The initial speed of the girl's ball relative to the boy is 3 m/s.
What is the initial speed of the girl's ball?
The initial speed of the girl's ball relative to the boy depends on the time of motion of the girls ball.
The time of motion of the ball from the given height is calculated as follows;
h = vt + ¹/₂gt²
where
v is the initial velocity of the ballt is the time of motion of the ballg is acceleration due to gravityh = 0 + ¹/₂gt²
h = ¹/₂gt²
t = √(2h/g)
t = √(2 x 1.5 / 9.8)
t = 0.55 s
The final velocity of the ball is calculated as;
v = gt
v = 9.8 x 0.55
v = 5.39 m/s
However, since we are looking for the initial speed of the girl's ball relative to the boy, we will ignore the final velocity of the ball.
The initial velocity of the ball = 0
The initial velocity of the girl's ball = 2 m/s + 1 m/s = 3 m/s
The relative velocity = 3 m/s - 0 m/s = 3 m/s
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according to karl popper, a discipline that claims to be a science is really a pseudoscience like astrology if it:
A scientific theory should make testable predictions and if those predictions are found to be incorrect the theory should be dismissed.
He argued that science advances best through the use of deductive reasoning, known as critical rationalism, as its primary emphasis. Popper coined the term critical rationalism to describe his philosophy. Popper rejected the empiricist view that basic statements are infallible.
Karl Popper was a scientific realist against his will. Despite his own limitations regarding the forms of acceptable scientific reasoning and the extent of empirical evidence, he advocated a very real conception of scientific goals and outcomes. A significant contribution stems from his rejection of induction in empirical science.
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A diver runs horizontally off the end of a 3.0-m-high diving board with an initial speed of 1.8 m/s. Find her y positions at the times t = 0.25 s , t = 0.50 s , and t = 0.75 s .
(a) At time, t = 0.25 s, the y position of the driver is 0.31 m.
(b) At time, t = 0.50 s, the y position of the driver is 1.2 m
(c) At time, t = 0.75 s, the y position of the driver is 2.76 m
What is the position of the driver?The position of the driver at the various time is determined by applying the following kinematic equation.
y = vt + ¹/₂gt²
where;
v is the initial vertical velocity of the drivert is the time of motion of the drivery is the vertical position of the driver at various timet is the time of motionSince the driver runs horizontally, the initial vertical velocity = 0
y = 0 + ¹/₂gt²
y = ¹/₂gt²
at time, t = 0.25 s, the y position of the driver is calculated as;
y = ¹/₂gt²
y = ¹/₂(9.8)(0.25)²
y = 0.31 m
at time, t = 0.5 s, the y position of the driver is calculated as;
y = ¹/₂gt²
y = ¹/₂(9.8)(0.5)²
y = 1.2 m
at time, t = 0.75 s, the y position of the driver is calculated as;
y = ¹/₂gt²
y = ¹/₂(9.8)(0.75)²
y = 2.76 m
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what is the rotational inertia of a solid iron disk of mass 41.0 kg with a thickness of 5.00 cm and radius of 30.0 cm, about an axis perpendicular to the disk and passing through its center?
Answer:
I = 1/2 M R^2 moment of inertia of solid disk
I = 1/2 * 41.0 kg * (.3 m)^2
I = 20.5 kg * .09 m^2 = 1.85 kg-m^2
(b) The cars collide and car B experiences an impulse. Car A continues to move in the same
direction, with a momentum of 21 000 kg m/s.
(i) Calculate the momentum of car B immediately after the collision.
momentum =
llicion
[1]
The momentum of car B immediately after the collision if the momentum of car A is 21 000 kg m/s after collision is 15000 kg m / s
p = m v
p = Momentum
m = Mass
v = Velocity
m1 = 2000 kg
u1 = 18 m / s
pi1 = 2000 * 18
pi1 = 36000 kg m / s
m2 = 1200 kg
u2 = 0
pi2 = 0
pf1 = 21000
According to law of conservation of momentum
pi1 + pi2 = pf1 + pf2
pi1 = Initial momentum of car A
pi2 = Initial momentum of car B
pf1 = Final momentum of car A
pf2 = Final momentum of car B
pf2 = pi1 + pi2 - pf1
pf2 = 36000 + 0 - 21000
pf2 = 15000 kg m / s
Therefore, the momentum of car B immediately after the collision is 15000 kg m / s
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an electron is released within a uniform electric field of a magnitude of 28,000 n/c generated by two parallel plates. the plates are separated by 4 cm. if the electron has moved across the entire gap between the plates, what is its speed?
Within a uniform electric field of magnitude 28,000 n/c produced by two parallel plates, an electron is expelled at a speed of 3.51 * 10^15 m/s^2. The distance between the plates is 4 cm.
The electron is a subatomic particle with the symbol e or with an electric field of one elementary negative charge. Due to their lack of known components or substructure, electrons, which are part of the first generation of the lepton particle family, are typically considered to be elementary particles. When the electric field strength at the electron's location, E, is taken into account, the force acting on it has the size F=eE. Newton's second law provides the electron's acceleration as follows:
a= F/m = eE/m
= (1.60*10^-19)(2.00*10^4)/9.11*10^-31
= 3.51 *10^15 m/s^2
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A brick is thrown upward from the top of a building at an angle of 25 to the horizontal and with an initial speed of 15 m/s. The brick hits the ground after 3.0s of flight.
(a) Calculate the height of the building.
The vertical height of the building is determined as 44.1 m.
What is the height of the building?
The height of the building is calculated by applying the following kinematic equation as shown below.
h = vyt + ¹/₂gt²
where;
vy is the initial vertical velocity of the brickt is the time of motion of the brickh is the height of fall of the brickg is acceleration due to gravityh = (v sinθ)t + ¹/₂gt²
where
θ is the angle of inclination of the velocityThe given parameters include the following;
initial vertical velocity of the brick, vy = 0the time of motion of the brick, t = 3.0 sthe height of fall of the brick, h = ?acceleration due to gravity = 9.8 m/s²h = (0 x sin25)(3) + ¹/₂(9.8)(3²)
h = 44.1 m
Thus, the height of the building is equal to the vertical distance travelled by the brick thrown at the given initial velocity.
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A small nail stuck in your car tire moves on a circular path with a radius of 35 cm. when the nail has traveled a linear distance of 5.5 m, through what angle has the tire rotated in both radians and degrees?
To cover 5.5 meters in a straight line, the tire rotated at an angle of 15.714rad.
What is a circle's simple definition?To put it simply, a circle is a spherical shape without any corners or line segments. In geometry, it has the shape of a closed curve.
A definition from Euclid
A circle is a plane figure that is bounded by a single curved line and in which all straight lines drawn from any point inside the circle to the boundary are equal. Its center is the point, and its circumference is the bounding line. — Book I of Euclid's Elements.
Given,
circular path with a radius of 35cm,
Circumference of car tire is 2πr = 2×3.14×0.35 = 2.198m
For traveling a distance of 5.5m
5.5 = angle in rads ×radius
angle = 5.5/0.35
angle = 15.714 rad
To cover 5.5 meters in a straight line, the tire rotated at an angle of 15.714rad.
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when a star is moving towards us (the earth) due to a planet orbiting it and tugging on it, we see a blue shift in the star's spectrum. this corresponds to what in terms of its radial velocity?
When the radial velocity is positive, it means the distance between the objects is or was becoming closer; when it is negative, it means the distance between the source and the observer is or was getting closer.
What is radial velocity?The portion of a particle's velocity that is moving in the direction of its radius vector. or radial motion, which is the speed at which an observer approaches or recedes from a celestial body or other source of radiation in the line that connects the two: speed in the visual field.
This technique is one of the detection methods that enables us to calculate an exoplanet's mass, a crucial factor in the hunt for worlds similar to Earth and other extraterrestrial life.
Radial velocity has been used to locate hundreds of distant planets and was the first effective approach for exoplanet discovery. Because stars do not need to be continuously monitored as they do with transit photometry, it is perfect for ground-based telescopes.
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How many moles of CaCo2 are in 50g of calcium carbonate
a solenoid of length 1.50 cm and radius 0.550 cm has 37 turns. if the wire of the solenoid has 1.15 amps of current, what is the magnitude of the magnetic field inside the solenoid? magnitude of the magnetic field: t ignoring the weak magnetic field outside the solenoid, find the magnetic energy density inside the solenoid. magnetic energy density: j/m3 what is the total magnetic energy inside the solenoid? total magnetic energy: j
a) magnitude of the magnetic field = 8.02 X [tex]10^{-3}[/tex] T
b)Energy Density = 5.03 J/[tex]m^{3}[/tex]
c) Total magnetic energy inside the solenoid = 2.01 X [tex]10^{-5}[/tex] J
What is magnetic field?A magnetic field, a vector field in the vicinity of a magnet, an electric current, or a changing electric field in which magnetic forces can be observed. Magnetic fields, such as those found on Earth, cause magnetic compass needles and other permanent magnets to align in the field's direction. Magnetic fields cause electrically charged particles to move in a circular or helical pattern. The operation of electric motors is based on this force, which is exerted on electric currents in wires in a magnetic field.Calculation
a) B = uNI/L
B = (4π X [tex]10^{-7}[/tex])(37)(1.15)/(.015)
B = 8.02 X [tex]10^{-3}[/tex] T
b) Energy Density = [tex]B^{2}[/tex]/2u
Energy Density = [tex](8.02 *10^{-3} )^{2}[/tex]/(2)(4π X [tex]10^{-7}[/tex])
Energy Density = 5.03 J/[tex]m^{3}[/tex]
c) Total magnetic energy inside the solenoid
Multiply by volume for total energy.
Total Energy = 5.03(π[tex]r^{2}[/tex])(L)
Total Energy = (5.03)(π)[tex](8.5*10^{-3})^{2}[/tex])(.015)
Total Energy = 2.01 X [tex]10^{-5}[/tex] J
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a)The magnitude of the magnetic field [tex]$=\mathbf{8 . 0 2} \times 10^{-3} \mathbf{T}$[/tex]
b)The Energy Density [tex]$=\mathbf{5 . 0 3} \mathrm{J} / \mathrm{m}^3$[/tex]
c) Total magnetic energy inside the solenoid [tex]$=\mathbf{2} . \mathbf{0 1} \mathbf{X} 10^{-5} \mathbf{J}$[/tex]
What is magnetic field?A magnetic field, a vector field in the vicinity of a magnet, an electric current, or a changing electric field in which magnetic forces can be observed.Magnetic fields, such as those found on Earth, cause magnetic compass needles and other permanent magnets to align in the field's direction.Magnetic fields cause electrically charged particles to move in a circular or helical pattern.The operation of electric motors is based on this force, which is exerted on electric currents in wires in a magnetic field.a) [tex]$B=u N I / L$[/tex]
[tex]&B=\left(4 \pi \times 10^{-7}\right)(37)(1.15) /(.015) \\[/tex]
[tex]&B=8.02 \times 10^{-3} \mathrm{~T}[/tex]
b) Energy Density[tex]$=B^2 / 2 \mathrm{u}$[/tex]
Energy Density[tex]$=\left(8.02 * 10^{-3}\right)^2 /(2)\left(4 \Pi \times 10^{-7}\right)$[/tex]
Energy Density [tex]$=5.03 \mathrm{~J} / \mathrm{m}^3$[/tex]
c) Total magnetic energy inside the solenoid
Multiply by volume for total energy.
Total Energy [tex]$=5.03\left(\pi r^2\right)(\mathrm{L})$[/tex]
Total Energy [tex]$\left.=(5.03)(\pi)\left(8.5 * 10^{-3}\right)^2\right)(.015)$[/tex]
Total Energy [tex]$=2.01 \times 10^{-5} \mathrm{~J}$[/tex]
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an object is 16.0cm from a concave mirror whose focal length is 10.0cm. (a) how far is the image from the mirror? answer: cm (b) what is the magnification? include any sign answer: (c) is the image real or virtual? answer: (d) is the image upright or inverted? answer:
The distance of the image is 26.67 cm
The magnification is -1.67
The image is real
The image is inverted
The focal length of the concave mirror = 10 cm
The distance of the object from the concave mirror = 16 cm
The distance of the image can be found using the formula1/p + 1/q = 1/f
where p is the distance of the object
q is the distance of the image
f is the focal length
1/q = 1/f - 1/p
1/q = (p - f)/fp
q = fp / (p - f)
q = 16 x 10 / ( 16 - 10)
= 160 / 6
= 26.67 cm
The distance of the image from the concave mirror is 26.67 cm
The magnification of the concave mirror can be found usingM = -q/p
where M is the magnification
M = -26.67 / 16
= -1.67
The distance of the image is positive, so the image is realThe magnification value is negative, so the image is inverted.Learn more about the concave mirror is
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an object has mass 0.2 kg, how much force is required to throw it vertically with velocity 5ms
0.2×51000)
Explanation:
change 5ms into cms before multiplying by 0/2 kgs
how is the energy that powers radio galaxies, quasars, and other active galactic nuclei thought to be produced?
The energy that powers radio galaxies, quasars, and other active galactic nuclei is thought to be produced by accreting matter onto a supermassive black hole. This process is called active galactic nucleus (AGN) fueling.
The gas that surrounds the black hole is heated to millions of degrees as it falls into the black hole. Because the gas is so hot, it emits a great deal of radiation in many different wavelengths.
This radiation can be seen across the electromagnetic spectrum, from low-energy gamma rays to high-energy X-rays. In some cases, jets of charged particles are ejected at nearly the speed of light along magnetic field lines; these jets can create shock waves in the surrounding medium that emit radio waves.
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robin started at point a. she walked 4m south, then 8m east, then 4m north, then 8m west so that she was back at point a. if her walk took 5 minutes, what was her velocity in meters per minute?
Robin started at point a. she walked 4m south, then 8m east, then 4m north, then 8m west so that she was back at point a. if her walk took 5 minutes her velocity in meters per minute is 0.96.
Displacement = distance / time = 24m/5 = 4.8
Velocity = displacement / Time = 4.8/5 = 0.96m/min
Its scientific definition and velocity are presumably similar. You are aware that a significant displacement over a short period of time indicates a large velocity, and that velocity has measures of distance / time, like miles/hour or kilometers/hour.
The change in position divided by the distance travelled is the definition of average velocity. However, the average speed of an object tells us nothing about what happens to it between the starting and finishing points. For instance, average velocity does not allow us to determine whether a passenger in an airplane briefly stops or reverses before relocating to the rear of the aircraft. We must consider shorter distances travelled over shorter times in order to obtain more information.
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Calculate the efficiency of a machine that requires 20 J of input work to do 10 J of output work. What is the efficiency of the machine? (in percent, but write the number only)
The efficiency of a machine that requires 20 J of input work to do 10 J of output work. The efficiency of the machine η = 50 %
The engine efficiency is defined as ratio of the useful work done to the heat provided.
By using the formula for efficiency of a machine and substituting the values in it, we get :
η = (Wo/Wi × 100)%
η = (10/20 × 100)%
η = 50 %
The efficiency of the machine will be η = 50 %
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two copper wires (in different circuits) carry the same current, but wire a has twice the radius of wire b. if the drift speed of the conducting electrons in wire a is 0.1 mm/s, what is the drift speed of the conduction electrons in wire b? assume the number density of conducting electrons is the same in both wires.
4 is the drift speed of the conduction electrons in wire b.
I = neA [tex]V_{d}[/tex]
[tex]V_{d}[/tex] = [tex]\frac{I}{neA}[/tex]
= [tex]\frac{I}{ne\pi r^{2} }[/tex]
[tex]V_{d}[/tex] [tex]\alpha[/tex] [tex]\frac{1}{r^{2} }[/tex]
r' = 2r
A' = [tex]\pi 2r^{2}[/tex]
= 4[tex]\pi r^{2}[/tex]
[tex]\frac{Vd'}{Vd}[/tex]= [tex]\frac{r^{2} }{2r^{2} }[/tex] = 1/4
[tex]V_{d}[/tex] = 4
What is drift speed?Subatomic particles like electrons move in random directions all the time. When electrons are exposed to an electric field, they move randomly but slowly drift in one direction, the direction of the applied electric field. The net speed at which these electrons drift is called the drift speed. Curvature can be defined as follows:
The average speed of charged particles (eg electrons) in a material under the influence of an electric field. the SI unit of yard speed is m/s. It is also measured in [tex]m^2[/tex]/(V.s).
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a 70 kg man is floating at rest near his spaceship. he throws a 1.5 kg wrench away from the ship at a speed of 10 m/s in order to move himself toward it. with what speed does he move toward the ship?
0.218 m/s speed does he move toward the ship.
use the formula from conservation of Momentum
mu + MV = (m-M)V'
u = o
so
MV = (m-M)V'
V' = (1.5 * 10)/(70-1.5)
V' = 0.218 m/s
What is speed?The most crucial scientific notion is measurement. Base or physical fundamental units are used to quantify a wide range of quantifiable quantities. One such measurable metric is speed, which calculates the ratio between the distance an object travels and the time needed to cover that distance. Let's explore speed in-depth in this session.
The distance traveled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.
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two workers are sliding 260 kg crate across the floor. one worker pushes forward on the crate with a force of 450 n while the other pulls in the same direction with a force of 370 n using a rope connected to the crate. both forces are horizontal, and the crate slides with a constant speed. what is the crate's coefficient of kinetic friction on the floor?
To find out the kinetic friction, using the coefficient friction formula.
What is kinetic friction?
A force that acts between moving surfaces is called "kinetic friction." A force acting in opposition to the direction of a moving body on the surface is felt. The two materials' kinetic friction coefficients will determine how much force is applied.
What is coefficient friction?
A measure of the degree of friction between two surfaces is the coefficient of friction. A coefficient of friction is determined by calculating the resistance to motion at the intersection of two surfaces made of the same or different materials.
UK
U-coefficient of friction
K-Kinetic friction
Using UK
450+370-f=m*o
f=820=UK*260*9.8
UK=2.548
820/2.548
UK= 321.8210361
Therefore the coefficient of kinetic friction is 321.8210361
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explain the differences between linear speed and angular speed when describing motion along a circular path.
The difference between linear speed and angular speed is linear speed calculates the distance to time whereas angular speed calculates the angle to time.
The difference between the linear speed and the angular speed is that linear speed is just a measurement determined by calculating the distance of an arc versus time taken, and angular velocity is also a measurement determined by calculating the angle of an arc versus time taken.
The formula of the linear speed is
s = d / t
where s is the speed
d is the distance
t is the time taken
The formula of the angular speed is
ω = θ / t
where ω is the angular speed
θ is the angular rotation
t is the time taken.
The relation between the linear speed and angular speed in a uniform circular motion is
s = rω
where s is the linear speed
r is the radius
ω is the angular speed.
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How does a white dwarf differ from a neutron star? how does each form? what keeps each from collapsing under its own weight?.
An electron degenerate object is a white dwarf, whereas a neutron star is a neutron degenerate object. A white dwarf is less compact and has a larger radius than a neutron star.
How is a white dwarf transformed into a neutron star?A white dwarf would collapse into a denser entity known as a neutron star if it reached the Chandrasekhar limit and nuclear reactions were to stop. This would happen if nuclear reactions continued to occur.
How is a white dwarf prevented from exploding into a neutron star?White dwarf stars are prevented from collapsing by the fact that electrons are fermions, while neutron stars are prevented from collapsing by the fact that electrons are fermions.
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if the test section is designed to have a velocity of 200 m/s, determine the mach number, temperature and pressure in the test section. is the pressure in the test section greater than or less than the surrounding atmospheric pressure?
The test section's pressure is lower than the ambient pressure.
What exactly does pressure mean?In the physical sciences, pressure is defined as the perpendicular force per unit area or the stress at a particular location within a confined fluid.
Given,
Diameter of Test section, d₂ = 0.5m
Area, A₂ = π/4d₂² = π/4×0.5² = 0.19635m²
Now, At Inlet,
Po = 101325Pa
To = 288 k
s = 122 kg/m³
(a) Using Bernoulli Theorem, i'n Test Section,
Po = [tex]P_{t}[/tex] +1/2γ [tex]v_{t^{2} }[/tex]
101325 = [tex]P_{t}[/tex] + ½ (1.22) (200) ²
[tex]P_{t}[/tex] = 76925 Pa
[[tex]v_{t}[/tex] = 200m/s]
Now,
Static Temperature, [tex]T_{t}[/tex]
[tex]T_{0}[/tex] = [tex]T_{t}[/tex] +v²/2[tex]c_{p}[/tex]
288 = [tex]T_{t}[/tex] +200²/2×1005
[tex]T_{t}[/tex] = 268.09k.
Thus,
[tex]M_{t}[/tex] = [tex]v_{t}[/tex]/[tex]\sqrt{\nu RT_{t} }[/tex]
[tex]M_{t}[/tex] = 200/1.4×287×268
[tex]M_{t}[/tex]= 0.609
The test section's pressure is lower than the ambient pressure.
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x. a 0.015-kg marble moving to the right at 0.40 m/s has a head-on, elastic collision with a 0.045-kg marble sitting at rest on a smooth, level surface. a) what are the magnitudes and directions of the velocities of the two marbles after the collision? b) show that the ke is conserved.
The magnitudes and directions of the velocities of the two marbles after the collision is: v1f is left and v2f is right.
What is collision?The initial marble weighs m1 = 0.015 kg.
Second marble's mass is m2=0.045kg.
The first marble's initial velocity is v1i=0.40m/8 before to contact.
The second marble's initial velocity is v2i=0m/8 prior to impact.
After the impact, the first marble's final speed is v1f.
Following the collision, the initial marble's final velocity is v2f.
If the collision is elastic, the kinetic energy is preserved.
We'll write 1/2 m1 for KE = 1/2 mv2 (v1i)
2 + 1/2 m2(vi) (vi)
2 = 1/2 m1(v1f)2 + 1/2 m2 (v2f) (v2f)
2.
Using this equation, we can establish a new relationship between velocities and determine each marble's post-collision velocity:
v1f=(m1-m2)/(m1+m2)
v1\sv1f=(0.015kg-0.045kg)/(0.015kg+0.045kg)
0.40m/s\s=-0.20m/s
First marble is moving leftward at 0.20 m/s, as indicated by the negative sign.
Find the second marble's final velocity.
v2f=2m1v1/(m1+m2)\s
v2f=2⋅0.015kg⋅0.40m/s/(0.015kg+0.045kg)\s
v2f=0.20
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the tide that results from a lunar wave is larger than the solar wave. group of answer choices true false
The given statement is true. A lunar eclipse happens when the Moon passes into the shadow of the Earth. A solar eclipse happens when the Moon passes between Earth and the Sun.
What is lunar wave and solar wave?A lunar eclipse happens when the Moon passes into the shadow of the Earth. This is only possible when the Sun, Earth, and Moon are precisely or extremely closely aligned with Earth between the other two, which can happen only on a full moon night when the Moon is close to either lunar node.
A solar eclipse happens when the Moon passes between Earth and the Sun, completely or partially blocking Earth's view of the Sun. A new moon corresponds with such an alignment, showing that the Moon is closest to the plane of the Earth's orbit. The Moon completely obscures the disk of the Sun during a total eclipse.
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The given statement is true. A lunar eclipse happens when the Moon passes into the shadow of the Earth. A solar eclipse happens when the Moon passes between Earth and the Sun.
What is lunar wave and solar wave?When the Moon enters the shadow of the Earth, an eclipse occurs. This can only occur on a full moon night when the Moon is close to either lunar node, when the Sun, Earth, and Moon are precisely or extremely closely aligned with Earth between the other two.When the Moon passes in front of Earth and the Sun, covering Earth's view of the Sun entirely or in part, a solar eclipse occurs. Such an alignment is accompanied by a new moon, demonstrating that the Moon is closest to the plane of the Earth's orbit. A total eclipse occurs when the Moon totally blocks out the Sun's disk.To learn more about Lunar and solar eclipse refer to:
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the force F acting on a body along a circular path depends on a mass of the body (m),velocity(v) and radius (r) of the circular path.obtain the expression for the force by dimensional analysis method(take constant k to be 1)
the required equation for centripetal force is F = k m¹ v¹ r⁻¹.
A particle traveling uniformly in a circle experiences a centripetal force, F, which is dependent on the mass (m), velocity (v), and radius (r) of the circle.
the F formula using the dimensions method is
Suppose F = k mᵃvᵇrⁿ. (i)
Where a, b, and n are the respective powers of m, v, and r and k is the dimensionless constant of proportionality.
Upon putting the measurements of various amounts in (i)
we get
[M¹L¹T‐²] = Mᵃ[LT‐¹]ᵇ Lⁿ
=> [M¹L¹T‐²] = Mᵃ Lᵇ Lⁿ T⁻ᵇ
=> [M¹L¹T-²] = Mᵃ Lᵇ⁺ⁿ T⁻ᵇ
on comparing both sides we get
a = 1
b+n = 1
-b = -2 => b = 2
Then n = -1
Onputting these values in (i),
we get
F = k m¹ v¹ r⁻¹
Or
F=k(mv²)/r
This is the required equation for centripetal force.
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2. It takes 1,200 J of work to lift a car high enough to change a tire.
How much work must be done by the person operating the jack
if the jack is 25% efficient?
The work done by the person operating the jack is 4,800 J
Efficiency is described as the potential to perform something with the least quantity of wasted time, cash, and attempt or competency in performance. Effectiveness is described because the diploma to which some thing is successful in producing a preferred result; achievement.
calculation:-
work input = (1200 J)/(0.25)
= 4800 J.
There are numerous styles of performance, consisting of allocative and effective performance, technical efficiency, 'X' efficiency, dynamic performance and social efficiency.
The prime focus of performance is for customers to get the goods and offerings they want at the bottom possible resource price. Inside the have a look at of economics, the dreams of efficiency and equity are frequently in warfare with each other.
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a 0.111 kg hockey puck moving at 55 m/s is caught by a 80 kg goalie at rest. with what speed does the goalie slide on the (frictionless) ice?
The goalie slides on the frictionless ice at a speed of 0.076 m/s.
collision energy equals collision momentum
What generates momentum?An object's momentum will vary as a result of a force applied for a specific length of time. In other words, an uneven force an object regardless of whether it is speeding up or slowin accelerates g down. When a force exerted against an object's motion slows it down.
The puck weighs 0.111 kg in terms of mass.
Hockey puck velocity is 55 meters per second.
Goalkeeper weight: 80 kg
Goalkeeper's speed is 0 meters per second.
Following the rule of linear momentum conservation, (0.111 kg 55 m/s) + (80 kg 0 m/s) = (0.111 kg + 80 kg) V V = (6.105 / 80.111) = 0.076 m/s (0.111 kg 55 m/s) + (0.111 kg + 80 kg) V = 0.076 m/s
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the frequency content of an analog signal to be digitized has a range roughly covering the range of the auditory system of a young child: 200 hz to 20,000 hz. for accurate sampling, what is the minimal sampling rate necessary for an a/d convertor?
For accurate sampling, -44.1khz is minimum sampling rate for an a/d convertor.
What is sampling rate?The number of samples per second (or other unit) taken from a continuous signal to form a discrete or digital signal. The sample rate or sample rate specifies the number of samples per second (or other unit). of a continuous signal to form a discrete or digital signal..
The sampling rate can be thought of as the audio version of frames per second. This is the number of "clips" taken from an analogue sound wave to make a digital file. In addition, the sample rate also controls the highest frequency that can be accurately reproduced by a digital file.
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a mass m is attached to an ideal massless spring. when this system is set in motion with amplitude a, it has a period t. how does the period of the motion change if the amplitude of the motion is increased to 2a? explain.
System is set in motion with an amplitude of a and a period of T. If the amplitude of the motion is increased to 2a, the period of the motion changes.
A straightforward harmonic oscillator's period is independent of its amplitude. with the graphs of acceleration and velocity produced by the time derivatives. These oscillators also show how kinetic and potential energy can be transferred.
The acceleration of the mass increases proportionally with the increase in force, causing the mass to travel farther in the same amount of time. Therefore, increasing the amplitude has no overall impact on the oscillation's period.
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On level ground, how much farther can a person jump on the moon as compared to the earth if the takeoff speed and the angle are the same? The free-fall acceleration on the moon is one-sixth what it is on Earth.
The person can jump 6 times higher on the moon compared to Earth.
What is the maximum height jumped by an object?The maximum height an object can Jump is the height vertical displacement of the object during an upward motion.
Mathematically, the maximum height an object can jump is given as;
H = u²sin²θ/2g
where;
u is the initial velocity of the objectθ is the angle of projection of the objectg is acceleration due to gravityh is the maximum height of jumpWhen a person moves to the moon, the acceleration due to gravity becomes ; ¹/₆
The new height the object can jump is calculated as follows;
H = u²sin²θ/(2 x ¹/₆g)
H = 6( u²sin²θ/2g)
Thus, the person will jump higher on the moon due to lesser acceleration due to gravity.
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A 65-kg diver jumps off a 9.7-m tower.
(a) Find the diver's velocity when he hits the water.
____m/s
(b) The diver comes to a stop 2.0 m below the surface. Find the net force exerted on the diver while in the water.
______N
(a) The diver's velocity when he hits the water is 13.795 m/s.
(b) The diver's net force while in the water was -3092.7N.
Newton's second law states that the force F acting on a body is equal to the mass m of the body multiplied by the acceleration an of its center of mass, F = ma.
The three equations of motion are: v = u + at, v2 = u2 + 2as, and s = ut + 12at2.
Given
A 65-kg diver jumps off a 9.7-m tower
(a) Using newton's equation of motion,
v² = u² + 2gs ......... (1)
Where v = final velocity,
u = initial velocity,
s = height of the tower,
g = acceleration due to gravity.
Given: s = 9.7 m, u = 0 m/s (height jump), g = 9.81 m/s2.
Substitute into equation 1
v² = 0² + 2×9.81×9.7
v² = 190.314
v = √(190.314)
v = 13.795 m/s.
As a result, the driver's velocity when he hits the water is 13.795 m/s.
(b)
F = ma. ......... (2)
Where F is the force applied to the diver, m is the diver's mass, and an is the diver's acceleration below the water's surface.
Also using
v² = u² + 2as ......... (3)
When the diver enters the water, u = 13.795 m/s, and when the diver comes to a complete stop, v = 0 m/s.
Given are the following values: s = 2.0 m, u = 13.795 m/s, and v = 0 m/s.
Substitute in equation 3
0² = 13.795²+2(2a)
0 = 190.30203 + 4a
-4a = 190.30203
a = 190.30203/-4
a = -47.58 m/s²
Also given: m = 65 kg,
Substitute into equation 3
F = (-47.58)(65)
F = -3092.7
The Force is negative because it acts against the diver's motion.
As a result, the net force exerted on the diver while in the water equals -3092.7N.
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