The velocity function is v(t)=1/2 t^2+4t + 3
The acceleration function is given by a(t) = t + 4 where v(0) = 3. The acceleration function a(t) is a known function of time. The velocity function is integral of the acceleration function plus a constant of integration. The time derivative of the velocity function is acceleration, hence d/dt v(t)=a(t)
Taking indefinite integral of both sides,
∫d/dt v(t)dt=∫a(t)dt+C1
Where C1 is the constant of integration. Since
∫d/dt v(t)dt=v(t)
Hence,
v(t)=∫a(t)dt + C1
Inserting the acceleration function, a(t) = t + 4
v(t)=∫(t +4)dt + C1
v(t)=1/2 t^2+4t + C1
In order to find C1, let v = 3 when t = 0 as given
3=1/2 (0)^2+4(0) + C1
3=0 + C1
C1=3
Hence,
v(t)=1/2 t^2+4t + 3
Note: The question is incomplete. The complete question probably is: The acceleration function (in m/s-) and the initial velocity are given for a particle moving along a line a(t) = t + 4, v(0) = 3, 0 ≤ t ≤ 11 (a) Find the velocity at time t.
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Blood pressure in Argentinosaurus. (a) If this long-necked, gigantic sauropod had a head height of 21m and a heart height of 9.0m, what (hydrostatic) gauge pressure in its blood was required at the heart such that the blood pressure at the brain was 80torr (just enough to perfuse the brain with blood)? Assume the blood had a density of. (b) What was the blood pressure (in torr or mm Hg) at the feet?
The gauge pressure at the heart of the Argentinosaurus is 1000torr and its feet is 1722 torr.
(a)Heart of the Argentinosaurus has gauge pressure of
pheart = pbrain + ρgh = 80 + 1.06 × [tex]10^{3}[/tex] * 9.8 (21 - 9) = 1000torr
b) The Argentinosaurus's foot have a pressure gauge that reads
Pfeet = pbrain + ρgh = 80 + 1642 = 1722 torr
When the atmospheric pressure is above a certain level, the gauge pressure is positive; when it is below that level, it is negative. In actuality, air pressure raises the pressure in any fluid that isn't contained by a hard container. Pascal's principle is the reason why this occurs. Pg denotes gauge pressure, which is related to absolute pressure in the manner shown below: Where pa is the local atmospheric pressure, the equation is pg = p - pa. Example: Tire pressure of 32.0 psi is determined using an automobile tire gauge. There are 14.2 psi in the nearby atmosphere. Gauge pressure and atmospheric pressure are added to determine the total pressure, or absolute pressure: Absolute pressure (Pabs), gauge pressure (Pg), and atmospheric pressure (Patm) are all expressed as Pabs=Pg+Patm.
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A rocket fires a projectile at a speed of 0.95c while traveling past the Earth. An earthbound scientist measures the projectile's speed to be 0.88c. What was the rocket's speed as a fraction of c?
The speed of rocket travelling past the earth is 0.34c.
Consider the earth frame of reference as S and rocket's frame S moving along the direction.
Lorentz transformation equations for addition of relativistic velocities is
u' = u - v / 1 - (uv/c²)
Here,
u = observed speed of the projectile on earth frame of reference
u' = speed of the projectile leaving the rocket
c = speed of the light
If we rearrange the equation for v, we get
u'[1- (uv/c²)] = u - v
u' - (uu'v/c²) = u - v
v - (uu'v/c²) = u - u'
v = u-u' / [1-(uu'/c²)]
The rocket speed is given as
v = u-u' / [1-(uu'/c²)]
Substituting the values,
v = 0.90-0.95u' / [1-(0.90*o.95/c²)]
v = - 0.34c
Our assumptions contradicts that the rocket moving along the same direction of the projectile.
Therefore, the speed of rocket travelling past the earth is 0.34c.
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The speed of rocket travelling past the earth is 0.34c.
Consider the earth frame of reference as S and rocket's frame S moving along the direction.
Lorentz transformation equations for addition of relativistic velocities is
u' = u - v / 1 - (uv/c²)
Here,
u = observed speed of the projectile on earth frame of reference
u' = speed of the projectile leaving the rocket
c = speed of the light
If we rearrange the equation for v, we ge
u'[1- (uv/c²)] = u - v
u' - (uu'v/c²) = u - v
v - (uu'v/c²) = u - u'
v = u-u' / [1-(uu'/c²)]
The rocket speed is given as
v = u-u' / [1-(uu'/c²)]
Substituting the values,
v = 0.90-0.95u' / [1-(0.90*o.95/c²)]
v = - 0.34c
Our assumptions contradicts that the rocket moving along the same direction of the projectile.
Therefore, the speed of rocket travelling past the earth is 0.34c.
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put the following events in order the describe the effects of light exposure on the retina. start with rhodopsin absorbing light, and finish with ganglion cells firing action potentials.
The order of events that that describes effects of light exposure on the retina are;
Rhodopsin absorbs lightCis-retinal isomerizes to trans-retinalOpsin triggers signaling cascade in outer segment of rod cellsGlutamate release from rod cells decreasesBipolar cells detect changes in glutamate releaseGanglion cells fire action potentialsWhat is the effect of light on the retina?Light acts directly on the retina in mammals to perform two important functions; visual function via rod and cone photoreceptor cells and non-image forming tasks such as circadian rhythm synchronization to a 24 hours solar cycle, pineal melatonin suppression, and pupil light reflexes.
This process takes place first in the rhodopsin and trans-retina isomerizes from cis-retinal. Opsin initiates a signaling cascade in rod cell outer segments where rod cell glutamate release is decreased. Changes in glutamate release are detected by bipolar cells and lastly action potentials are emitted by ganglion cells.
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the field vectors point into the page. the magnetic field is then turned off. select the correct statement. incorrect the magnitude of the induced electromotive force is always the same no matter how quickly the the magnetic field is turned off. incorrect the induced electromotive force is larger in magnitude if the magnetic field is turned off more slowly. correct: the induced electromotive force is larger in magnitude if the magnetic field is turned off more quickly. incorrect the induced electromotive force is smaller in magnitude if the magnetic field is turned off more quickly.
If indeed the magnetism is removed more quickly, the magnitude of the induced electromagnet force increases. incorrect If the magnetic field is removed more quickly, the amplitude of the generated electromotive force is reduced.
How do you define magnitude?huge or highly significant: An average man would have given up due of the task's size. earth science The brilliance of a sun as seen from Earth is also measured by magnitude.
What does physical force magnitude mean?The strength of a force is expressed numerically as its magnitude. Now let us say the force equals 10 N and it is coming from the east. "towards east" indicates the force's direction, while "10" indicates its strength. In essence, magnitude is the "value" or "quantity" of any numerical value.
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How much work would it take to push two protons very slowly from a separation of 2e-10 m. (a typical atomic distance) to 3e-15 m. (a typical nuclear distance)?
If the protons are both released from rest at the closer distance, how fast are they moving when they reach their original separation?
The amount of work done to push the protons is 7.67 X 10⁻¹⁴ J. If the protons are both released from rest at the closer distance, then the speed at which they reach their original separation is 6.77 X 10⁶ m/s.
Initial distance = d = 2 X 10⁻¹⁰ m
Final distance = d' = 3 X 10⁻¹⁵ m
Mass of both protons = 1.6 X 10⁻²⁷ Kg each
Charge of both protons = q = 1.6 X 10⁻¹⁹ C each
The constant for proton energy = 1/(4πε) = 9 X 10⁹ Nm²/C²
The potential change changes when their is a change in the work done, thus, potential energy initially = U =
= U = 1/(4πε) X (q₁q₂ / d)
= U = ( 9 X 10⁹ X 1.6 X 10⁻¹⁹ X 1.6 X 10⁻¹⁹ ) / 2 X 10⁻¹⁰
= U = 11.52 X 10⁻¹⁹ J
Now, finial potential energy = U' =
= U' = 1/(4πε) X (q₁q₂ / d')
= U' = ( 9 X 10⁹ X 1.6 X 10⁻¹⁹ X 1.6 X 10⁻¹⁹ ) / 3 X 10⁻¹⁵
= U' = 7.68 X 10⁻¹⁴ J
Thus, the work done to push the two protons is the different between final potential energy and the initial potential energy = W =
= W = U' - U
= W =11.52 X 10⁻¹⁹ - 7.68 X 10⁻¹⁴
= W = 7.67 X 10⁻¹⁴ J
Now, the speed of protons while coming back to the original positions = V;
Work done is also equal to the sum of kinetic energy's, hence,
= W = KE + KE'
= W = (1/2)mv² + (1/2)mv'²
= W = 2 X (1/2)mV²
= V = √ (W / m)
= V = √ (7.67 X 10⁻¹⁴ / 1.6 X 10⁻²⁷)
= V = 6.77 X 10⁶ m/s
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as light reflected off an object reaches your eye, it passes through several structures before it reaches the retina. describe the functions of the following structures:.
Eye's cornea, are in front, bends and concentrates light rays. The pupil serves as the eyeball's entry for light, while the lens, a transparent behind pupil that may change form, aids in focusing images on the retina.
What else do you call reflecting?The verbs cogitate, deliberate, reason, conjecture, and think are some frequent synonyms for reflect. All of these phrases refer to "using one's faculties of conceptualization, judgment, or inference," but reflect denotes thoughtful reflection on a memory.
What comes when you suspect about this at all?You can enjoy each small victory if you take the time to think back on life you did well and your triumphs. You are able to see how much of your selflessness and life accomplishments you have accomplished. Without introspection, it's all too simple to lose sight of these things and concentrate only on our gaps.
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A monochromatic beam of light is sent through each of the following six optical slides.
Rank these scenarios on the basis of the angle of the first interference maximum.
Rank from largest to smallest. To rank items as equivalent, overlap them.
a.) difraction grating with 1000 lines/cm
b.)single slit slide with width .04mm
c.)single slit slide with width .01mm
d.) double slit slide with spacing .08mm
e.)diffraction grating with 500 lines/cm
f.)double slit slide with spacing .02mm
c>a>f=e>b>d is the rank from largest to smallest, which scenarios on basis of the angle of interference.
single-slit slide with width 0.01 mm> diffraction grating with 1000 lines/cm> double-slit slide with spacing 0.02 mm=diffraction grating with 500 lines/cm> single-slit slide with width 0.04 mm> double-slit slide with spacing 0.08 mm
Monochromatic lights are called single-wavelength light, where mono refers to a single, and chroma means color which is essentially electromagnetic radiation derived from photon emissions from atoms.
A sodium lamp is one example of monochromatic light. There are some applications like:
It is used in crime detection to scan specific and delicate evidence. It also helps to recognize hidden bloodstains, fingerprints, fibers, and lesions under the skin.To know more About Monochromatic beams:
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Problems 2-3 refer to the following situation. A lake has a depth of
27.5 m
. The lake is filled with water, with has a density of
1000 kg/m^3
. Since the top of the lake is open to the air, the pressure at the top of the lake is the atmospheric pressure,
P 0​ =1.0×10^5
. Problem 2: What is the pressure at the bottom of the lake? a.
1.7×10^5 Pa
b.
3.7×10^5 Pa
c.
5.7×10^5 Pa
d.
7.7×10^5 Pa
Problem 3: An underwater vehicle is at the bottom of the lake. The vehicle has a circular window of radius
0.175 m
. What is the force on this window, due to the water? a.
1.6×10^4 N
b.
3.6×10^4 N
c.
5.6×10^4 N
d.
7.6×10^4 N
A pressure at the bottom of the lake of: P = 3.7 x 10^5 Pa So the answer to problem 2 is 3.7 x 10^5 Pa the answer to problem 3 is 3.6 x 10^4 N.
To find the pressure at the bottom of the lake, you can use the formula for hydrostatic pressure: P = P0 + rho * g * h Where P is the pressure at the bottom of the lake, P0 is the atmospheric pressure at the top of the lake, rho is the density of the water, g is the acceleration due to gravity, and h is the depth of the lake. Plugging in the given values, you get: P = 1.0 x 10^5 Pa + 1000 kg/m^3 * 9.8 m/s^2 * 27.5 m This gives a pressure at the bottom of the lake of: P = 3.7 x 10^5 Pa. To find the force on the circular window, you can use the formula for the force exerted by a fluid on a surface: F = P * A Where F is the force on the window, P is the pressure at the bottom of the lake, and A is the area of the window. The area of the window can be calculated using the formula for the area of a circle: A = pi * r^2 Where A is the area of the window, pi is the mathematical constant pi (approximately 3.14), and r is the radius of the window. Plugging in the values, you get: F = 3.7 x 10^5 Pa * (pi * (0.175 m)^2) This gives a force on the window of: F = 3.6 x 10^4 N So the answer to problem 3 is b. 3.6 x 10^4 N.
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Neutron stars, such as the one at the center of the Crab Nebula, have about the same mass as our Sun, but a much smaller diameter.
If you weigh 715 N on the Earth, what would you weigh on the surface of a neutron star that has the same mass as our Sun and a diameter of 20.0 km?
Express your answer with the appropriate units.
We would weigh 9.68x1013 N on the surface of a neutron star with the same mass as our Sun and a diameter of 20.0 km if we were to weigh 715 N on Earth.
According to the information provided, a neutron star has the same mass as the Sun, making its mass (m2) = 1.99x10^30 kg.
We must first determine our mass using the formula Fg = mg.
Given force (F) = 715N
mass (m) = 715/9.8 = 72.95kg
The distance from a planet's centre to its surface, as determined by the force of gravity equation, is equal to r.
Since the issue gives us the diameter, we can utilise it to find the radius, which is given by r = d/2.
Given distance (d) = 20km
r = 20/2 = 10km = 10000m
Now, using the formula for the force of gravity, we can determine our weight at the star: F = Gm1m2/r^2
G = gravitational constant = 6.67×10-11 N* m^2/kg^2
F = (6.67×10-11)x72.95x 1.99×10^30/10^8 = 9.68x10^13N
Hence the weight on surface of neutron star = 9.68x10^13N
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Which of the following describes the independent variable?
It is called the respondent variable.
It is plotted on the vertical axis when graphed.
It refers to a quantity changed by the experimenter.
It is something that remains controlled during trials.
The one that describes the independent variable is it is something that remains controlled during trials. The correct option is D.
What is an independent variable?A variable that is independent is precisely what it sounds like. It is a stand-alone variable that is unaffected by the other variables you are attempting to assess.
On the abscissa, the independent variable is plotted (also called the x-axis or horizontal axis), It is not the respondent variable because it does not respond to changes.
Therefore, the correct option is D, It is something that remains controlled during trials.
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Suppose a 36 kg squid (not including water) at rest at the surface of the water brings in and quickly ejects 3.0 kg of water to achieve a takeoff speed of 3.5 m/s; these are typical numbers. At what speed does the squid eject the water? If we ignore lift and drag forces as the squid flies through the air, what is the maximum horizontal range that the squid can achieve before splashing down?
The speed with which the squid ejects the water is 42 m/s. If we ignore lift and drag forces, the maximum horizontal range that the squid can achieve before splashing down is about 1.25 m
From the conservation of momentum,
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
(36 kg) (3.5 m/s) - (3 kg) v = 0
(3 kg)v= (36 kg) (3.5 m/s)
v = 42 m/s
Hence, required speed is 42 m/s.
The maximum horizontal range is,
R = u ² sin 20/g
Rmax = u²sin 2 (45°)/g
= (3.5 m/s) ² sin 90° / 9.8
=1.25 m
The maximum horizontal range is 1.25 m.
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as a jet is taking off, it is accelerating down the runway with acceleration , with . you are sitting inside the jet and holding a simple pendulum consisting of a bob of mass attached to a string of length . the pendulum comes to rest in the equilibrium position where the string makes an angle with respect to the vertical. when the bob is in the equilibrium position, which of the following free-body force diagrams on the bob is correct in a reference frame fixed to the accelerating jet.
A jet plane's acceleration is a critical phase of flight that necessitates intense focus on the part of both pilots.
On the ground, things can get hectic and demand a lot of situational awareness, especially when there is little traffic separation, a runway is wet, visibility is poor, and there are heavy winds. Nevertheless, you start to relax a little and take in the beauty of flying as the engines begin to accelerate and you take off and break through the clouds. We have put up this essay with all you need to know so that you may master the takeoff phase in complete confidence.
You must commit to memory three call-outs for the acceleration and takeoff phases of your flight. You will first check your instruments at 80 knots. When you push the nose of your aircraft upward and rotate in V1, you are too quick to abort the takeoff.
This was merely a succinct justification. In order to help you mentally prepare, we will go over every important stage of a jet plane's acceleration.
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a pulley on a friction- less axle has the shape of a uniform solid disk of mass 2.50 kg and ra- dius 20.0 cm. a 1.50 kg stone is attached to a very light wire that is wrapped around the rim of the pul- ley (fig. e9.47), and the system is released from rest. (a) how far must the stone fall so that the pulley has 4.50 j of kinetic energy? (b) what percent of the total kinetic energy does the pulley have?
a)The stone fall so that the pulley has 4.50 j of kinetic energy is 0.673 m
b) Percent of the total kinetic energy does the pulley have 45.5%
Given, the mass of the pulley disk mₚ = 2.50 kg
Its radius r = 20.0 cm = 0.2 m
Its moment of inertia I = (1/2)mₚr²
I = (1/2)(2.50 kg)(0.2 m)²
I = 0.05 kgm²
Given, the kinetic energy of the pulley disk = 4.50 J
If w the angular velocity of the pulley,
(1/2)Iw² = 4.50 J
(1/2)(0.05 kgm²)w²= 4.50 J
w² = 9/0.05 rad²/s²
w² =180 rad²/s²
v² = 180(0.2)^2 m²/s²
v² = 7.2 m²/s²
Given, the mass of the stone mₛ = 1.50 kg
Its kinetic energy = (1/2)(1.50 kg)(7.2 m²/s²) = 5.4 J
Potential energy loss of the stone = (1.50 kg)(9.80 m/s²)h
(a) Therefore, from equation (1), w get
(1.50 kg)(9.80 m/s²)h = 4.5 J + 5.4 J
h = (9.9 J)/(1.50 kg)(9.80 m/s²)
h = 0.673 m
So, the. stone. mus.t fall by a distan.ce of 0.673 m.
(b) Total kinetic. energy of the. system. = 9.9 J
The kinetic energy. of the pulley = 4.50 J
The pulley’s fraction. of kinetic energy. = 4.50 J/9.9 J
= 0.455 = 45.5%
Therefore, the pulley has 45.5% of the total kinetic energy.
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in the circuit at right, the bulbs are identical, and the battery is ideal. rank the brightness of the bulbs in the ircuit at right
Brightest resistor is the one with the most current. The current via bulb C is the highest since it receives the same amount of current as the battery.
What is an example of a resistor?Digital potentiometers and rheostats are variable resistors. Electrical parts called rheostats are constructed from resistive thin wire around for a ceramic core. They were once employed to regulate the quantity of power utilized by ovens, heaters, and motors.
How do resistors function?By decreasing the voltage and obstructing the passage of electricity, the resistance absorbs the electrical energy, which is then released as heat. The heat dissipation in electronic circuits today is typically a few hundredths of a watt.
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9. A 0.25 kg steel ball experiences a net force of 1.15 N as it rolls down a ramp. What is the
acceleration of the ball?
a. 0.29 m/s²
b. 0.90 m/s²
c. 1.4 m/s²
d. 4.6 m/s²
Answer:
4.6 option d
Explanation:
from second Newton law of motion
F=ma
to find acceleration
a= F/m
a= 1.15/0.25
a = 4.6
find ds in terms of dv and approximate the change in the surface when the volume change from 1,000 m3 to 999 m3 .
Terms of dv and approximate the change in the surface when the volume change from 1,000 m3 to 999 m3 is 2.9 M2.
What is volume?Volume is a measure of the amount of three-dimensional space occupied by a solid, liquid, gas, or plasma. It is measured in cubic meters, liters, or milliliters. Volume is an important measurement when dealing with liquids and other substances since it determines the amount of material that can fit in a given container. Volume also has an effect on pressure and temperature, as the pressure and temperature of a substance increase when its volume decreases.
The change in the surface of a given volume can be found by taking the derivative of the volume in terms of the surface. The derivative of V (volume) with respect to S (surface) is S = 3√V. Therefore, the change in surface when the volume changes from 1000 m3 to 999 m3 is approximately 3√999 - 3√1000 = 2.9 m2.
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You are in your car driving on a highway at 24 m/s when you glance in the passenger side mirror (a convex mirror with radius of curvature 150 {\rm cm}) and notice a truck approaching.
If the image of the truck is approaching the vertex of the mirror at a speed of 1.5 m/s when the truck is 2.0 {\rm m} away, what is the speed of the truck relative to the highway?
The speed of the truck relative to the highway is 44m/s.
Given that the radius of curvature is [tex]$R=150 \mathrm{~cm}$[/tex]
Then the focal length is [tex]$\mathrm{f}=\mathrm{R} / 2=75 \mathrm{~cm}$[/tex]
Object distance is [tex]$\mathrm{s}=2.0 \mathrm{~m}$[/tex]
Speed of imge is [tex]$v^{\prime}=1.5 \mathrm{~m} / \mathrm{s}$[/tex]
From thin lens equation
[tex]$$\begin{aligned}1 / \mathrm{f} & =1 / \mathrm{s}+1 / \mathrm{s}^{\prime} \\\mathrm{s}^{\prime} & =\mathrm{f}^* \mathrm{~s} /(\mathrm{s}-\mathrm{f}) \\\mathrm{s}^{\prime} / \mathrm{s} & =\mathrm{f} /(\mathrm{s}-\mathrm{f})\end{aligned}$$[/tex]
Velocity of the image is [tex]$v^{\prime}=d s^{\prime} / \mathrm{dt}$[/tex]
[tex]$\mathrm{v}^{\prime} & =\left(d \mathrm{~s}^{\prime} / \mathrm{ds}\right)(\mathrm{ds} / \mathrm{dt}) $[/tex]
[tex]$ =[\mathrm{f} /(\mathrm{s}-\mathrm{f})]^2\left(\mathrm{v}^{\prime \prime}\right) $[/tex]
[tex]$ =\mathrm{f}^2 \mathrm{v} /(\mathrm{s}-\mathrm{f})^2$[/tex]
[tex]$\mathrm{v}^{\prime \prime} & =\mathrm{v}^{\prime}(\mathrm{s}-\mathrm{f})^2 / \mathrm{f}^2 $[/tex]
[tex]$= & \mathrm{v}^{\prime}(\mathrm{s}-\mathrm{f})^2 / \mathrm{f}^2$[/tex]
[tex]& =(1.5 \mathrm{~m} / \mathrm{s})(2.0 \mathrm{~m}-(-0.75))^2 /(-0.75 \mathrm{~m})^2 $[/tex]
[tex]$=20.17 \mathrm{~m} / \mathrm{s}$[/tex]
[tex]$$\text { Then we get } \quad v^{\prime \prime}=v^{\prime}(s-f)^2 / f^2$$[/tex]
Therefore the speed of the truck relative to the highway [tex]v=24+20.17=44.17 \mathrm{~m} / \mathrm{s}$ or $44 \mathrm{~m} / \mathrm{s}$[/tex].
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Listed following is a set of statements describing individual stars or characteristics of stars. Match these to the appropriate object category.a. Red Giant or Supergiant Starts.b. Main-sequence starsc. White dwarfs1. Very cool but very luminous2. Found in the upper right of the H-R diagram3. The majority of stars in our galaxy4. The Sun, for example5. A very hot and very luminous star6. not much larger in radius than Earth7. Very hot but very dim
The five fundamental features of a star are its brightness, color, surface temperature, size, and mass.
Supergiant or Red Giant Stars are located in the upper right corner of the H-R diagram and are extremely cool but bright.
The majority of the stars in our galaxy are main-sequence stars, such as the Sun, which is an extremely hot and brilliant star.
White dwarfs are tremendously hot, but they are also quite dim. Their radii are not much larger than Earth's.
The largest and hottest stars are those in the 'O' class, with temperatures over 30,000 °C. The smallest and coldest stars are those in the 'M' class, with temperatures below 3,000 °C. The stars in the sky are not all the same color when you look attentively at them.
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a load of 300 kw has a power factor of 0.65 lagging. how much reactive power is required in order to improve the power factor to unity. please indicate if the additional load is capacitive or inductive.
A 300 kw load has a trailing power factor of 0.65. The reactive power required in order to improve the power factor to unity is 346.12kVAR
Given Power of load (P) = 300KW
power factor = 0.65
We know that kVA = KW/cosФ
kVAR = kVA sinФ
sin = √1-cos^2Ф
here kVA is apparent power(S)
KW is active power(P)
kVAR is reactive power(Q)
cosФ = power factor
S = P/cosФ = 300/0.65 = 461.5kVA
sinФ = √1-(0.65)^2 = 0.75
Now Q = (461.5)(0.75) = 346.12kVAR lagging
the additional load is capacitive
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based on galactic rotation curves and cluster dynamics, we think dark matter based on galactic rotation curves and cluster dynamics, we think dark matter will have no effect on the fate of the universe. comprises over 90% of the entire mass of the universe. will doom the universe to collapse, overcoming the redshifts we now observe. is a minor component of the entire mass of the universe. is best detected from the x-rays it produces in the intergalactic medium.
Dark matter comprises of 90% of the mass of the universe which is based on galaxy rotation curves and cluster dynamics.
The Galaxy rotation curves remains the same from the center of the galaxy to the periphery which means that there must be non-luminous matter that is spread in our galaxy. This matter is called dark matter.
The rotation of stars and gas in distant galaxies cannot be measure directly. Only the component along the line of sight is known from precise spectroscopic measurements.
If the galaxy is viewed almost face on, then it would mostly rotate within the plane of the sky. This could mislead observers into thinking that the galaxy is actually rotating very slowly, which would require them to overestimate the inclination between disk and sky planes. This inclination was estimated from how elliptical the galaxy appears.
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Jane, looking for Tarzan, is running at top speed (4.5 m/s) and grabs a vine hanging vertically from a tall tree in the jungle. How high can she swing upward?
Does the length of the vine affect your answer?
Jane could swing 1.03316 m high and the length of the vine does not affect the answer .
In the question ,
it is given that ,
the top speed of Jane is = 4.5 m/s .
she grabs a vine that is hanging vertically from a tall tree in the jungle .
The kinetic energy of running Jane can be converted into gravitational potential energy, and
the highest point is reached when all the Kinetic Energy has been changed to Potential energy .
we know , KE = 1/2mv²
PE = mgh
So Equating KE = PE
and solving for h:
we get , h = v²/2g
So , h = 4.5²/(2*9.8)
= 1.03316 m
also we can conclude that , the length of the vine does not affect the answer .
Therefore , the Jane could swing 1.03316 m high .
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The spring in the figure (Figure 1)/ (a) is compressed by length delta x . It launches the block across a frictionless surface with speed v0. The two springs in the figure (Figure 2) (b) are identical to the spring of the figure (a). They are compressed by the same length delta x and used to launch the same block. What is the block's speed now?
The speed from two springs is √2 times the speed with one spring.
The rate of change in position of an object in any course. Speed is measured because the ratio of distance to the time wherein the distance became included. Speed is a scalar amount because it has handiest route and no significance.
A quick-moving object has a high speed and covers a notably big distance in a given amount of time, whilst a sluggish-shifting item covers a relatively small amount of distance in the same amount of time.
The primary unit or the S.I. unit of speed is m/s or ms?¹.
Calculation :
The energy stored in the spring is 0.5*k*∆x²; this must equal the kinetic energy of the released block. 0.5*m*v0²:
0.5*m*v0² = 0.5*k*∆x²
v0 = ∆x*√[k/m]
Two springs will store twice the energy, so the stored energy in the two springs is k*∆x²
0.5*k*∆x² = k*∆x²
v0 = ∆x*√[2*k/m]
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How is heat energy transferred from the ground to the atmosphere
Answer:
Heat energy is transferred from the ground to the atmosphere through the process of convection. Convection occurs when warm air rises, carrying heat energy with it, and cooler air moves in to take its place. This process continues until the air reaches the upper atmosphere, where it cools and sinks, releasing its heat energy into the atmosphere.
Explanation:
Answer:
Through sun's radiation
Explanation:
The sun's radiation strikes the ground, thus warming the rocks. As the rock's temperature rises due to conduction, heat energy is released into the atmosphere, forming a bubble of air which is warmer than the surrounding air. This bubble of air rises into the atmosphere.
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a block of mass 3 kg slides down an inclined plane at an angle of p with a massless tether attached to a pulley with mass 1 kg and radius 0.5 m at the top of the incline (see the following figure). the pulley can be approximated as a disk. the coefficient of kinetic friction on the plane is 0.4. what is the acceleration of the block?
The acceleration of the block is 4.16 m/s^2 when the block slides down on inclined plane at an angle 45 degrees.
Acceleration is a dynamic characteristic of an object. Acceleration (a) can be obtained via inertial force (F) on a mass (m) subjected to acceleration (a) of the moving object:
F = - m a
The inertial force can be measured either through strain (if deformation is min) or through the deformation of elastic element. Equal increments of speed gained in equal time intervals,Distance increases in each time interval.The unit of acceleration in the System International: m/s2.
Acceleration shows how fast an object changes its velocity. If an object is moving with constant velocity, acceleration is equal zero: Positive and Negative Acceleration.Positive acceleration: velocity increases with the time and Negative acceleration: velocity decreases with the time.
Given,
m=3kg
angle = 45 degrees
Uk= 0.2
by the equation ,
mgsinФ-f-T=ma
3* 9.81*sin45-UkN-T=3a----(1)
T=a----(2)
Now,N= mgcos45
= 3*9.81/sqrt2
solve eqn (1) and put value in (2)
a=4.16 m /s^2
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the total potential energy of a system of multiple springs is defined to be the sum of the potential energies stored in each of the springs. The blacks all have the same mass nctonles the instant shown, each block is ele leoxk on a horizontal, rhecks n dea th spring constant k. At Case A the four block- m, and all of the released from rest a a ro the right of its equilibrium position nt indicated by the dashed line). me that each spring is at its equilibrium Case B a case B, assume length when the block is at its equilibrium tank the cases according to magnitude of the net Ran or on the block at the instant shown, from largest to smallest. (Hint: In case C, how far was the point was displaced a distance A?) Explain Case C Case D b Use your answers above to rank the cases according to the time it takes the block n reaun its equilibriam position
Sort the scenarios based on how long it takes the block n to reach equilibrium T[tex]_{c}[/tex]>T[tex]_{A}[/tex]>T[tex]_{B}[/tex]=T[tex]_{D}[/tex].
F[tex]_{net}[/tex]=kx₁=kx₂
x₁+x₂=A
[tex]\frac{F}{k}[/tex]+[tex]\frac{F}{k}[/tex]=A
A=[tex]\frac{2F}{k}[/tex]
F[tex]_{net}[/tex]=[tex]\frac{kA}{2}[/tex]
point of connecting spring displaced by A/2
Ranking ⇒[(case-B)=(case-D)>(case-A)>(case-C)]
Part-(b)
Now, time period T=2π[tex]\sqrt{\frac{m}{k_{eq} } }[/tex]
case-A [tex]k_{q}[/tex]=k,
case-B [tex]k_{eq}[/tex]=2k
case-C [tex]k_{eq}[/tex]=k/2
case-D [tex]k_{eq}[/tex]=2k
so,T[tex]_{c}[/tex]>T[tex]_{A}[/tex]>T[tex]_{B}[/tex]=T[tex]_{D}[/tex]
A process is in equilibrium when the observable properties, such as color, temperature, pressure, concentration, etc., do not change.
Equilibrium, which literally means "balance," denotes that the reactants and products involved in a chemical process are in balance with one another. The equilibrium condition can also be seen in some physical processes, such as the melting point of ice at 0 degrees Celsius, when both ice and water are present.
The equilibrium is known as a physical equilibrium in the case of physical processes like the melting of solids, the dissolution of salt in water, etc., whereas the equilibrium connected to chemical reactions is known as a chemical equilibrium.
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The proper time between two events is measured by clocks at rest in a reference frame in which the two events: A. occur at the same time B. occur at the same coordinates C. are separated by the distance a light signal can travel during the time interval D. occur in Boston E. satisfy none of the above
The proper time between two events is measured by clocks at rest in a reference frame in which the two events occur at the same coordinates. (Option B)
In physics and astronomy, a frame of reference or reference frame refer to an abstract coordinate system whose origin, orientation, and scale are specified by a set of reference points which are geometric points whose position is identified both mathematically (with numerical coordinate values) and physically (signaled by conventional markers). Hence, the proper time between two events is measured by clocks at rest in a reference frame in which the two events occur at the same coordinates.
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Q1: A pupil fires an elastic band gun. Just before it is released the band is at its most stretched point. If the band is extended by 0.36m and the band is fired with 412J of energy, what is the spring constant of the band?
The spring constant of the given band is equal to 6.36 × 10³ N/m.
What is Hooke's law?Hooke's law can be demonstrated as a law that states that the force (F) required to extend or compress a spring by displacement linearly w.r.t. that distance along a straight line.
The spring force can be represented in the form of mathematical equation:
F = -kx,
where k is a spring constant and x is the deformation of the spring. The negative sign shows that the spring returns to its original position.
The energy stored in the spring when it is extended is given by:
E = (1/2)kx²
Given, the energy stored in the band when it is extended, E = 412 J
The distance by which the band is extended, x = 0.36 m
412 = (1/2)×k (0.36)²
k = 6.36 × 10³ N/m
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Part A Which of the following statements are true? Check all that apply. View Available Hint(s) Mechanical energy is conserved because no dissipative forces perform work on the ball. The forces of gravity and the spring have potential energies associated with them. No conservative forces act in this problem after the ball is released from the spring gun.
The statement that is true is Mechanical energy is conserved because no dissipative forces perform work on the ball. The correct option is A.
What is mechanical energy?Mechanical energy, also known as kinetic energy or potential energy, is the energy that an object possesses when it is in motion or the energy that an object stores due to its location.
Renewable energy is also fueled by mechanical energy. In order to efficiently produce electricity or convert energy, many sources of renewable energy depend on mechanical energy.
Therefore, the correct option is A, Mechanical energy is conserved because no dissipative forces perform work on the ball.
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for lunch you and your friends decide to stop at the nearest deli and have a sandwich made fresh for you with 0.300 kg of italian ham. the slices of ham are weighed on a plate of mass 0.400 kg placed atop a vertical spring of negligible mass and force constant of 200 n/m . the slices of ham are dropped on the plate all at the same time from a height of 0.250 m . they make a totally inelastic collision with the plate and set the scale into vertical simple harmonic motion (shm). you may assume that the collision time is extremely small. Express your answer numerically in meters and take free-fall acceleration to be g= 9.80m/s^2
What is the period of oscillation T of the scale?
Express your answer numerically in seconds.
The amplitude of oscillation of the scale is 0.0581 m after the slices of ham land on the plate.
The amplitude of oscillation of a body performing oscillation is the maximum distance traveled from its mean position.
The peaks in the sinusoidal graph are the amplitude of oscillation which describes, how much distance the body oscillates from the mean position on either side. Within any oscillation system, the magnitude of variation in the oscillation variable of the body with each oscillation is termed oscillation amplitude.
The frequency of the pendulum s oscillations does not depend on amplitude or mass. It depends only upon the acceleration due to gravity and the length of the pendulum.
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eudora ran from her home to her secret laboratory at an average speed of 12\text{ km/h}12 km/h12, start text, space, k, m, slash, h, end text. she then took one of her jetpacks and flew to her school at an average speed of 76\text{ km/h}76 km/h76, start text, space, k, m, slash, h, end text. eudora traveled a total distance of 120120120 kilometers, and the entire trip took 222 hours.
Eudora used her jetpack for around 1.5 hours of flying and 0.5 hours of jogging.
Given: Eudora moved at an average pace of 12 km/h as she sprinted from her house to her underground laboratory. She then hopped into one of her jetpacks and soared 76 km/h to her school. Eudora covered 120 kilometres in all, and the journey took her two hours.
To determine: How much time Eudora spent running and how much time she spent using her jetpack to fly
Solution:
If she utilised the jet pack for x seconds, then
76x + 12 (2-x) = 120
76x + 24 – 12x = 120
x = 96/64
x= 1.5
She spent 0.5 hours running, thus when we simplify, x = 1.5 hours.
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