Generally speaking, the object distance indicates that the light rays emanating from the object are parallel to one another, resulting in f=-4.221.
What kind of thing is a light ray like?A ray is defined as a small, usually straight-traveling beam of light. The laser or laser pointer's light beam is an illustration of a ray. According to the ray model of light, a ray moves in a straight line until it encounters an object, such as a mirror or the boundary between two materials.
image distance is v = 4.7 + (2.1 * 10-2) = -4.721 m the negative
means image is formed behind the lens
Generally the object distance is u = ∞ this mean the light ray coming from the object are parallel to each other.
So from lens equation
=-고=수
=> f = -4.721 m
What is a light ray, exactly?As an electromagnetic wave, light travels in straight lines along narrow beams of light, which are referred to as rays. Despite the fact that reflection or refraction can alter its direction, light always moves in a straight line.
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what theoretical device would generate the maximum possible amount of work from a given amount of heat?
Answer:
An ideal "Carnot" engine
E = (Q2 - Q1) / Q2 or 1 - Q1 / Q2
Q1 (heat wasted) would have to be zero for 100% efficiency
a train is moving at a speed of 65 mph. the ticket collector is walking 2 mph toward the front of the train. how fast, in mph is the ticket collector moving from the point of view of an observer on the side of the tracks?
The ticket collector's speed is the sum of the train's speed (65 mph) and their walking speed (2 mph).
What is speed?
The speed of an object, also known as v in kinematics, is a scalar quantity that refers to the size of the change in that object's position over time or the size of the change in that object's position per unit of time. An object's average speed over a period of time is calculated by dividing its distance travelled by length of the interval This same instantaneous speed is indeed the maximum possible speed as the interval's duration gets closer to zero. Velocity and speed are different concepts. Distance divided by the time is the dimension of speed.
From the point of view of an observer on the side of the tracks, the ticket collector is moving at a speed of 67 mph (65 mph + 2 mph). This is because the observer is stationary relative to the ground, and the ticket collector is moving relative to the ground. Therefore, the ticket collector's speed is the sum of the train's speed (65 mph) and their walking speed (2 mph).
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A luge and its rider, with a total mass of 85 kg, emerge from a downhill track on to a horizontal straight track with an initial speed of 37 m/s. If a force slows them to a stop at a constant rate of 2.0 m/s 2
, (a) what magnitude F is required for the force, (b) what distanced do they travel while slowing, and (c) what work W is done on them by the force? What are (d) F, (e) d, and (f) W if they, instead,slow at 4.0 m/s 2
?
Force required is: -170N for the distance of 342.25m.
a) F=ma
F= - 85×2.0 = - 170
b) using energy
5×85×37²=170×d
d = 342.25 m
c) The work done would be given by
W= F×d
W =(−1.7×10²N)×(3.4×10²)
W=−5.8 × [tex]10^{4}[/tex] J
d) The net force on the mass would be
F = ma
F = -340 NF
-ve sign indicates that the force acts opposite to the direction of motion.
e) Using the kinematic equation
v²= u² + 2ad
d= 1.7 × 10² m
f) The work done would be given by
W= F×d
W= -5.8 × [tex]10^{4}[/tex] J
-ve sign indicates that the energy of the rider decreases by the force
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a car speeds up from 3 m/s to 23 m/s. if the car has a mass of 749 kg,what is the change in the car’s momentum?
Answer:
f
Explanation:
Two blocks, each of mass m=3.50kg, are hung from the ceiling of an elevator as in above figure. (a) If the elevator moves with an upward acceleration aof magnitude 1.60m/s 2, find the tensions T 1and T 2in the upper and lower strings. (b) If the strings can withstand a maximum tension of 85.0N, what maximum acceleration can the elevator have before a string breaks.
The tension in the upper and lower string is 79.8 N and 39.9 N respectively and the maximum acceleration of the elevator at tension of 85 N is 2.34 m/s².
(a) Mass of blocks = m = 3.5 Kg
Acceleration of the elevator = a = 1.6 m/s²
Gravitational force experienced by both strings = G
= m X g
= 3.5 X 9.8
= 34.3 N
For the lower block, apply Newton's Second Law of Motion,
Net force on the lower block =
= F = T₂ - (m X g)
= (m X a) = T₂ - (m X g)
= T₂ = (m X a) + (m X g)
= T₂ = m X (a + g)
= T₂ = 3.5 X (1.6 + 9.8)
= T₂ = 39.9 N
For the upper block, apply Newton's Second Law of Motion,
Net force on the Upper block =
= F = T₁ - T₂ - (m X g)
= (m X a) = T₁ - T₂ - (m X g)
= T₁ = T₂ + (m X g) + (m X a)
= T₁ = 39.9 + 3.50 X (9.8 + 1.6)
= T₁ = 79.8 N
(b) Now we know that T₁ > T₂, thus the upper string will break before the lower string. So, acceleration will increase when the upper string breaks.
Tension given = T₁ = 85 N
Acceleration = a =
= T₁ = T₂ + (m X g) + (m X a)
But, T₂ = m X (a + g)
Thus,
= T₁ = m X (a + g) + (m X g) + (m X a)
= T₁ = 2 X (m X a) + 2 X (m X g)
= a = (T₁ - ( 2 X (m X g))) / (2 X m)
= a = (85 - [ 2 X ( 3.5 X 9.8)] ) / (2 X 3.5)
= a = 2.34 m/s²
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a 50.0-kg skater is traveling due east at a speed of 3.00 m/s. a 70.0-kg skater is moving due south at a speed of 7.00 m/s. they collide and hold on to each other after the collision, managing to move off at an angle θ south of east, with a speed of vf. find (a)the angle θ and (b)the speed vf, assuming that friction can be ignored.
a 50.0-kg skater is traveling due east at a speed of 3.00 m/s. a 70.0-kg skater is moving due south at a speed of 7.00 m/s. they collide and hold on to each other after the collision, managing to move off at an angle θ south of east, with a speed of vf. find
(a)the angle θ and
(b)the speed vf, assuming that friction can be ignored. 4.28 m/s
I used tan theta=(opposite/adjacent) but I got 66.8 degrees as my answer with 7 as the opposite and 3 as the adjacent, whereas my answer booklet says 73.0 degrees. I thought velocities could be treated as vectors.
someone who skates. same as skateboarderSee skateboarder. British informal a young man or woman who usually wears saggy garments and spends lots of time skateboarding.
travel is the motion of human beings among distant geographical places. journey can be performed by using foot, bicycle, vehicle, educate, boat, bus, airplane, ship or other approach, with or without baggage, and can be one way or spherical ride.
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the temperature of an object is 172°c. what is the peak wavelength (in µm) of the radiation emitted by the object at this temperature?
Peak wavelength of the object is 6.49 µm.
Peak wavelength is the wavelength at which the line is brightest.
At optical wavelengths, a spectrograph can measure the amount of light emitted by stars.The wavelength of the peak emission depends on the temperature of the object emitting the radiation.Mathematically, T = 2.89 * [tex]10^{-3}[/tex] / λmaxA higher temperature causes the wavelength of the peak emission to be at a shorter wavelength. As the temperature increases, the amount of energy emitted (radiation) increases, while the wavelength of the peak emission decreases.Temperature of the object = 172°c
Temperature in kelvin = 172 + 273 = 445 K
λmax = 2.89 * [tex]10^{-3}[/tex] / T
λmax =2.89 * [tex]10^{-3}[/tex] / 445
λmax = 6.49 * [tex]10^{-6}[/tex] m
λmax = 6.49 µm
The peak wavelength of the radiation emitted by the object at temperature 172°c is 6.49 µm.
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suppose you have a diffraction grating which has 300. lines/mm and you shine light with a wavelength of 589 nm through it. what is the angle at which you will observe the second order (m
The answer indicates that the range about which you will see the second order (m=2) brilliant fringe is 17.76°.
What distinguishes a diffraction grating from a grating?Diffraction gratings could really separate kaleidoscopic light in with its constituent wavelengths, so even though transmission vertical slats are an a kind of interferometer that includes diffraction of light at various angles to produce a diffraction pattern. This is a main distinction between the two types of gratings.
Briefing:As we know that,
300 lines/mm = 1/d
d = 0.00333E-3 m
now use
m λ = d sin θ
θ = arc sin( 2*508E-9/0.00333E-3) = 17.76°
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The complete question is-
Suppose you have a diffraction grating which has 300. lines/mm and you shine light with a wavelength of 589 nm through it. What is the angle at which you will observe the second order (m=2) bright fringe?
a 25.0-mh inductor, a 2.00-μf capacitor, and a certain resistor are connected in series across an ac voltage source at 1000 hz. if the impedance of this circuit is 200 ω, what is the resistance of the resistor?
Resistor 184Ω has a resistance of.
Explanation of voltageThe "pressure" that drives electricity is known as voltage. Higher voltages cause more electricity to flow to an electronic equipment. The voltage is measured in units called volts (V), and it is symbolized by this unit.
What exactly are voltage and current?The difference in electric potential between two places is what is referred to as voltage, in other words. Simple electric charge flow rate is known as current. The current, put simply, is the rate at which electrical charge moves across a circuit at a specific location. Volts is the voltage measurement unit used in the SI (V).
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An electromagnetic wave transfers energy as it travels. During this process, what is the relationship between the magnetic and electric fields along its path?.
An electromagnetic wave transfers energy as it travels, then electric and magnetic fields in an EM wave are perpendicular to each other and also perpendicular to the direction of wave propagation.
What is electromagnetic wave?Waves that move through space and carry electromagnetic radiant energy is termed the electromagnetic waves. They include radio waves and microwaves and others.
During the transfer of energy, they are the sinusoidal movement that are perpendicular to each other in the direction of wave motion. They also show synchronized oscillations.
A changing magnetic field induces changing electric field and vice-versa as the two are linked. Changing fields form electromagnetic waves.
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a thin hubcap is modeled by the part of the sphere that lies above the plane , and is made of a material of constant density . what is the moment of inertia of when it is rotated around the -axis?
The moment of inertia of when it is rotated around the -axis [tex]\frac{10\pi }{3}[/tex].
Solution:
= [tex](\sqrt{2\pi _{d6} } ) (\sqrt{3} \frac{r^{3} dr}{4-r^{2} }[/tex]
= [tex]2\pi *\frac{5}{3}[/tex]
= [tex]\frac{10\pi }{3}[/tex]
Consider a line that passes through the center of the ring and is perpendicular to the plane of the ring. Let R be the radius of the ring and M be its mass. All elements are at the same distance from the axis of rotation. The moment of inertia formula is the sum of the mass products of each particle multiplied by the square of the distance from the axis of rotation.
Moments of inertia oppose the rotational motion, so they are called moments of inertia rather than moments of force. A moment of inertia is defined with respect to a particular axis of rotation. The moment of inertia of a mass with respect to an axis is defined as the square of the mass times the distance from the axis.
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a diode laser emits at a wavelength of 987 nm. (a) in what portion of the electromagnetic spectrum is this radiation found? (b) all of its output energy is absorbed in a detector that measures a total energy of 0.52 j over a period of 32 s. how many photons per second are being emitted by the laser?
Answer: A
Explanation:
I took the test
A student set up a test tube containing sodium bicarbonate and topped it with a volumeter, but forgot to add the Elodea plant! Which of the statements below gives the result that the student would be likely to observe?
A. The level of liquid in the volumeter would rise due to diffusion.
B. The level of liquid in the volumeter would remain constant since gas is being produced and used at the same rate.
C. The level of the liquid in the volumeter would remain constant since gas is neither being produced nor being used.
D. The level of liquid in the volumeter would fall since there is less mass in the test tube.
E. The level of liquid in the volumeter would fall since atmospheric pressure is greater than the pressure within the test tube.
The result that the student would be likely to observe when A student set up a test tube containing sodium bicarbonate and topped it with a volumeter, but forgot to add the Elodea plant is he level of the liquid in the volumeter would remain constant since gas is neither being produced nor being used. the correct answer is c.
A volumetric meter can be described as any instrument used to measure the volume of solids, liquids, or gases.
Sodium bicarbonate dissolves in water to form carbonic acid and sodium hydroxide. This carbonic acid is further broken down into water and carbon dioxide.
The carbon dioxide produced can be used by Elodea plants for photosynthesis, a process that uses carbon dioxide to produce oxygen and energy.
However, in this case he did not add the Elodea plant, so no sodium bicarbonate was consumed or produced, and the volumetric level remained constant.
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The measure of an object's mass and velocity is called __________. A. Gravityb. Accelerationc. Inertiad. Momentum.
the answer is momentum.
a long straight conductor has a circular cross section of radius r and carries a current i. inside the conductor, there is a cylindrical hole of radius a whose axis is parallel to the axis of the conductor and at a distance b from it.
When current is straight, it means the current is passing through a straight conductor, the magnetic field produced due to current through a straight conductor is in the form of concentric circle and are in a plane perpendicular to the plane of linear conductor. It means the magnetic field is circular.
What is straight line conductor?a straight conductor is a wire having magnetic field lines centre on it.
When a current in a circular loop is?Electric current in a circular loop creates a magnetic field which is more concentrated in the center of the loop than outside the loop. Stacking multiple loops concentrates the field even more into what is called a solenoid.
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the heaviest flying bird is the trumpeter swan which weighs in at 38 pounds. what is its weight in newtons
The heaviest flying bird is the trumpeter swan which weighs in at 38 pounds than its weight in newtons is = 169.1N
Given:
Flying bird Trumpeter swan weighs in pound = 38 pound
We have that each pound has 4.45 newtons
⇒ 38 × 4.45 = 169.1
What's the distinction between pounds and newtons?
Pound force is defined as the gravitational pull of one avoirdupois pound of mass on the surface of the earth. 1 lbf is equivalent to 4.4482216152605 Newton [N], the corresponding metric unit.
Is a pound of mass or force?
The fact that the Imperial (or U.S. Customary) system of measuring uses the same unit, the pound, to measure both mass and force, is one of the biggest sources of misunderstanding in this system. We refer to one sort of pound as the pound-mass (lbm) and the other as the pound-force to distinguish between the two (lbf).
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A rocket launched vertically rises with a constant speed for 60 s to a height of 10000 m. If the mass of the rocket is 1000 kg (and assume mass is constant), what is the power of the engine? (use g
The power of the rocket has a mass of 1000 kg is 16,33,333.33 Watt
The mass of the rocket = 1000 kg
The rocket travels at a constant speed for 60 s
The displacement of the rocket = 10000 m
The formula to find the power of the rocket engine is
P = F x v
where F is the force and
v is the velocity
Thus P = (m x g x d)/t
where m is the mass of the rocket
g is the acceleration due to gravity
d is the displacement
t is the time taken
Let us substitute the known values in the above equation, we get
P = ( 1000 x 9.8 x 10000 ) / 60
= 98000000 / 60
= 1633333.33
Therefore, the power of the rocket is 16,33,333.33 W
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what can the radial velocity method determine about an exoplanet that the transit detection method cannot?
A transiting exoplanet in relation to the star that it is orbiting. The photometric approach can figure out a planet's radius whereas the radial velocity technique can tell you how much mass a planet has.
How can you find extrasolar planets using the radial velocity method?Utilizing the Doppler changes in the wavelength of the planet's star, the radial velocity approach finds extrasolar planets. A star would show a bluish change as it approached the earth. The radial velocity technique detects the redshift of the spectrum of a star that is travelling away from Earth.
Why is it that low mass stars benefit from the radial velocity method?Because of the fact that planets' gravitational pull on low mass stars is stronger and also because these stars often spin slower rate.
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The radial velocity method can determine the mass of an exoplanet, while the transit detection method cannot.
The radial velocity method, also known as the Doppler spectroscopy method, measures the slight shifts in the wavelength of light emitted by a star due to the gravitational tug of an orbiting exoplanet. This method allows scientists to determine the mass of the exoplanet. When an exoplanet orbits its host star, it induces a small wobble in the star's motion. By measuring these periodic changes in the star's radial velocity (motion along the line of sight), scientists can infer the mass of the exoplanet.
On the other hand, the transit detection method involves observing the periodic dimming of a star's brightness as an exoplanet passes in front of it, blocking a fraction of the star's light. This method provides information about the exoplanet's size, orbital period, and distance from its host star. However, it cannot directly determine the exoplanet's mass.
By combining the radial velocity method with the transit detection method, scientists can gather more comprehensive information about exoplanets. The combination of these two techniques enables the determination of an exoplanet's density, which provides insights into its composition and potential characteristics such as whether it is rocky or gaseous.
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a 500 kg motorcycle accelerates from rest to 25 m/s over a time interval of 5.5 s. find the force exerted on the motorcycle by the road due to friction. group of answer choices 2273 n 1800 n 1500 n 2500 n
The force exerted on the motorcycle by the road due to friction is 2273n.
Solution:
m = 500 kg
v = 25 m/s
u = 0 m/s
t = 5.5 s
F = 500(25-0)/5.5
F = 2272.72 N
Friction offsets the weight to keep the motorcycle moving on the loop at a constant speed. Both weights and normals point down towards the center of the loop. The net force is the centripetal force. Dry friction always opposes sliding between surfaces and can react or act on bodies in motion. This motorcycle creates dry friction between the tires and the road surface.
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As a result of the experiment scientists did with mexican tetras, it seems likely that their first hypothesis about blindness in the tetras is right. Explain how the result of the experiment supports their first hypothesis.
The first hypothesis put out by the researchers holds that the fish's blindness indirectly confers some form of evolutionary advantage.
Why can't the Mexican tetra see?
The loss of eyes is largely caused by cellular deterioration in the eye lens, according to experiments . Theoretically, the emergence of these eyeless fish was caused by this process in combination with natural selection over many generations.
Regressive evolution can be shown in cave fishes. This kind of evolution involves the loss of a property within a species. That characteristic is vision in cave fishes.
In conclusion, a finding supporting the theory that "blindness affords the fish some evolutionary advantage, although not directly" may be a greater fitness in fish relatives.
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while cruising at 190 knots, you wish to establish a climb at 160 knots. when entering the climb (full panel), it would be proper to make the initial pitch change by increasing back elevator pressure until the group of answer choices airspeed indication reaches 160 knots. attitude indicator, airspeed, and vertical speed indicate a climb. attitude indicator shows the approximate pitch attitude appropriate for the 160-knot climb.
The correct answer is option D.
The attitude indicator shows the approximate pitch attitude for the 160-knot climb.
What is Weather station model?
Weather station model is basically the weather forecaster which tells about the weather conditions such speed of the wind, temperature of the weather, atmospheric pressure, sea levels change and the change in the weather since three years.
Therefore, knots established, can change the pressure until the attitude indicator shows the approximate pitch attitude appropriate for the 160-knot climb.
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Two trains emit 516-Hz whistles. One train is stationary. The conductor on the stationary train hears a 3.5-Hz beat frequency when the other train approaches. What is the speed of the moving train? b = beat f'_b = 3.5 Hz f = 516 Hz
The speed of the moving train is 2.31 m/s
What is called speed?
Speed is described as. the rate at which an object's position changes in any direction. Speed is defined as the distance traveled divided by the travel time. Speed is a scalar quantity because it only has a direction and no magnitude.
Speed is calculated as follows: speed = distance/time. Knowing the units for distance and time is necessary to calculate the units for speed.
According to the given information:
[tex]f=\frac{v}{s} *f_{0}[/tex]
s = speed in air,
v is the speed of the train,
f₀ is the frequency of the siren,
f₀ = 516 Hzs = 340.29 m/s
f = 3.5 Hz
v = (3.5 / 516) × 340.29 = 2.31 m/s.
So, the speed of the moving train is 2.31 m/s
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. A rock is thrown vertically upwards at 67 km/h. Find the height at which the rock is
going 23 km/h [down]. (DON'T FORGET UNITS CONVERSION)
The height at which the rock is going 23 km/h downwards be 15.59 m.
What is law of conservation of energy?Energy cannot be created or destroyed, according to the rule of conservation of energy. However, it is capable of change from one form to another. An isolated system's total energy is constant regardless of the types of energy present. The law of energy conservation is adhered to by all energy forms.
The law of conservation of energy essentially says that: The total energy of the system is conserved in a closed system, also known as an isolated system.
Given that: A rock is thrown vertically upwards at 67 km/h = 18.6111 m/s.
We have to find its height, when downwards velocity is 23 km/h = 6.389 m/s.
Let the mass of the rock be m and using law of conservation of energy:
1/2 m (18.6111)² = mgh + 1/2m(6.389)²
⇒ h = (18.611² - 6.389²)/(2×9.8) m = 15.59 m.
Hence, the height at which the rock is going 23 km/h downwards be 15.59 m.
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calculate the charge on the maximum capacitor if a battery of potential difference 1.5 volts is placed across the plates.
If a battery with a potential difference of 1.5 volts is placed across the plates, the maximum capacitor will have a charge of 36 V.
What possible variations are there in a 1.5 volt battery?1 V is, by definition, a potential energy differential between two places equal to one joule for every coulomb of charge. Your query is resolved by that. Between the sites where that potential difference is measured, 1.5V denotes a potential energy differential of 1.5 joules per coulomb.
How do you determine the difference in potential energy?ΔV=VB−VA=ΔPEq. By dividing the potential energy of a charge q that has been transported from point A to point B by the charge, we may define the potential difference between points A and B as VBVA. The joules per coulomb, sometimes known as volts (V) in honor of Alessandro Volta, are the units of potential difference.
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was newton a realist or anti-realist?
Answer: Newton was a realist
Explanation: Newton held a realist reading of scientific theory as based upon inference from facts and observation, and his gravitational theory (or NGT) as deduced from observed phenomena and Kepler's laws.
what is the kinetic energy of the object on the spring when the spring is compressed 3.2 cm from its equilibrium position? express your answer in joules using three significant figures.
The kinetic energy K of the toy when the spring is compressed 3.2 cm from its equilibrium position if the maximum velocity achieved by the toy is 3.2 m/s is 0.19 J
KE = 1 / 2 m ( ω √ ( A² - x² ) ²
KE = Kinetic energy
m = Mass
A = Amplitude
x = Displacement of spring
ω = Angular velocity
ω = v / A
m = 50 g = 0.05 kg
v = 3.2 m / s
A = 6 cm = 0.06 m
x = 3.2 cm = 0.032 m
KE = 1 / 2 m ( v / A √ ( A² - x² )²
KE = 1 / 2 * 0.05 ( 3.2 / 0.06 √ ( 0.06² - 0.032² )²
KE = 0.025 * ( 53.33 * 0.051 )²
KE = 0.025 * 7.39
KE = 0.19 J
Therefore, the kinetic energy is 0.19 J
The given question is incomplete. The complete question is:
A child's toy consists of a spherical object of mass 50 g attached to a spring. One end of the spring is fixed to the side of the baby's crib so that when the baby pulls on the toy and lets go, the object oscillates horizontally with a simple harmonic motion. The amplitude of the oscillation is 6 cm and the maximum velocity achieved by the toy is 3.2 m/s . What is the kinetic energy K of the toy when the spring is compressed 3.2 cm from its equilibrium position?
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monochromatic light of wavelength 694 nm is incident on two parallel slits. what is the distance y to the first maximum on a screen beyond the slits? answer in units of m.
The distance to the first maximum on a screen beyond the slits is 0.009512 m.
It is given that,
The wavelength of the monochromatic light = 694 nm
It is given that, monochromatic light is incident on two parallel slits.
We have to determine the value of the distance y to the first maximum on a screen beyond the slits
As we know,
The distance to the first maxima is given as,
[tex]\mathrm{y} & =\frac{\lambda \mathrm{D}}{\mathrm{d}} \\[/tex], y = distance to first maxima.
λ= wavelength of light
d = distance between slits
D = distance between slits and screen
From above given equation,
The value of distance y to the first maxima will be:
[tex]& =\frac{694 \times 10^{-9} \times 3.18}{0.232 \times 10^{-3}} \\\\ =0.009512 \mathrm{~m}[/tex]
Hence the distance to the first maxima is 0.009512 m
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The missing diagram is attached:
how does the image distance (the distance from the lens to the focused image) change with the object distance (the distance from psy to the lens?)
The image distance (the distance from the lens to the focused image) change with the object distance (the distance from object to the lens) due to the lens formula.
Lens formula is defined as the relationship between object distance (u), image-distance (v) and the focal length (f). Following is the mathematical representation of lens formula:
Lens Formula : 1/f = 1/v - 1/u
Where f = focal length
v = image distance
u = object distance
The lens is a transparent material which is bound by two surfaces. It has a principal axis, principal focus, centre of curvature of lens, aperture and optical centre.The images obtained from these lenses can be either a real image or a virtual image.To know more about lens visit:
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a runner moving at a speed of 8.8 m/s rounds a bend with a radius of 25 m. what is the centripetal acceleration of the runner, and what agent exerts force on the runner?
The force on the runner is equal to the mass of the runner multiplied by the acceleration due to gravity, which is the force of gravity acting on the runner.
What is centripetal force?
A force that causes a body to follow a curved path is known as a centripetal force. It always moves in a direction that is the opposite of the body's motion and in the direction of the instantaneous centre of curvature of the path. It is "a force through which bodies are attracted or impelled, or in any other way tend, toward that point in relation to a centre," according to Isaac Newton. Gravity is the centripetal force that drives astronomical orbits according to Newtonian mechanics. A common illustration of centripetal force is when a body moves uniformly fast in a circular motion. The centripetal force is applied towards the center of the circle path both along the radius and at sharp angles to the motion. Dutch physicist Christiaan Huygens developed the mathematical description in 1659.
The centripetal acceleration of the runner can be calculated using the formula a = v²/r, where a is the centripetal acceleration, v is the speed of the runner, and r is the radius of the bend.
Therefore, the centripetal acceleration of the runner is:
a = (8.8 m/s)²/25 m
= 4.6 m/s²
The agent that exerts force on the runner is gravity, which acts downwards on the runner and produces the centripetal force needed to accelerate the runner around the bend. This can be demonstrated mathematically using the equation F = ma, where F is the force, m is the mass of the runner, and a is the centripetal acceleration.
F = m*(v²/r)
= m*4.6 m/s²
= m*g
Therefore, the force on the runner is equal to the mass of the runner multiplied by the acceleration due to gravity, which is the force of gravity acting on the runner.
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t is 165 cm from your eyes to your toes. you are standing 200 cm in front of a tall mirror. how far is it from your eyes to the image of your toes?
The calculated total distance from the eyes to the toes is given by 432.7 cm.
Given:
Distance, x = 200 cm
Horizontal distance, h = 165 cm
We can use the idea of virtual images created by mirrors to calculate the distance between your eyes and the image of your toes in the mirror.
When you stare at a mirror, light rays from your eyes reflect off of it and give the impression that they are coming from behind the mirror. The virtual reflection created by the mirror appears to be at the same height as you are in front of it.
The horizontal distance is:
d = 2x
d = 2 × 200
d = 400 cm
The total distance from eyes to toes is:
D = √(d² + h²)
D = √(400² + 165²)
D = 432.7 cm
Hence, the calculated distance from the eyes to the toes is given by 432.7 cm.
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