Answer: 1 kilometer = 1,000 meters
Explanation:
The decimal metric system is the predecessor of the International System of Units (SI) and consists of a system in which the multiples and submultiples of the unit of measure are related to each other by multiples or submultiples of ten (10).
It should be noted that this system was created to be neutral and that it could be easily used, understood and adopted by all countries. However, so far only the United States, Myanmar (Burma) and Liberia have retained their traditional units of measurement instead of the Decimal Metric System, which was then replaced by the current SI.
In this sense, two main basic units of this system are the meter (to measure length) and the gram (to measure mass). In the specific case of the meter there are submultiples of the same nature that follow a decimal scale, for example:
[tex]1km = 10^{3} m = 1000m[/tex]
Therefore, among the given options, the one that fulfills the explained conditions is 1 kilometer = 1,000 meters
The other options do not follow a decimal system.
Final answer:
The decimal system of measurement is represented by the option '1 kilometer = 1,000 meters' because it follows the base ten structure of the metric system, where conversions are based on powers of ten.
Explanation:
The decimal system of measurement is exemplified by the base ten structure, which is integral to the SI or metric system. Of the options provided, 1 kilometer = 1,000 meters represents a decimal system of measurement, as it’s based on a multiple of ten, specifically 103 or one thousand. This system is characterized by the ease of conversion among different units of measurement using powers of ten. In comparison, other measurements listed, such as quarts to fluid ounces, miles to feet, and pounds to ounces, are based on the English system, which uses different conversion factors that are not consistently multiples of ten.
what is the best description of a wave
A wave is a disturbance that travels through space and matter, characterized by its wavelength, frequency, and amplitude.
Explanation:A wave is a disturbance or oscillation that travels through space and matter, transferring energy from one place to another. Waves are characterized by three main features: wavelength, frequency, and amplitude. The wavelength is the distance between two identical points on successive waves. The frequency refers to the number of wave cycles that occur in a second. The amplitude is a measure of the wave's height from the rest position.
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On a 100m straight track, Zak runs to the 80m mark in 15s. He then runs back to the 20m in 10s. He then runs to the 100m mark in 20s. Finally he runs to the 70m mark in 5s. The total distance travelled by Zak is ____ m and total displacement is ____ m.
Answer:
The total distance traveled by Zak is 250 m and total displacement is
70 m
Explanation:
Distance is a scalar quantity that represents how much ground an
object has covered during its motion
Displacement is a vector quantity that represents how far out of place
an object is, means the change in its position
Displacement = final position - initial position
The straight track is 100 m
Zak runs to the 80 m mark
That means he runs forward from zero to 80
Then his distance = 80 m
His displacement = + 80 m
He then runs back to the 20 m
That means that he runs back from 80 m to 20 m
Then his distance = 80 - 20 = 60 m
His displacement = 20 - 80 = -60 m
He then runs to the 100 m mark
That means he runs forward from 20 m to 100 m
Then his distance = 100 - 20 = 80 m
His displacement = 100 - 20 = + 80 m
Finally he runs to the 70 m mark
That means he runs back from 100 m to 70 m
Then his distance = 100 - 70 = 30 m
His displacement = 70 - 100 = - 30 m
His total distance is the sum of all distances he runs
The total distance = 80 + 60 + 80 + 30 = 250 m
His total displacements is the sum of all displacements he runs
The total displacement = (+80) + (-60) + (+80) + (-30) = + 70 m
The total distance traveled by Zak is 250 m and total displacement is
70 m
can you help me??????????????????????????)?
Answer:
Velocity is a change in displacement over change in time and uses the units m/s.
Both are rates of change and can be positive or negative.
Acceleration is a change in velocity over change in time and uses the units m/s².
Explanation:
Velocity is the change in displacement over change in time, this makes it a rate of change. It can be positive or negative because it is a vector quantity. It uses the units m/s because that is a displacement unit over a time unit.
Acceleration is the change in velocity over change in time, this makes it a rate of change. It can be positive or negative because it is also a vector quantity. It uses the units m/s² (m/s/s) because that is a velocity unit over a time unit.
With which part of the brain is awareness typically associated?
Answer:cerebral cortex
Explanation:
Answer:
Cerebral Cortex
Explanation:
The cerebral cortex has a left and a right hemisphere. Each hemisphere can be divided into four lobes: the frontal lobe, temporal lobe, occipital lobe, and parietal lobe. The lobes are functional segments. They specialize in various areas of thought and memory, of planning and decision making, and of speech and sense perception.
5. A car is traveling at 100 km/hr. How many hours will it take to cover a displacement of 750 km?
Answer:
It will take 1 hour for a car to cover a displacement of 750 km at a constant speed of 100 km / hr.
Explanation:
Velocity is associated with the change of position of a body over time. In other words, speed expresses the relationship between the space traveled by an object, the time taken for it and its direction.
That is, speed implies the change of position of an object in space within a certain amount of time (that is, speed), added to the direction in which said movement occurs.
Then, 100 km / hr is the speed of the car and indicates that every hour the car travels 100 kilometres.
Then it is possible to apply a rule of three to calculate the time it takes for the car to travel 750 km. The three employee rule is: if 100 km are traveled in 1 hour, 750 km in how long is it traveled?
[tex]time=\frac{750 km*1hour}{100 km}[/tex]
time=7.5 hour
It will take 1 hour for a car to cover a displacement of 750 km at a constant speed of 100 km / hr.
The number of neutrons is equal to the atomic number
O A True
B. False
Answer:false
Explanation:
The total number of the neutrons in a atom is the difference of mass number of the atom and its atomic number.
The number of neutrons is not equal to the atomic number. Thus the given statement is false.
What is atom?Atom is the smallest unit of the matter consist the positive charged nucleus and the electrons which moves around it. The atom can not be divided further.
The atom of a matter is made by three elements-
1) Neutron-Neutron is the element of atom, which has zero charge.2) Proton-Proton is the element of atom, which has positive charge.3) Electron-Electron is the element of atom, which has negative charge.The relation between the atomic number and neutrons-
The total number of the neutrons in a atom is the difference of mass number of the atom and its atomic number.
Thus total number of the neutrons in a atom is,
[tex]N=M-n[/tex]
Here, [tex]M[/tex] is the mass number of the atom and [tex]n[/tex] is the atomic number of it.
Thus, the number of neutrons is not equal to the atomic number. Thus the given statement is false.
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At summer camp, the swimming course runs the length (L) of a small lake. To determine the length of the course, the camp counselors measure the two "dry" legs of a right triangle. What is the length in meters of the swimming course in the figure below? A right triangle overlaps a lake. It has sides 25 and 40 meters. Hypotenuse labeled L goes through the lake.
Answer:
The length of the swimming course is 47.16 meters.
Explanation:
It is given that the right triangle overlaps the lake and hypotenuse L runs through the length of the lake. Thus length of the lake will be the length of this hypotenuse.
The instructors have conducted measurements of the right triangle and has found the legs to be 25 and 40 meters. The sum of squares of base and height of a right triangle gives the value of its hypotenuse according to Pythagoras theorem.
Thus [tex]h^2+b^2=H^2[/tex]
b - base
h - height.
[tex]40^2+25^2=1600+625=2225[/tex]
[tex]H=\sqrt{2225}=47.16 m[/tex]
How are energy of motion and speed are related to each other?
The energy transferred is known as kinetic energy, and it depends on the mass and speed achieved. Kinetic energy can be transferred between objects and transformed into other kinds of energy.
the kind of graph that would best show the
results of a survey of 144 people where 75 ride a bus, 45 drive cars,
15 carpool, and 9 walk to work.
Answer:
a bar graph would be the kind of graph that you should use for this problem because it would be easier to read and also do
Explanation
A Pie Chart is the best type of graph to represent the results of this survey, as it visually expresses each commuting mode as a portion of the total survey responses.
Explanation:The type of graph that would present this data most clearly is a Pie Chart. The Pie Chart would provide a visual representation of each commuting method as a proportion of the total survey responses. For instance, the section corresponding to bus riders would be rather large, as 75 out of 144 individuals, or approximately 52% of the participants, use the bus. In contrast, the segment for individuals who walk would be smaller, as 9 out of 144 or about 6% of respondents walk to work. As such, a Pie Chart offers a visual distribution of responses, making it easy to compare different categories.
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significant digits show the _____ of measurements and calculations.
1) accuracy
2) precision
What is needed to create change in a system?
A 50 newton force is required to push a 10 kg box 30 meters across the floor. The box is then lifted up 6 meters and placed on a shelf. How much total work was done?
Answer:
2088 J
Explanation:
Work = net force × distance
When the box is being pushed across the floor, the force is 50 N, and the distance is 30 m.
W = (50 N) (30 m)
W = 1500 J
When the box is being lifted, the force is the weight of the box (10 kg × 9.8 m/s²), and the distance is 6 m.
W = (98 N) (6 m)
W = 588 J
So the total work done is:
W = 1500 J + 588 J
W = 2088 J
A car is traveling at 10m/s before it increases its speed to 30m/s for 120m. How long does it take to do this ?
Answer:
60 seconds
Explanation:
Given:
v₀ = 10 m/s
v = 30 m/s
Δx = 120 m
Find: t
Δx = ½ (v + v₀)t
120 = ½ (30 + 10) t
t = 60
It takes 60 seconds.
What will happen to an object at rest if no unbalanced forces act on it,
according to Newton's First Law?
Explanation:
Newton's first law says that an object at rest stays at rest, and an object in motion stays in motion, until acted upon by an unbalanced force.
If there's no unbalanced force, then an object at rest will stay at rest.
Which of the following is a way that microwaves and x-rays are similar?
A. They both have technological uses.
B. They are both high energy waves,
C. They are both to be exposed to at high doses.
D. They are both used to transmit information.
(I’m between A and B)
Answer:
A
Explanation:
In my opinion I'm pretty sure it's A because WE DO use microwaves and x-rays as techonological uses.
Answer:
A
Explanation:
An object is thrown directly up (positive direction) with a velocity (vo) of 20.0 m/s and do= 0. How high does it rise (v = 0 cm/s at top of rise). Remember, acceleration is -9.80 m/s2.
d = _____ m
1.02
2.04
20.4
40.8
Answer:
20.4
Explanation:
Given:
y₀ = 0 m
v₀ = 20.0 m/s
v = 0 m/s
a = -9.80 m/s²
Find: y
v² = v₀² + 2a (y − y₀)
(0 m/s)² = (20.0 m/s)² + 2 (-9.80 m/s²) (y − 0 m)
y = 20.4 m
A box is being pulled to the right. What is the direction of the gravitational force?
up
down
Oright
left
Answer:
The correct answer would be downwards
Hope this helps have a good day
Final answer:
The gravitational force on a box being pulled to the right is downward towards the Earth's center.
Explanation:
The direction of the gravitational force on a box being pulled to the right is downward towards the Earth's center. This is because gravitational force is a vector that points downwards, regardless of any horizontal movement or force applied to an object. The gravitational force can be calculated using the equation F = mg, where F is the gravitational force, m is the mass of the object, and g is the acceleration due to gravity, which is approximately 9.81 m/s² near the Earth's surface. Therefore, even when the box moves to the right, the gravitational force only acts downward.
19) Suppose that a car traveling to the east (+x direction) begins to slow down as it approaches a traffic
light. Which statement concerning its acceleration must be correct?
A) Its acceleration is in the -x direction.
B) Its acceleration is zero.
Its acceleration is decreasing in magnitude as the car slows down.
D) Its acceleration is in the +x direction.
Answer: C) Its acceleration is decreasing in magnitude as the car slows down.
Explanation:
According to the described situation the car's final velocity is less than its initial velocity, this means the car's velocity decreased as it slows down.
On the other hand, acceleration [tex]a[/tex] is defined as the variation of velocity in time:
[tex]a=\frac{\Delta V}{\Delta t}[/tex]
If the car's velocity decreases, its acceleration is negative. Hence, the acceleration is decreasing in magnitude as well.
In the context of a car slowing down while traveling east, its acceleration must be in the -x direction (towards the west) which means its acceleration is in the opposite direction of its motion, hence option A is correct.
The question concerns the acceleration of a car traveling east (considered the +x direction) as it begins to slow down when approaching a traffic light. According to the principles of physics, when an object is slowing down, its acceleration is in the opposite direction of its motion. Since the car is moving to the east and slowing down, its acceleration must be towards the west, which is the -x direction in our coordinate system. Therefore, its acceleration is in the -x direction, making the correct answer to the question Option A.
To further clarify, when a car traveling in a positive direction (to the east in this case) decelerates or slows down, it undergoes negative acceleration because the deceleration is opposite to the direction of its velocity. Hence, in the context of our coordinate system where the east is positive, the westward acceleration (slowing down) is considered negative.
A block with mass m = 6 kg is sitting on a horizontal surface and not moving. The free-fall acceleration is g = 9.81 m/s2. Please answer the following questions.
a. Write an expression for the magnitude of the force of gravity Fg on the block.
b. Calculate the magnitude of the force of gravity Fg on the block in Newtons.
c. In what direction is the force of gravity in this problem?
d. What is the magnitude of the normal force FN in Newtons?
e. In what direction does the normal force act?
Answer:
a. expression for force of gravity is mg
b. Value of force of gravity is 58.86 N
c. Direction of force of gravity is downwards
d. Value of normal force is -58.86 N
e. direction of normal force is upwards.
Explanation:
Given that mass of the block [tex]m=6 kg[/tex]
acceleration due to gravity [tex]g=9.81 m/s^2[/tex]
a. Expression for force of gravity is [tex]F_g=m\times g[/tex]
b. [tex]F_g=mg=6 \times 9.81=58.86 N[/tex]
force of gravity is [tex]58.86 N[/tex]
c. Force of gravity always acts in the downward direction.
d. Normal force[tex]F_N[/tex] acts in the direction opposite to the weight of the block and their magnitudes are same. since the object is at rest the upward and downward forces on the block are balanced.
[tex]F_N=-F_g=-58.86 N[/tex]
e. Normal force [tex]F_N[/tex]acts in the upwards.
The force of gravity on a 6 kg block is 58.86 N, acting downwards, while the normal force is 58.86 N, acting upwards, since the block is stationary on a horizontal surface.
Explanation:Forces Acting on a Stationary Block
a. The expression for the magnitude of the force of gravity Fg on the block is given by Newton's second law of motion: Fg = m × g where m is the mass of the object and g is the acceleration due to gravity.
b. To calculate Fg, simply multiply the mass m by the acceleration due to gravity g: Fg = 6 kg × 9.81 m/s² which equals 58.86 N.
c. In this problem, the direction of the force of gravity is vertically downwards, towards the center of the Earth.
d. The magnitude of the normal force FN on the block is equal to the force of gravity acting on the block when it is stationary on a horizontal surface, therefore FN = 58.86 N.
e. The normal force acts in a direction perpendicular to the surface, which in this case is vertically upwards.
In the periodic table of elements, what do all of the elements in group 2 have in common?
Answer:
The correct answer is chemical properties.
Explanation:
In a group, the chemical properties are very similar, because all the elements of the group have the same number of electrons in their last or last layers. The electronic configuration of its last layer is the same, varying only the period of the element. Alkaline earth metals are harder than alkaline metals, have brightness and are good electrical conductors; less reactive than alkalines, good reducing agents and form ionic compounds.
Have a nice day!
How does the scattering of tiny particles in the air affect the colors of the sky at sunrise and sunset
It affects the colors of the sky at sunrise and sunset because only the longer-wavelengths colors are visible.
Hey:) what is a monatomic molecule?
Answer:
"mono" and "atomic" means single atom this term is used in both physics and chemistry and it applied to the gasses as a monatomic gas
Answer and Explanation:
Good Day mate!
A monatomic molecule is that some of the elements do not have a tendency to form a molecule. Which means, the molecule of an element is made up of only one atom. Thus, there are called as Monatomic molecule.
Some common examples of monatomic molecules :
1. Helium (He)
2. Neon (Ne)
3. Argon (Ar)
4. Xenon (Xe)
Bernoulli’s principle states that fluid velocity decreases when flow is restricted. True False
A sailor pulls a 2,000 kilogram boat 25 meters along the dock with a rope attached to the boat that makes a 45 degree angle with the dock. How much work is done by the sailor if he exerts a force of 400 newtons while pulling the boat?
Answer: 7071.067 Joules
Explanation:
The Work [tex]W[/tex] done by a Force [tex]F[/tex] refers to the release of potential energy from a body that is moved by the application of that force to overcome a resistance along a path [tex]d[/tex].
It should be noted that it is a scalar, and its unit in the International System of Units is the Joule (like energy). Therefore, 1 Joule is the work done by a force of 1 Newton when moving an object, in the direction of the force, along 1 meter:
[tex]1J=(1N)(1m)=Nm[/tex]
Now, when the applied force is constant and the direction of the force and the direction of the movement are parallel, the equation to calculate it is:
[tex]W=(F)(d)[/tex] (1)
When they are not parallel, both directions form an angle, let's call it [tex]\alpha[/tex]. In that case the expression to calculate the Work is:
[tex]W=Fdcos{\alpha}[/tex] (2)
In this case the force and the distance in the path form an angle [tex]\alpha=45\°[/tex], so we will use the second equation, where [tex]F=400N[/tex] and [tex]d=25 m[/tex]:
[tex]W=(400 N)(25 m) cos(45\°)[/tex] (3)
Then:
[tex]W=7071.067 Nm=7071.067 J[/tex]
The work done by the sailor to pull the boat 25 meters with a force of 400 newtons at a 45-degree angle to the dock is approximately 7,071 Joules.
The amount of work done by the sailor on the boat can be calculated by using the formula for work done by a force at an angle, which is W = F imes d imes ext{cos}( heta). In this case, the force (F) is 400 newtons, the distance (d) is 25 meters, and the angle ( heta) is 45 degrees.
First, we calculate the cosine of the angle, which in this case is ext{cos}(45^{ ext{o}}) = rac{ ext{ extsqrt{2}}}{2}.
Then, we multiply the force, distance, and cosine of the angle: W = 400 N imes 25 m imes rac{ ext{ extsqrt{2}}}{2}.
Therefore, the work done by the sailor is 400 imes 25 imes rac{ ext{ extsqrt{2}}}{2}, which equals 7,071 Joules approximately.
3. A car drives horizontally off of a cliff that is 40 meters tall and lands 65 meters from the base of
the cliff. What was the initial velocity of the car?
Answer:
23 m/s
Explanation:
First, find the time it takes for the car to fall 40 meters.
y = y₀ + v₀ t + ½ at²
0 = 40 + (0) t + ½ (-9.8) t²
0 = 40 − 4.9 t²
t = 2.89 s
Next, find the velocity needed to travel 65 meters in that time.
x = x₀ + v₀ t + ½ at²
65 = 0 + v₀ (2.89) + ½ (0) (2.89)²
v₀ = 22.75 m/s
Rounding to two significant figures, the car's initial speed was 23 m/s.
An astronaut on spacewalk floats a little to far from space station without air to push against he can’t paddle back however he is holding a hammer explain how he could use the hammer to get him back to space station l
Answer:
The astronaut can throw the hammer in a direction away from the space station. While he is holding the hammer, the total momentum of the astronaut and hammer is 0 kg • m/s. According to the law of conservation of momentum, the total momentum after he throws the hammer must still be 0 kg • m/s. In order for momentum to be conserved, the astronaut will have to move in the opposite direction of the hammer, which will be toward the space station.
Explanation:found this as a verified answer on here
Answer:
He can throw the hammer in the direction opposite to the direction he wants to travel in. The hammer will exert an equal and opposite force on him, as per Newton's third law, and this will help him move towards the space station
Explane
above
Gravitational pull is determined by
-the sun and stars
-acceleration and volume
-volume and mass
-mass and distance
Answer:
The gravitational pull is determined by the mass and distance.
Explanation:
According to Newton's law of universal gravitation
[tex]F = G\frac{m1.m2}{r^{2} }[/tex]
where F is the gravitational pull, G is gravitational constant, m₁ and m₂ are masses of bodies and r is the distance between them.
It can be seen from the above equation that F is directly proportional to the product of the masses and inversely proportional to the square of distance between them.
F ∝ m₁m₂
F ∝ 1/r²
What is gas pressure
Answer:
Pressure is a force exerted by the substance per unit area on another substance. The pressure of a gas is the force that the gas exerts on the walls of its container. When you blow air into a balloon, the balloon expands because the pressure of air molecules is greater on the inside of the balloon than the outside.xplanation:
Answer:
Pressure is a force exerted by the substance per unit area on another substance. The pressure of a gas is the force that the gas exerts on the walls of its container. When you blow air into a balloon, the balloon expands because the pressure of air molecules is greater on the inside of the balloon than the outside.
Explanation:
A nonuniform, but spherically symmetric, distribution of charge has a charge density ρ(r) given as follows:
ρ(r)=ρ0(1−r/R) for r≤R
ρ(r)=0 for r≥R
where ρ0=3Q/πR3 is a positive constant.
Express your answer in terms of some or all of the variables r, R, Q, and appropriate constants.
Obtain an expression for the electric field in the region r≥R.
Obtain an expression for the electric field in the region r≤R.
Find the value of r at which the electric field is maximum.
Find the value of that maximum field.
Answer:
r ≥ R, E = Q / (4πR²ε₀)
r ≤ R, E = 12Q (⅓ (r/R)³ − ¼ (r/R)⁴) / (4πr²ε₀)
Maximum at r = ⅔ R
Maximum field of E = Q / (3πε₀R²)
Explanation:
Gauss's law states:
∮E·dA = Q/ε₀
What that means is, if you have electric field vectors E passing through areas dA, the sum of those E vector components perpendicular to the dA areas is equal to the total charge Q divided by the permittivity of space, ε₀.
a) r ≥ R
Here, we're looking at the charge contained by the entire sphere. The surface area of the sphere is 4πR², and the charge it contains is Q. Therefore:
E(4πR²) = Q/ε₀
E = Q / (4πR²ε₀)
b) r ≤ R
This time, we're looking at the charge contained by part of the sphere.
Imagine the sphere is actually an infinite number of shells, like Russian nesting dolls. For any shell of radius r, the charge it contains is:
dq = ρ dV
dq = ρ (4πr²) dr
The total charge contained by the shells from 0 to r is:
q = ∫ dq
q = ∫₀ʳ ρ (4πr²) dr
q = ∫₀ʳ ρ₀ (1 − r/R) (4πr²) dr
q = 4πρ₀ ∫₀ʳ (1 − r/R) (r²) dr
q = 4πρ₀ ∫₀ʳ (r² − r³/R) dr
q = 4πρ₀ (⅓ r³ − ¼ r⁴/R) |₀ʳ
q = 4πρ₀ (⅓ r³ − ¼ r⁴/R)
Since ρ₀ = 3Q/(πR³):
q = 4π (3Q/(πR³)) (⅓ r³ − ¼ r⁴/R)
q = 12Q (⅓ (r/R)³ − ¼ (r/R)⁴)
Therefore:
E(4πr²) = 12Q (⅓ (r/R)³ − ¼ (r/R)⁴) / ε₀
E = 12Q (⅓ (r/R)³ − ¼ (r/R)⁴) / (4πr²ε₀)
When E is a maximum, dE/dr is 0.
First, simplify E:
E = 12Q (⅓ (r/R)³ − ¼ (r/R)⁴) / (4πr²ε₀)
E = Q (4 (r³/R³) − 3 (r⁴/R⁴)) / (4πr²ε₀)
E = Q (4 (r/R³) − 3 (r²/R⁴)) / (4πε₀)
Take derivative and set to 0:
dE/dr = Q (4/R³ − 6r/R⁴) / (4πε₀)
0 = Q (4/R³ − 6r/R⁴) / (4πε₀)
0 = 4/R³ − 6r/R⁴
0 = 4R − 6r
r = ⅔R
Evaluating E at r = ⅔R:
E = Q (4 (⅔R / R³) − 3 (⁴/₉R² / R⁴)) / (4πε₀)
E = Q (8 / (3R²) − 4 / (3R²)) / (4πε₀)
E = Q (4 / (3R²)) / (4πε₀)
E = Q (1 / (3R²)) / (πε₀)
E = Q / (3πε₀R²)
For question 1:
For the region [tex]r \geq R[/tex], an expression for the electric field can be calculated by using the Gauss law:
Use gauss law of electrostatics, the charge electric flux through the Gaussian surface is,
[tex]\int \vec{E} \cdot d\vec{A}=\frac{q_{enc}}{\varepsilon_{0} }\\\\E(4\pi r^2)=\frac{Q}{\varepsilon_0}\ \ \ \ \ \ \ \ \ \ \ \ \ (Since\ \ q_{enc}=Q )[/tex]
Here, Q is the enclosed charge and [tex]\varepsilon_0[/tex] , is the permeability.
[tex]E=\frac{1}{4\pi \varepsilon_0 } \frac{Q}{r^2}[/tex]
Therefore, the required electric field is [tex]\frac{Q}{4\pi\varepsilon_0 r^2 }[/tex]
For question 2:
For Gaussian sphere of radius [tex]r \leq R[/tex], the charge enclosed within a spherical shell is,
[tex]dq =\rho_0(1-\frac{r}{R}) 4\pi r^2 dr[/tex]
Hence, the total charge enclosed with in the radius r is as follows,
[tex]q_{enc}=\int^{r}_{0} \rho_{0} (1-\frac{r}{R}) 4\pi r^2 \ dr\\\\[/tex]
[tex]=4\pi \rho_0 |\frac{r^3}{3}-\frac{r^4}{4R}|^4_{0}\\\\=\frac{12 Q}{R^3}(\frac{r^3}{3}-\frac{r^3}{4R})\\\\=\frac{Qr^3}{R^3}(4-\frac{3r}{R})\\\\[/tex]
Use Gauss's law for the Gaussian sphere of radius r,
[tex]\int \vec{E}\cdot dA=\frac{q_{enc}}{\varepsilon_0}\\\\E(4\pi r^2)=\frac{Qr^3}{\varepsilon_0 R^3}(4-\frac{3r}{R})\\\\E=\frac{Qr}{4\pi \varepsilon_0 R^3}(4-\frac{3r}{R})\\\\[/tex]
Therefore, the required electric field at [tex]r\leq R[/tex] is [tex]\frac{Qr}{4\pi \varepsilon_0 R^3}(4-\frac{3r}{R})\\\\[/tex]
For question 3:
The change in electric filed with respect to distance is zero when the electric field has a maximum value.
[tex]\frac{dE}{dr}= 0\\\\\frac{d(\frac{Qr}{4\pi \varepsilon_0 R^3}(4-\frac{3r}{R}))}{dr}=0\\\\(\frac{Q}{4\pi \varepsilon_0 R^3})\frac{d(4r-\frac{3r^2}{R})}{dr}=0\\\\[/tex]
Here, [tex](\frac{Q}{4\pi \varepsilon_0 R^3})[/tex] is not equal to zero. Hence,
[tex]\frac{d(4r-\frac{3r^2}{R})}{dr}=0\\\\4-\frac{6r}{R}=0\\\\r=\frac{4R}{6}=\frac{2R}{3}[/tex]
Therefore, the required value of [tex]r \ \ is\ \ \frac{2R}{3}\\\\[/tex]
For question 4:
Maximum value of the electric filed is as follows
[tex]E= \frac{Q}{4\pi \varepsilon_0 R^3} (4-\frac{3r}{R})\\\\[/tex]
[tex]= \frac{Q(\frac{2R}{3})}{4\pi \varepsilon_0 R^3} (4- \frac{3(\frac{2R}{3})}{R})\\\\=\frac{Q}{3 \pi \varepsilon_0 R^2}[/tex]
Therefore, the required maximum value of the electric field is [tex]\frac{Q}{3 \pi \varepsilon_0 R^2}[/tex]
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brainly.com/question/12577441
A bulldozer does 4,500 J of work to push a mound of soil to the top of a ramp that is 15 m high. The ramp is at an
angle of 35° to the ground. How much force did the bulldozer apply to the mound of soil? Round your answer to two
significant figures.
Its 520 N
Answer:
520 N
Explanation:
Work is the dot product of the force vector and displacement vector.
W = F · x
This means it is the product of the magnitudes of the vectors and the cosine of the angle between them.
W = F x cos θ
The displacement of the soil is 15 m up. The force is parallel to the ramp. So the angle between the vectors is 90° − 35° = 55°.
Plugging in the values and solving for F:
4500 J = F (15 m) (cos 55°)
F = 523 N
Rounded to two significant figures, the force is 520 N.