the bar. In your account
() describe the readings to be taken,
(i)
state the instruments used to make the readings,
(ill) describe how the density is calculated from the readings.
We know that water is denser than air or a piece of paper is denser than rock.
How do we determine density?
Density is determined by measuring it’s mass and then dividing it by it’s volume.
Let us take a solid cube of aluminium.
(i) The readings to be taken are the mass of aluminium and volume of aluminium.
(ii) Instruments used are :
digital weighing scale to measure mass a measuring cylinder to measure volume which is filled with water using pair of tongs we will put the aluminium cube in the water.(iii) We will check the mass of the aluminium cube by simply putting it on the weighing machine. Now we will check the volume by putting that cube into the water. The initial level was x. The water level rises to y after putting the cube into it. To know the volume, we will simply subtract y-x. Hence, we know the volume.
To know the density, divide mass by volume. (Mass / volume)
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A high-mass star near the end of its life undergoes successive cycles of energy generation within its core in which gravitational collapse increases the temperature to the point where a new nuclear fusion cycle generates sufficient energy to stop the collapse. This process does not work beyond the silicon-fusion cycle that produces iron. Why is this?.
A high mass star will not be able to generate enough energy beyond the silicon fusion cycle to stop its collapse because iron fusion doesn't generate excess energy and gas pressure to prevent the core from collapsing. Instead, it requires additional energy.
Stars get all of their energy through nuclear fusion in the core of the star. The light and heat we get from the sun come from the fusion of nuclei in the core of the sun. Initially, all stars generate energy by fusing the lightest elements, hydrogen and helium at the core of the star. This is the longest phase of nuclear fusion, and stars in this phase are said to be in their main sequence. After the main sequence however, low mass stars become white dwarfs, while high mass stars continue to fuse heavier elements.
Due to the fact that high mass stars are so huge, they have very high temperature and pressure. This high temperature enables elements like helium to fuse and form other heavier nuclei like carbon and oxygen. Other adverse fusions of these heavy elements produce silicon and iron.
After the silicon fusion, no further cycle of energy generation occurs. This is because fusing iron with any other element requires energy and doesn't give out any significant amount of energy. Due to this, the core can't generate enough gas pressure to prevent its core from collapsing, thus, the core collapses and releases a huge amount of energy in an explosion called a supernova.
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You are asked to determine the identity of an unknown liquid and can measure only one physical property. You hear the liquid and record that the liquid turns into vapor at 100°C.
Which physical property does this demonstrate?
A. Melting point
B. Boiling point
C. Ability to conduct electricity
D. Meltability
The answer is The boiling Point as the transition from liquid to gas occurs at the boiling point.
The actuality that it changes from liquid to vapor indicates that you are working with the substance's boiling point.
The material is pure if its temperatures does not change when it turns phases. Since water turns liquid at 100°C in this situation, water is likely the culprit.
The temperature at which a specific liquid will boil is known as its boiling point. For instance, water reaches its boiling point at 1 atm, or 100 degrees Celsius. The temperature of the liquid, the pressure of the atmosphere, and the pressure of the vapor all affect its boiling point.
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The driver of a car traveling at 10.0 m/s along a straight road depresses the accelerator and uniformly increases her speed at a rate of 2.00 m/s2. how fast will the car be moving as it passes a parked police cruiser 140 m away?
Answer:
60m/h
Explanation:
Consider what you know about our sun and ways that energy is released
Answer:
Solar energy is created by nuclear fusion that takes place in the sun. Fusion occurs when protons of hydrogen atoms violently collide in the sun's core and fuse to create a helium atom. This process, known as a PP (proton-proton) chain reaction, emits an enormous amount of energy.
Explanation:
Solar energy is created by nuclear fusion that takes place in the sun. Fusion occurs when protons of hydrogen atoms violently collide in the sun’s core and fuse to create a helium atom.
This process, known as a PP (proton-proton) chain reaction, emits an enormous amount of energy. In its core, the sun fuses about 620 million metric tons of hydrogen every second. The PP chain reaction occurs in other stars that are about the size of our sun, and provides them with continuous energy and heat. The temperature for these stars is around 4 million degrees on the Kelvin scale (about 4 million degrees Celsius, 7 million degrees Fahrenheit).
Calculate the volume of copper that has a mass of4.5g and has a density of 8.96g/cm^3
The volume of the copper having a mass of 4.5 g and a density of 8.96 g/cm³ is 0.502 cm³
Formula for densityThe mathematical representation of the density of a substance can be expressed as
Density = mass / volume
With the above formula, we can obtain the volume. Detail below.
The volume of the copper can be determined as illustrated below:
Mass of copper = 4.5 gDensity of copper = 8.96 g/cm³Volume of copper =?Density = mass / volume
8.96 = 4.5 / volume of copper
Cross multiply
8.96 × volume of copper = 4.5
Divide both sides by 8.96
Volume of copper = 4.5 / 8.96
Volume of copper = 0.502 cm³
Thus, the volume of the copper is 0.502 cm³
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a ball is thrown vertically upward from the ground with an initial velocity of 25 m/s; at the same instant, a ball dropped from rest from a building 15 m high. after how long will the balls be at the same height
The time at which both the balls will be at the same height is 0.6 s.
The height of the ball that is dropped from a building
= 15 m
The initial velocity of the ball that is thrown vertically upward from the ground = 25 m/s
The height of the ball that is dropped from a building is,
[tex]y _{t} = y _{i} + v _{i}t - \frac{1}{2} \: gt ^{2} [/tex]
[tex] - (15 \: m \: - h) = - \frac{1}{2} \: gt ^{2} [/tex]
[tex] h =15 \: m - \frac{1}{2} \: gt ^{2} [/tex]
The height of the ball that is dropped from a building is
[tex]15 \: m - \frac{1}{2} \: gt ^{2} .[/tex]
The height of the ball that is thrown vertically upward from the ground is,
[tex]y _{t} = y _{i} + v _{i}t - \frac{1}{2} \: gt ^{2} [/tex]
[tex] h =(25 \:) \: t \: - \frac{1}{2} \: gt ^{2} [/tex]
The height of the ball that is thrown vertically upward
[tex]from \: the \: ground \: is \: (25 \:) \: t \: - \frac{1}{2} \: gt ^{2} .[/tex]
The time at which both the balls will be at the same height is,
[tex]15 \: m - \frac{1}{2} \: gt ^{2} =(25 ) \: t \: - \frac{1}{2} \: gt ^{2} [/tex]
[tex]t \: = \frac{15}{25} [/tex]
t = 0.6 seconds
Therefore, the time at which both the balls will be at the same height is 0.6 s.
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11. A boat is rowed at 8 km/h directly.
across a river that flows at 6 km/h
a. What is the resultant speed of that boat?
b. How fast and in what direction can the
boat be rowed to reach a destination directly
across the river?
The correct answer is a. 10 km/h.
b. The boat would move at 10 km/h at a 37-degree upstream angle to cross straight (into the current)
To be more precise, the rate of change in an object's position relative to a frame of reference and time is another way to describe velocity. It determines how quickly or slowly something is going. Consider a scenario in which there are two moving items. If both items are going in the same direction, it is simple to determine which one is moving faster than the other.
v = √v_x^2 +v_y^2
v = √((8 km/h)^2 + (6 km/h)^2)
=10 km/h
direction = θ = tan^-1 (opposite / adacrent)
= tan^-1 (6/8)
= tan^-1 (37)
= 37 degree down stream.
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You whirl a 2-kg body attached to a 1-meter cord around your head in a nearly horizontal circle with a speed of 4 m/s. the tension in the cord is:_________
The tension in the cord is 32 N if a 2-kg body attached to a 1-meter cord is whirled around the head.
CalculationF = (2 x [tex]4^{2}[/tex])/1
F = 2*16
F = 32N
Concept of tension force:In physics, tension is defined as the pulling force transmitted axially by a string, cable, chain, or another similar object, or by either end of a rod, truss member, or another comparable three-dimensional object.
Tension can also be thought of as the action-reaction pair of forces acting at each end of the aforementioned elements.
What is the tension force formula?The tension formula is expressed as. T=mg+ma. Where g = the acceleration caused by gravity (9.8 m/s2) and T = tension (N or kg-m/s2).
What kind of force is tension explain with an example?The example would be drawing Water with a bucket from a Well.
One of the best illustrations of tension forces is the process of drawing water from a well. It uses a rope with one end fastened to the bucket handle and the other end free to move.
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When light generated by a lamp in a light microscope passes into a lens, the speed of the light _________
The speed of light Slows because the lens has a greater refractive index.
What is the light speed in Lens?In a vacuum, which has a refractive index of 1, light moves at a speed of about 300,000 km/s, but in water and glass, its speed drops to 225,000 km/s and 200,000 km/s, respectively.
Is glass faster for light to travel through?Light moves. Slower in lens but faster in the air That’s because light refracts when it comes into contact with various materials.
Why does glass affect the speed of light?The density of the medium affects the speed at which light propagates. The only thing that happens when a light beam enters glass from a vacuum (air) is that the wave is delayed (takes longer to go the same distance as a result of the delay).
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Correct question:
When light generated by a lamp in a microscope passes into a lens, the speed of the light _______ because the glass lens has a _______ refractive index than the air from which the light came.
A typical high pressure on a bicycle might have a volume of 365 ml and a pressure of 7. 80 atm at 25oc. Suppose the rider filled the tire with helium to minimize weight. What is the mass of the helium in the tire?.
By ideal gas approximation, the mass of the helium in the tire is 0.465 grams.
We need to know about the ideal gas theory to solve this problem. The ideal gas is assumed that there is no interaction between particles in a gas. It can be determined by the equation
P . V = n . R . T
where P is pressure, V is volume, n is the number of moles of gas which represents mass, R is the ideal gas constant (0.0821 L.atm/mol.K) and T is temperature.
From the question above, we know that
V = 365 mL = 0.365 L
P = 7.8 atm
T = 25⁰ C = 298 K
Mr = 4
By using the equation of ideal gas, we get the mass
P . V = n . R . T
7.8 . 0.365 = gr / Mr . 0.0821 . 298
7.8 . 0.365 = gr / 4 . 0.0821 . 298
gr = 0.465 grams
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A car moving with a speed of 20m/s has a momentum of 32,000 kg. m/s.
What is the mass of the car
Answer:
See below
Explanation:
momentum = m * v
so
momentum / v = m = 32 000 kg m/s / 20 m/s = 1600 kg
38. The decomposition of animal waste by anaerobic bacteria produces biogas (change A). The biogas is
then burnt fuel (change B). What are the similarities between two changes.
The decomposition of animal waste by anaerobic bacteria produces biogas methane . The biogas is then burnt fuel (carbon dioxide).
methane and carbon dioxide both are carbon compound, both are in gaseous form, and both are green house gasesA gas without color or smell, methane. It is also known as methyl hydride or marsh gas. It is quickly set ablaze. They are lighter than air, the vapors. The canisters may violently burst and shoot into the air when exposed to fire or extreme heat for an extended period of time. It is a component of natural gas, a fuel, and is utilized in the production of other chemicals.One carbon atom makes up the molecule methane, which has four hydrogen atoms bound to the carbon by single bonds. It is a colorless, odorless, non-toxic, flammable gas with a melting point of -161°C. It performs three functions: fossil fuel, greenhouse gas, and bacterial metabolite.To know more about methane visit : https://brainly.com/question/2127750
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Speed calculation
1. Your bus is travelling at an average speed of 25km/hr. How long will it take you to get from your bus stop to the shopping centre that is 4km away?
2. If you are able to run at an average of 8km/hr, how far can you run in 3.4 hours?
1. The time taken to get to the shopping centre is 0.16 hour
2. The distance you can run in 3.4 hours is 27.2 Km
What is speed?Speed is the distance travelled per unit. Mathematically, it can be expressed as:
Speed = distance / time
1. How to determine the timeThe time taken to get to the shopping centre can be obtain as follow:
Speed of light = 25 Km/hrDistance = 4 KmTime =?Speed = distance / time
25 = 4 / time
Cross multiply
25 × time = 4
Divide both side by 25
Time = 4 / 25
Time = 0.16 hour
2. How to determine the distance Speed = 8 Km/hrTime = 3.4 hoursDistance =?Speed = distance / time
Cross multiply
Distance = speed × time
Distance = 8 × 3.4
Distance = 27.2 Km
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1. Hooke's law states that the force F in a spring extended by a length x is given by F= -kx . Calculate the dimension of spring constant k.
2. The force between two wires 1,2 length 1 meters separated by a distance d meters and carrying currents I1 AND I2 Amperes is given by :
[tex]F = \frac{kI_1I_2}{d}[/tex] .
find (a.) the units of constant k
(b.) dimension of k
1. With N = Newtons, m = meters, we have
[tex]F = -kx \iff \mathrm N = -k (\mathrm m) \implies k = \dfrac{\rm N}{\rm m}[/tex]
N itself can be broken down according to Newton's second law,
[tex]F=ma \iff \mathrm N = \mathrm{kg} \, \dfrac{\rm m}{\rm s^2}[/tex]
so the dimension of the force [tex]F[/tex] is
[tex][F] = [M\cdot L\cdot T^{-2}][/tex]
(where M = mass, L = length, T = time) and hence the dimension of [tex]k[/tex] is
[tex][k] = \left[\dfrac{M\cdot L\cdot T^{-2}}{L}\right] = \boxed{[M\cdot T^{-2}]}[/tex]
2.
a. With N = Newtons, A = amperes, and m = meters,
[tex]F = \dfrac{k I_1 I_2}d \iff \mathrm N = \dfrac{k \,\mathrm A\,\mathrm A}{\rm m} \implies k = \boxed{\dfrac{\rm Nm}{\rm A^2}}[/tex]
b. The dimension of [tex]k[/tex] is
[tex][k] = \left[\dfrac{(M\cdot L\cdot T^{-2})\cdot L}{I^2}\right] = \boxed{[M\cdotL^2\cdot T^{-2}\cdot I^{-2}]}[/tex]
(where I = current, with "I" as in capital i)