Answer: 2B + 3F^2 → 2BF^3
Which statement can be made about the amplitude of any transverse wave?
It is the length from the midpoint to the crest.
It is half the length from the midpoint to the trough.
It is the length of the wavelength.
It is half the length of the wavelength.
Answer:
A) It is the length from the midpoint to the crest.
Explanation:
The correct statement about the amplitude of any transverse wave is: It is the length from the midpoint to the crest. The correct option is A.
What is a transverse wave?A transverse wave is a type of wave in which the displacement of the medium is perpendicular to the direction of wave propagation.
Examples of transverse waves include light waves and water waves in which the surface of the water oscillates up and down while the wave moves horizontally.
The properties of a transverse wave include:
Amplitude: The maximum displacement of the medium from its rest position. This represents the intensity or strength of the wave.
Wavelength: The distance between two adjacent points in the wave that are in phase with each other, for example, between two consecutive crests or troughs. It is typically represented by the symbol λ.
Frequency: The number of complete wave cycles that pass a point in a given amount of time, usually measured in hertz (Hz). The frequency is inversely proportional to the wavelength and is represented by the symbol f.
Period: The time taken for one complete wave cycle to pass a given point, usually represented by the symbol T. The period is directly proportional to the wavelength and inversely proportional to the frequency.
Speed: The speed at which the wave propagates through the medium, usually represented by the symbol v. The speed is directly proportional to the frequency and wavelength.
These properties are related to each other by the wave equation:
v = fλ,
Where v = the speed of the wave,
f = the frequency,
and λ = the wavelength.
Therefore, The correct statement about the amplitude of any transverse wave is A. It is the length from the midpoint to the crest.
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In any vector space au=bu implies a=b ? Trou or False
Answer:
False
Explanation:
(I guess if it were written "properly" it would be ax=bx implies a=b).
Given the axioms we were given, it would seem that the statement should be true, no?
A related statement -- also listed as false -- is that "in any vector space, ax=ay implies that x=y." Again, given the axioms we have.
Answer:
False
Explanation:
Simply use the counterexample u = 0
For zero vector:
au=bu=0
holds for a=3, b=4
False
50 POINTS
A velocity vs time graph is shown. What is the acceleration of the object?
Answer:
Explanation:
Given:
V₀ = 0 m/s
V = 20m/s
t = 5 s
___________
a - ?
The acceleration:
\(a = \frac{(V -V_{0} )}{t} \\\\\)
\(a=\frac{(20 - 0)}{5} = 4 \frac{m}{s^{2} } \\\)
What are autotrophs? Name three types of organisms that are autotrophs.
Match each word to its correct meaning.
1. humus
the thin upper layer of Earth's crust that supports plant life
2. inorganic
a vertical section of soil that shows the horizon and parent material
3. organic
the layer of loose rock on the surface of the earth; also called mantle rock
4. parent material
dark colored organic material in soil; it is left over from the decay of living things
5. regolith
a physical property of soil that describes how the soil feels, and the relative components of sand, silt, and clay sized particles
6. soil
a chemical property of soils that describes the measure of hydrogen ions in a soil sample; how acidic or basic a soil sample is
7. soil horizon
a substance that does not contain carbon and hydrogen atoms, such as salts, rocks, and minerals
8. soil ph
a distinct layer of soil that has characteristic properties
9. soil profile
the rock material that was weathered to form the sediments in a given soil
10. soil texture
a substance that contains carbon and hydrogen atoms, such as carbon dioxide, glucose, methane, and nucleic acid
Answer:
1. Soil.
2. Soil profile.
3. Regolith.
4. Humus.
5. Soil texture.
6. Soil pH.
7. Inorganic.
8. Soil horizon.
9. Parent material.
10. Organic.
Explanation:
1. Soil: the thin upper layer of Earth's crust that supports plant life. There are three (3) main types of soil; sandy, clay and loamy soil.
2. Soil profile: a vertical section of soil that shows the horizon and parent material.
3. Regolith: the layer of loose rock on the surface of the earth; also called mantle rock.
4. Humus: dark colored organic material in soil; it is left over from the decay of living things.
5. Soil texture: a physical property of soil that describes how the soil feels, and the relative components of sand, silt, and clay sized particles.
6. Soil pH: a chemical property of soils that describes the measure of hydrogen ions in a soil sample; how acidic or basic a soil sample is.
7. Inorganic: a substance that does not contain carbon and hydrogen atoms, such as salts, rocks, and minerals.
8. Soil horizon: a distinct layer of soil that has characteristic properties.
9. Parent material: the rock material that was weathered to form the sediments in a given soil.
10. Organic: a substance that contains carbon and hydrogen atoms, such as carbon dioxide, glucose, methane, and nucleic acid.
What do conduction and convection have in common?
5. You are driving at a constant speed of 35.0 m/s
when you pass a traffic officer on a motorcycle
hidden behind a billboard. One second after your
car passes the billboard, the traffic officer sets out
from the billboard to catch you, accelerating at a
constant rate of 3.0 m/s². How long does it take the
traffic officer to overtake your car?
The traffic cop needs 23.3 seconds to pass the automobile.
What is the acceleration of a car moving in a straight line at a constant speed?When your velocity (not speed) changes, you are accelerating. A automobile moving at a steady 100 km/h in a straight line has no acceleration. Average acceleration is equal to (change in velocity) / (duration). The car's acceleration is zero because its change in velocity is also zero.
\(d1 = v1*t1 = 35.0 m/s * 1 s = 35.0 m\)
\(d = d1 = 35.0 m\)
\(d2 = v2*t + (1/2)at^2\)
\(d2 = (1/2)at^2\)
\(v2*t + (1/2)at^2 = (1/2)at^2\)
\(v2*t = (1/2)at^2\)
Solving for t, we get:
\(t = (2v2/a) = (235.0 m/s)/3.0 m/s^2 = 23.3 s\) (rounded to 2 decimal places)
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the rear window in a car is approximately a rectangle, 1.6 m m wide and 0.55 m m high. the inside rearview mirror is 0.60 m m from the driver's eyes, and 1.70 m m from the rear window.
By the use of law of reflection To get a complete view of the rear window of the car is enough for the rear-view mirror to have a height of 0.1137m or 11.37cm
According to the law of reflection, the angle of incidence and reflection is equal.
\(\theta_r=\theta_i\)
Both the incident and reflected rays lay on the same plane.
Plane mirrors are reflective surfaces where each point of the mirror has the same normal direction to the surface. As a result, the size of the images produced by flat mirrors is equal to that of the object, and the image's distance is equal to that of the object.
Mathematically, the plane mirror equation yields,,
\(i=-o\)
The virtual nature of the image is represented by the negative symbol. The plane mirror's lateral magnification is,
\(m=\frac{-i}{o}\) = 1.
We are assuming that the top of the mirror, with unknown height
h, matches the driver's eyes. The height of the window is
H= 0.55m, while the distances from the mirror to the eyes and from the window to the mirror are d=0.60m and D=1.70m, respectively.
The following is how the reflection process works: An angle is created when a light beam from the window hits the mirror, reflected on the road, reaches the driver's sight. The worst case scenario occurs at the window's angle's lowest point. \(\theta_r\), . The mirror's height must be adjusted to guarantee that the reflected light hits the driver's eyes.
. Using the trigonometric relations,\(Tan \theta=\frac{H-h}{D+d}\)
for the large lower triangle, and,
\(Tan \theta=\frac{h}{d}\) for the small upper one.
Equating the tangents results in the equation,
\(\frac{h}{d}=\frac{H-h}{D+d}\)
solving for h
h=\(\frac{Hd}{D+2d}\)
Substituting the numeric values,
\(h=\frac{0.55m\times0.60m}{1.70m +2\times0.60m}\)
h=0.1137m
To get a complete view of the rear window of the car is enough for the rear-view mirror to have a height of 0.1137m or 11.37cm
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whit inn milne 10=120 milesS
Astronomy and Space Exploration: A satellite is orbiting a newly discovered planet. In
this situation, the satellite is orbiting in a low-altitude, circular orbit, to facilitate the
mapping of its surface. The altitude of the orbit is 120 miles and the time that it takes
the satellite to orbit is 2 hours 50 minutes. The radius of the planet is 9000 miles.
What is the orbital speed of the satellite (in miles per hour)?
What is the orbital speed of the satellite (in miles per hour) is 20465 miles per hour.
What is Orbital Velocity ?Orbital velocity is also called as critical velocity. It is minimum velocity must be given to the satellite or the body, so that it can revolve around the planet. i.e. orbital velocity is minimum velocity of body to revolve in stable orbit around a planet. Orbital velocity is given by,
\(v_{c}=\sqrt{\frac{GM}{R+h}}\)
where G = Gravitational constant (6.673×10⁻¹¹ Nm²/kg²) M = Mass of the planet R = Radius of the planet h = height of the object(satellite) Orbital velocity depends on mass of the planet, radius of the planet and height of the object(satellite). It is independent of mass of the body(satellite).
In this problem,
h = 120 miles,
R = 9000 miles
T = 2 hr, 50 min = 2.8 hr
ω = 2π/T
v/(R+h) = 2π/T
v = 2π(R+h)/T
putting all the values in the equation,
v = 2×3.14(120+9000)/2.8
v = 20465 miles per hour.
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In a DC generator, the generated emf is directly proportional to the
In a DC generator, the generated electromotive force (emf) is directly proportional to the rotational speed of the generator's armature and the strength of the magnetic field within the generator.
This relationship is described by the equation for the generated emf in a DC generator:
Emf = Φ * N * A * Z / 60
Where:
Emf is the generated electromotive force (in volts),
Φ is the magnetic flux density (in Weber/meter^2\(meter^2\) or Tesla),
N is the number of turns in the armature winding,
A is the effective area of the armature coil (in square meters),
Z is the total number of armature conductors, and
60 is a constant representing the conversion from seconds to minutes.
From this equation, we can see that the generated emf is directly proportional to the magnetic flux density (Φ) and the product of the number of turns (N), effective area (A), and the total number of armature conductors (Z). This means that increasing any of these factors will result in a higher generated emf.
The magnetic flux density (Φ) can be increased by using stronger permanent magnets or increasing the strength of the field windings in the generator.
The number of turns (N) and the effective area (A) are design parameters and can be optimized for a specific generator. Increasing the number of turns or the effective area will result in a higher generated emf.
Similarly, the total number of armature conductors (Z) can be increased to enhance the generated emf.
By controlling and optimizing these factors, the generated emf in a DC generator can be increased, resulting in higher electrical output. However, it is important to note that there are practical limits to these factors based on the design and construction of the generator.
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A wave has an amplitude of 0.0800 m
and is moving 7.33 m/s. One oscillator
in the wave takes 0.230 s to go from
one crest to the next crest. Find the
wavelength of the wave.
(Unit = m)
If a wave has an amplitude of 0.0800 m and is moving 7.33 m/s. The
wavelength of the wave is 1.69m.
What is the wavelength?The wavelength of a wave can be determined using the equation:
Wavelength = velocity / frequency
To determine the frequency we need to calculate the reciprocal of the time it takes for one complete oscillation.
frequency = 1 / time
frequency = 1 / 0.230
frequency ≈ 4.35 Hz
Substitute the values into the wavelength equation:
wavelength = velocity / frequency
wavelength = 7.33 / 4.35
wavelength ≈ 1.69m
Therefore the wavelength of the wave is approximately 1.69 meters.
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When comparing the types of electromagnetic waves, which has the
greatest energy?*
ultraviolet
X-rays
gamma-rays
visible
When comparing the types of electromagnetic waves, which had the greatest energy?
A ultraviolet
B x-rays
C gamma rays
D visible
Answer:
The right answer is gamma rays.
Explanation:
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A studious physics student is interrupted by a swarm of bees and chased off a cliff. Since she has her calculator in hand she quickly punches in numbers to figure out the initial velocity she needs to make it into the lake below. The cliff is 10 m high and the lake is 15 m away from the edge of the cliff. Find the time it takes her to drop. Find her initial velocity,
Answer:
The time is 1.4 sec
The initial velocity is 10.7 m/s.
Explanation:
Given that,
Height = 10 m
Distance = 15 m
We need to calculate the time
Using equation of motion
\(s=ut-\dfrac{1}{2}gt^2\)
Put the value into the formula
\(10=0+\dfrac{1}{2}\times9.8\times t^2\)
\(t^2=\dfrac{2\times10}{9.8}\)
\(t=\sqrt{\dfrac{2\times10}{9.8}}\)
\(t=1.4\ sec\)
We need to calculate the initial velocity
Using formula of velocity
\(v=\dfrac{d}{t}\)
Put the value into the formula
\(v=\dfrac{15}{1.4}\)
\(v=10.7\ m/s\)
Hence, The time is 1.4 sec
The initial velocity is 10.7 m/s.
A rock is at the top of a 20 meter tall hill. The rock has a mass of 10 kg. How much potential energy does it have?
Answer:
1960 JExplanation:
The potential energy of a body can be found by using the formula
PE = mgh
where
m is the mass
h is the height
g is the acceleration due to gravity which is 9.8 m/s²
PE = 10 × 9.8 × 20
We have the final answer as
1960 JHope this helps you
A charge +Q is located at the origin and a second charge, +4Q, is at distance (d) on the x-axis.
a. Where should a third charge, Q , be placed, so that all three charges will be in equilibrium? Express your answer in terms of d.
b. What should be its sign, so that all three charges will be in equilibrium?
c. What should be its magnitude, so that all three charges will be in equilibrium? Express your answer in terms of Q.
Answer:
a) x = ⅔ d , b) the charge must be negative, c) Q
Explanation:
a) In this exercise the force is electric between the charges, we are asked that the system of the three charges is in equilibrium, we use Newton's second law. Balance is on the third load that we are placing
∑ F = 0
-F₁₂ + F₂₃ = 0
F₁₂ = F₂₃
let's replace the values
k Q Q / r₁₂² = k Q 4Q / r₂₃²
Q² / r₁₂² = 4 Q² / r₂₃²
suppose charge 3 is placed at point x
r₁₂ = x
r₂₃ = d-x
we substitute
1 / x² = 4 / (d-x) 2
1 / x = 2 / (d-x)
x = 2 (x-d)
x = 2x -2d
3x = 2d
x = ⅔ d
b) The sign of the charge must be negative, to have an attractive charge on the two initial charges
c) Q
A certain asteroid is approximately 50 AU from the Sun. According to Kepler’s third law, what is the orbital period of this asteroid in terms of Earth years?
The orbital period of this asteroid is approximately 353.55 Earth years.
What is the orbital period of this asteroid?
Kepler's third law states that the square of the orbital period (in years) of a planet or asteroid is proportional to the cube of its semi-major axis (in AU).
Therefore, we can use the following formula to calculate the orbital period:
(T / 1 year)^2 = (a / 1 AU)^3
where;
T is the orbital period in years, and a is the semi-major axis in AU.Plugging in the values for the asteroid at 50 AU, we get:
(T / 1 year)^2 = (50 / 1 AU)^3
(T / 1 year)^2 = 125000
T / 1 year = √(125000)
T = 353.55 Earth years (rounded to two decimal places)
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An environmentally conscious physics student 250 N
mows her lawn with a push mower, exerting
a force of 250 N along the handle as shown. 40°
How much force is actually being used to push
the mower along the grou
The force actually being used to push the mower along the ground is 191 N.
When the physics student exerts a force of 250 N along the handle of the push mower, it's important to consider the components of this force that contribute to the actual force used to push the mower along the ground.
To determine the force used to push the mower along the ground, we need to find the horizontal component of the applied force. The angle of 40° indicates that the applied force can be broken down into two components: the horizontal component and the vertical component. The vertical component of the force is perpendicular to the direction of motion and does not contribute to pushing the mower forward.
To find the horizontal component, we can use trigonometry. The horizontal component is given by the formula:
Horizontal component = Applied force * cos(angle)
Plugging in the values, we get:
Horizontal component = 250 N * cos(40°)
Calculating this value, we find that the horizontal component of the applied force is approximately 191 N.
Therefore, the force actually being used to push the mower along the ground is 191 N. This is the component of the applied force that contributes to the forward motion of the mower, while the remaining vertical component is directed perpendicular to the ground and does not assist in pushing the mower forward.
By exerting a force of 250 N along the handle at a 40° angle, the student effectively applies 191 N of force to push the mower along the ground, ensuring efficient use of their effort while considering the environmental impact.
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1. What does Louis de Broglie's principle propose about electrons?
They have energy and momentum.
They behave as a wave and a particle.
They contain high-energy and low-energy photons.
They interact with other electrons to form new substances.
Louis de Broglie's principle of electrons states that (b) They behave as a wave and a particle.
The de Broglie equation is one of the equations that is commonly used to define the wave properties of matter. It basically describes the wave nature of the electron.Electromagnetic radiation, exhibit dual nature of a particle (having a momentum) and wave (expressed in frequency, wavelength). Microscopic particle-like electrons also proved to possess this dual nature property.Louis de Broglie in his thesis suggested that any moving particle, whether microscopic or macroscopic will be associated with a wave character. It was called ‘Matter Waves’. He further proposed a relation between the velocity and momentum of a particle with the wavelength, if the particle had to behave as a wave.Particle and wave nature of matter, however, looked contradictory as it was not possible to prove the existence of both properties in any single experiment. This is because of the fact that every experiment is normally based on some principle and results related to the principle are only reflected in that experiment and not the other.To know more about electrons visit:
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Liz rushes down onto a subway platform to find her train already departing. She stops and watches the cars go by. Each car is 8.60 m long. The first moves past her in 1.80 s and the second in 1.61 s. Find the constant acceleration of the train.
The constant acceleration of the train is 0.33 m/s.
The average velocity can be calculated by using the formula:
velocity = distance/time
For the 1st car, the velocity is calculated as:
v₁ = 8.60 m / 1.80 s = 4.78 m / s
For the second car, velocity can be calculated as:
v₂ = 8.60 m / 1.66 s = 5.34 m / s
Now we can solve for the acceleration using the formula:
v₂² = v₁² + 2 a d
Rewriting in terms of a, we get
a = (v₂² – v₁²) / 2 d
a = (5.34)² – (4.78)² / (2 × 8.6)
a = 0.33 m/s
Therefore, the constant acceleration of the train is 0.33m/s.
what is acceleration explain?
acceleration, fee at which speed modifications with time, in terms of each pace and course. A factor or an object shifting in a directly line is improved if it hastens or slows down. motion on a circle is improved even if the velocity is steady, due to the fact the route is constantly converting
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4. A ski jumper starts at the top of a 400m high hill before skiing down to the bottom. The ski jumper has a mass of 75kg. If after 10 seconds the skier is going 15m/s how much kinetic energy would the skier have?
A. 16,875.0 J
B. 8,437.5 J
C. 112.5 J
D. 562.5 J
Answer:
B. 8,437.5 J
Explanation:
Given the following data;
Height = 400m
Mass = 75kg
Velocity = 15m/s
Time = 10 secs
To find the kinetic energy of the skier?
Kinetic energy can be defined as an energy possessed by an object or body due to its motion.
Mathematically, kinetic energy is given by the formula;
\( K.E = \frac{1}{2}MV^{2}\)
Where;
K.E represents kinetic energy measured in Joules. M represents mass measured in kilograms. V represents velocity measured in metres per seconds square.Substituting into the equation, we have;
\( K.E = \frac{1}{2}*75*15^{2}\)
\( K.E = 37.5*225\)
K.E = 8,437.5 Joules.
A block of mass 15.0 kg slides down a ramp inclined at 28.0∘ above the horizontal. As it slides, a kinetic friction force of 30.0 N parallel to the ramp acts on it. If the block slides for 5.50 m along the ramp, find the work done on the block by friction.
Answer:
Work is done by friction = -165 J
Explanation:
Given:
Mass of block (m) = 15 kg
Ramp inclined = 28°
Friction force (f) = 30 N
Distance (d) = 5.5 m
Find:
Work is done by friction.
Computation:
Work is done by friction = -Fd
Work is done by friction = -(30)(5.5)
Work is done by friction = -165 J
Why is it important to to find information about if if crabs can or can't see the plankton, they eat near the ocean floor
Answer:
One possible explanation students can make: The crabs cannot see the plankton they eat near the ocean floor. For the crabs to see the plankton, some color of visible light would need to reach the plankton so that it can be reflected into the crabs' eyes.
An object is placed at 0 on a number line. It moves 3 units to the right, then 4 units to the left and then 6 units to the
right. What is the displacement of the object?
1
5
7
13
Answer:
5
Explanation:
when you move 3 unit to the right your object is at 3.then when you move 4 units to the left your object is at -1 because
a number line also has negative numbers.Then if you move 6 units your object is at 5
a ball is thrown directly downward with an initial speed of 8.45 m/s, from a height of 29.8m. After what time interval does it strike the ground?
Answer:
Approximately \(1.75\; {\rm s}\) (assuming that \(g = 9.81\; {\rm m\cdot s^{-2}}\) and that air resistance is negligible.)
Explanation:
Find the velocity of the ball right before landing using the following SUVAT equation:
\(\displaystyle v^{2} - u^{2} = 2\, a\, x\),
Where:
\(v\) is the velocity of the ball right before landing,\(u = 8.45\; {\rm m\cdot s^{-1}}\) is the initial velocity,\(a = 9.81\; {\rm m\cdot s^{-2}}\) is the acceleration, and\(x = 29.8\; {\rm m}\) is the change in the height of the ball.Rearrange this equation to find \(v\):
\(\begin{aligned}v &= \sqrt{u^{2} + 2\, a\, x} \\ &= \sqrt{(8.45)^{2} + 2\, (9.81)\, (29.8)}\; {\rm m\cdot s^{-1}} \\ &\approx 25.61\; {\rm m\cdot s^{-1}}\end{aligned}\).
Divide the change in velocity by acceleration to find the time elapsed:
\(\begin{aligned}t &= \frac{v - u}{a} \\ &\approx \frac{25.61 - 8.45}{9.81} \; {\rm s}\\ &\approx 1.75\; {\rm s}\end{aligned}\).
what tells you whether you are feeling hot, cold or in pain?
A. Nerves/Neurons
B. Spinal Cord
C. Brain
D. Skin
Answer:
i think its skin..think so this answre help you
A mars surface exploration vehicle drops a rock off a 1.00 I'm high vertical Cliff. The sound of the rock landing at the base of the cliff is recorded by instruments on the vehicle 27.1 seconds later. Calculate the acceleration due to gravity on Mars given that the speed of sound on Mars is 320 m/s
The acceleration due to gravity on Mars is 11.81 m/s².
The given parameters:
Height of the cliff, h = 1 mTime of motion of the sound wave, t = 27.1 sSpeed of sound in mass, v = 320 sThe equation of motion to determine the acceleration due to gravity on the moon is calculated as follows;
\(s = vt + \frac{1}{2} gt^2\)
where;
s is the distance traveledt is the time of motionSince the time measured is two way time, the new equation for the total distance traveled is calculated as;
\(v = \frac{2d}{t} \\\\2d = vt\\\\d = \frac{vt}{2} \\\\d = \frac{320 \times 27.1}{2} \\\\d = 4,336 \ m\)
The acceleration due to gravity is calculated as follows;
\(s = vt + \frac{1}{2} gt^2\\\\4,336 = 0 \ + \ \frac{1}{2} \times g \times (27.1)^2\\\\4,336 = 367.21g\\\\g = \frac{4,336}{367.21} \\\\g = 11.8 1 \ m/s^2\)
Thus, the acceleration due to gravity on Mars is 11.81 m/s².
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You hit a 1.25 kg billiard ball so that it eventually travels at a constant velocity of 0.44 m/s. if the billiard ball hits a stationary 1.55 Kg billiard ball inelastically (they stick together )what will be the final velocity of the balls? A) 0.355 m/s B) 0.196 m/s C) 0.55 m/sD) 0.44 m/s
This is the answer tab
First, we need to keep in mind that for inelastic collisions we cannot apply the Law of Conservation of Energy, as some of the energy will dissipate. However, we can apply the Law of Conservation of Momentum. This tells us that:
\(\vec{p}_{final}=\vec{p}_{initial}\)So, we'll start by writing the initial momentum of the system. This is:
\(\vec{p}_{initial}=mv=1.25*0.44=0.55\frac{kg*m}{s}\)This will have to be the same by the end. However, as we know, the mass will be 1.55+1.25=2.8kg. Then, we can write our equation as:
\(2.8*v=0.55\Rightarrow v=\frac{0.55}{2.8}=0.196\frac{m}{s}\)Then, our answer is b) 0.196 m/s
PLEASE HELP AND SHOW WORK,THANK YOU!!
4) Suppose that two identical
mass planets are sitting
million miles apart. At that
distance the planets have a
gravitational force of 1,000,000 N.
If the planets are moved
to two million miles apart, what
is the new gravitational force
between them?
The new gravitational force between the two planets, when they are moved to two million miles apart, is 250,000 N
The gravitational force between two objects can be calculated using Newton's Law of Universal Gravitation, which states that the force is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Given:
Initial distance between the planets = 1 million miles
Initial gravitational force = 1,000,000 N
Final distance between the planets = 2 million miles
To determine the new gravitational force, we need to compare the ratios of the distances and apply the inverse square law.
Let's denote the initial distance as d1, the initial gravitational force as F1, the final distance as d2, and the unknown final gravitational force as F2.
According to the inverse square law, the ratio of the gravitational forces is the square of the ratio of the distances:
(F2/F1) = (d1/d2)²
Substituting the given values:
(F2/1,000,000 N) = (1 million miles / 2 million miles)²
Simplifying:
(F2/1,000,000 N) = (1/2)²
(F2/1,000,000 N) = 1/4
F2 = (1/4) * 1,000,000 N
F2 = 250,000 N
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3. A circular section of copper cable has a resistance of 0.50. What will be the resistance of a
copper cable of the same length but of twice its diameter?
represent the reading of a vernier caliper with a diagram showing the reading 45.75mm
The reading on a vernier caliper can be represented as 45.75mm.
1. Understand the components of a vernier caliper: A vernier caliper consists of two main scales - the main scale and the vernier scale. The main scale is typically graduated in millimeters, while the vernier scale is a smaller scale that slides along the main scale.
2. Locate the main scale: Identify the main scale on the vernier caliper. The main scale is usually marked on the fixed jaw of the caliper and extends in a linear fashion.
3. Identify the vernier scale: The vernier scale is attached to the movable jaw of the caliper. It slides along the main scale and consists of smaller divisions.
4. Align the zero marks: Close the jaws of the caliper and ensure that the zero marks on both the main and vernier scales are aligned.
5. Determine the main scale reading: Read the main scale value that aligns with the zero mark on the vernier scale. In this case, the main scale reading will be 45mm.
6. Locate the vernier scale reading: Examine the vernier scale and identify the division on the vernier scale that lines up perfectly with a division on the main scale. This will give you the additional measurement beyond the main scale reading.
7. Determine the vernier scale reading: Find the division on the vernier scale that aligns with a division on the main scale. The value of this vernier division corresponds to the additional measurement. In this case, the vernier scale reading will be 0.75mm.
8. Add the main scale and vernier scale readings: Combine the main scale reading and the vernier scale reading to get the final measurement. In this case, the final reading will be 45.75mm.
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