Answer:
13. a) In Einstein's photoelectric equation, hf represents the energy of a single photon of the electromagnetic radiation, and mvmax² represents the maximum kinetic energy of the emitted photoelectrons.
b) i. To calculate the threshold frequency, we can use the equation c = fλ, where c is the speed of light, f is the frequency of the electromagnetic radiation, and λ is the wavelength:
c = fλ
f = c/λ
f = (3.00 x 10^8 m/s)/(6.5 x 10^-7 m)
f = 4.62 x 10^14 Hz
Therefore, the threshold frequency is 4.62 x 10^14 Hz.
ii. We can use the equation hf = Φ + KEmax, where hf is the energy of a single photon, Φ is the work function energy of the metal, and KEmax is the maximum kinetic energy of the emitted photoelectrons. We know that the wavelength of the incident electromagnetic radiation is 6.5 x 10^-7 m, which corresponds to a frequency of f = 4.62 x 10^14 Hz (as calculated in part i). We also know that this wavelength is the maximum for which photoelectrons are released, which means that the energy of the photons is equal to the work function energy:
hf = Φ
Substituting the values for h and f, we get:
(6.63 x 10^-34 J s)(4.62 x 10^14 Hz) = Φ
Φ = 1.93 x 10^-19 J
Converting this to electronvolts (eV), we get:
Φ = (1.93 x 10^-19 J)/(1.60 x 10^-19 J/eV)
Φ = 1.21 eV
Therefore, the work function energy of the metal is 1.9 eV.
c) If the intensity of the incident light is doubled, the rate of release of photoelectrons will also double. This is because the intensity of light is directly proportional to the number of photons incident on the metal surface per unit time. Each photon can cause the emission of one photoelectron, so doubling the number of photons will double the number of emitted photoelectrons per unit time. However, the kinetic energy of the emitted photoelectrons will not change, since this is determined only by the frequency (and therefore the energy) of the incident photons, and not by their intensity.
What two properties change when light is refracted?
Given what you learned from the figure, rank these types of light in order of increasing energy.
1. radio
2. infrared
3. orange
4. green
5. ultraviolet
6. gamma rays
The types of light in order of increasing energy are Radio, Infrared, Orange, Green, Ultraviolet, and Gamma rays. Radio waves have the lowest energy, followed by infrared, orange, green, and ultraviolet.
What is the sequence in which light energy increases?The parts of the electromagnetic spectrum are referred to as gamma rays, X-rays, ultraviolet radiation, visible light, infrared radiation, and radio waves, from highest to lowest energy.
Which light is the most powerful?Violet light has the shortest wavelength of all visible light, giving it the most energy. The longest wavelength and lowest energy are found in radio waves.
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how can astronomers measure the age of a meteorite that fell from the skies?
Astronomers can measure the age of a meteorite that fell from the skies by using radiometric dating techniques.
Specifically, they look for isotopes of certain elements in the meteorite that undergo radioactive decay at a known rate. By measuring the ratio of the parent isotopes to the daughter isotopes, scientists can determine how much time has passed since the meteorite was formed.
For example, the decay of radioactive isotopes of uranium and thorium to lead can be used to date rocks that formed more than 4.5 billion years ago, which is the estimated age of the solar system. Therefore, by analyzing the isotopes present in meteorites, astronomers can determine their age and gain insights into the early history of our solar system.
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what are the radii of a symmetric converging plastic lens (i.e., two equally curved surfaces) that will form an image on the screen twice the height of the object? (take the index of refraction of plastic to be 1.59.)
The radii of a symmetric converging plastic lens that will form an image on the screen twice the height of the object is [tex]R_1[/tex] = 4.28 cm and [tex]R_2[/tex] = 2.1333 cm.
The index of refraction of plastic is 1.59.
The height of the object = h
The height of the image = 2h
We know that the magnification formula is M = -v/u,
where M = -2 (since the height of the image is twice the height of the object),
v is the distance between the image and the lens and
u is the distance between the object and the lens.
Therefore, -v/u = -2 ... (1)
We also know that the lens formula is [tex]\frac{1}{v} - \frac{1}{u} = \frac{1}{f}[/tex],
where f is the focal length of the lens.
Since the lens is symmetric, the radius of curvature of the two surfaces will be equal, which is the same as the focal length of the lens.
Therefore, f = R/2, where R is the radius of curvature of the lens surfaces.
Substituting f = R/2 in the lens formula and simplifying it,
we get, u = 2f/3 ... (2)
We can get the value of v by substituting equation (2) in equation (1) and solving for v.
We get v = -4f/3.
Substituting u and v values in the lens formula, we get,
[tex]\frac{1}{v} - \frac{1}{u} = \frac{1}{f}[/tex], Solving for f, we get
f = 1.0667 cm.
We also know that f = R/2, so R = 2f.
Substituting f value, we get R = 2(1.0667) = 2.1333 cm.
The radii of the two surfaces of the lens will be equal, so [tex]R_1 = R_2[/tex] = 2.1333 cm.
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a horizontal force of 20 n is required to keep a 5.0 kg box traveling at a constant speed up a frictionless incline for a vertical height change of 3.0 m. (a) what is the work done by gravity during this change in height? (b) what is the work done by the normal force? (c) what is the work done by the horizontal force?
The work done by the horizontal force is found to be 60J and the work done by the gravity and the normal force is 0J.
The horizontal force that is applied is 20N and the mass of the box is 5.0 Kg and the force moves the box with a constant speed till a distance of 3.0m.
Now, first understand the work and force relation,
W= Fs.cosA, where, W is work, F is applied force, A is the angle between force and distance s.
For (a) and (b),
The work done by the gravity and the normal force on the block will be ) J because the angle A = 90 degrees.
(c). The work done by the horizontal force is given by the above formula by putting all the values, The value of the angle A is 0 degrees and the value of cos(0) = 1.
W = (20)(3)
W = 60J
So, the work done by the horizontal force is 60J.
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you are riding in a train. since the train car is almost empty, you and your friend are pushing a cart (with almost no friction) back and forth between the front and rear of the car. the train is moving at a speed of 5.4m/s and each time you push the cart, the cart has a speed of 2.4m/s. what is the velocity of the cart relative to the ground when the cart is moving toward the front of the car
The relative velocity of the cart relative to the ground when the cart is moving toward the front of the car is 3 m/s.
Given Data:
Train's speed, v = 5.4 m/s
Cart's speed, u = 2.4 m/s
The relative velocity of the cart relative to the ground when the cart is moving toward the front of the car is to be determined. The velocity of an object in a moving frame is equal to the sum of the velocity of the object relative to the moving frame and the velocity of the moving frame. We know that the velocity of the train, v = 5.4 m/s
When the cart is moving forward, the velocity of the cart is the sum of the velocity of the train and the velocity of the cart relative to the train. Therefore, the velocity of the cart when it is moving toward the front is given as:
v = v_train + v_cart (towards the front)v_cart = v - v_trainv_cart = 5.4 - 2.4v_cart = 3 m/s
Therefore, the relative velocity of the cart relative to the ground when the cart is moving toward the front of the car is 3 m/s.
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during which phase of the moon may a solar eclipse occur? responses third quarter moon third quarter moon first quarter moon first quarter moon full moon full moon new moon
A solar eclipse may occur during the new moon phase of the moon. During this phase, the moon is situated between the Earth and the sun. This positions the moon in such a way that it blocks the sun's rays, causing a solar eclipse.
There are different phases of the moon that occur in a lunar cycle. Each of these phases is determined by the relative position of the sun, Earth, and moon. The lunar cycle is approximately 29.5 days long, and it consists of eight different phases. These phases include the new moon, waxing crescent, first quarter, waxing gibbous, full moon, waning gibbous, third quarter, and waning crescent.
In general, solar eclipses occur during the new moon phase of the moon. This is because the moon's position during this phase is directly between the Earth and the sun. As a result, the moon casts a shadow on the Earth, blocking the sun's rays and causing a solar eclipse. However, not all new moon phases lead to a solar eclipse. This is because the moon's orbit is tilted in relation to the Earth's orbit around the sun. Therefore, it must be in the correct position to cause a solar eclipse to occur.
Additionally, it is important to note that not all solar eclipses are total eclipses. Sometimes, the moon only partially covers the sun, resulting in a partial solar eclipse.
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a 70 n force pulls a box straight up 5 m above the ground. if the box is not moving after it is lifted, what type of energy does it now have? a. chemical b. elastic c. gravitational d. kinetic
The box has gravitational energy. Therefore, option c is correct.
Gravitational potential energy is the energy an object has due to its position in a gravitational field. When the box is lifted to a height of 5m above the ground, it gains an amount of gravitational potential energy equal to the work done on it, which is equal to the force (70N) multiplied by the distance (5m).
When a 70 N force pulls a box straight up 5 m above the ground, and the box is not moving after it is lifted, the type of energy it now has is gravitational energy. Gravitational potential energy is the potential energy stored in an object because of its height over the Earth's surface. An object that has been lifted above the ground has the ability to do work when it falls back to the ground. The work is generated by the object's gravitational potential energy, which is a function of its mass and height over the ground.
As a result, the option c, gravitational, is the correct answer.
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Which of the following statements is true about electric current? (There is one correct answer)
Electric current is the flow of electrons from a positive terminal to a negative terminal.
Electric current is the flow of protons from a positive terminal to a negative terminal.
Electric current is the flow of protons from a negative terminal to a positive terminal.
Electric current is the flow of electrons from a negative terminal to a positive terminal.
A van increases its velocity from 20m/s to 10. 0m/s in 3. 0s what is the acceleration
The acceleration of van is -10.0 m/s².
Acceleration is defined as the rate of change of velocity. It is a vector quantity, which means it has both magnitude and direction. In the context of this problem, the van's velocity changed from 20 m/s to 10.0 m/s in a time of 3.0 s. We can calculate the acceleration of the van using the formula,
acceleration = (final velocity - initial velocity) / time
Substituting the given values, we get,
acceleration = (10.0 m/s - 20 m/s) / 3.0 s
= -10.0 m/s²
The negative sign indicates that the acceleration is in the opposite direction to the initial velocity. In other words, the van is decelerating, or slowing down.
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What type of volcanic material indicates an eruption under water? a) AA flows b) Pyroclastic flows c) Pillow lavas d) Pahoehoe flows. e) Pillow lavas.
The type of volcanic material that indicates an eruption underwater is pillow lavas. So the correct answer is option C or E.
Pillow lavas are igneous rock formations that occur when magma extrudes from a volcano's vent and cools quickly under seawater or other bodies of water. When magma comes into contact with the water, it cools quickly and solidifies into what looks like a pile of stacked pillows. Pillow lavas are a clear indication of an underwater eruption. Pillow lavas are typically found in submarine basaltic volcanoes, which are located near mid-ocean ridges, and can be found in a variety of other underwater volcanic settings.
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Which of the following would cause a change in the speed of a sound wave
Temperature and Density would cause change in the speed of a sound wave. Hence, the correct option is (c) i.e. both a & b.
A change in the speed of a sound wave can be caused by several factors:
1. Temperature: The speed of sound in a medium is directly proportional to the temperature of the medium. As the temperature of a medium increases, the speed of sound in that medium also increases.
2. Density: The speed of sound in a medium is inversely proportional to the density of the medium. As the density of a medium increases, the speed of sound in that medium decreases.
3. Pressure: The speed of sound in a gas is directly proportional to the pressure of the gas. As the pressure of a gas increases, the speed of sound in that gas also increases.
4. Humidity: The speed of sound in a gas, such as air, can be affected by the amount of water vapor present in the gas. As the humidity of the air increases, the speed of sound in that air decreases.
5. Composition of the medium: The speed of sound can also vary depending on the type of medium through which it is traveling. For example, sound travels faster through solids than through gases.
These factors can individually or collectively cause a change in the speed of sound waves.
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Question -
Which of the following would cause a change in the speed of a sound wave.
(a) Temperature
(b) Density
(c) Both a & b
(d) None of the above
What is the net force if two equal forces are acting in opposite directions on an object? [1MARK]
If two equal forces are acting in opposite directions on an object, the net force is zero.
The net force when two equal forces are acting in opposite directions on an object is zero. Here's a step-by-step explanation:
1. First, identify the magnitudes and directions of the two forces acting on the object. Let's say force F1 acts in the positive direction, and force [tex]F_2[/tex] acts in the negative direction.
2. Since the forces are equal in magnitude, we can represent them as [tex]F_1[/tex] = [tex]F_2[/tex]
3. Net force is the vector sum of all individual forces acting on the object.
In this case, we only have two forces: [tex]F_1[/tex] and [tex]F_2[/tex].
To calculate the net force, we can use the formula:
Net Force = [tex]F_1[/tex] + [tex]F_2[/tex]
4. As [tex]F_1[/tex] and [tex]F_1[/tex] are acting in opposite directions, we need to take into account their directions when calculating the net force.
As [tex]F_1[/tex] is in the positive direction and [tex]F_2[/tex] is in the negative direction, the formula becomes:
Net Force = [tex]F_1[/tex] - [tex]F_2[/tex]
5. Now, we can substitute the values of [tex]F_1[/tex] and [tex]F_2[/tex].
Since [tex]F_1[/tex] = [tex]F_2[/tex], the equation becomes:
Net Force = [tex]F_1[/tex] - [tex]F_1[/tex].
6. Finally, when we subtract [tex]F_1[/tex] from itself, the result is zero.
Therefore, the net force is zero when two equal forces are acting in opposite directions on an object.
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What is the magnitude of the force per meter of length on a straight wire carrying a 7.30 A current when perpendicular to a 0.90 T uniform magnetic field? What if the angle between the wire and field is 34.5∘?
The magnitude of the force per meter of length on the wire is 6.57 N/m when the wire is perpendicular to the magnetic field. The magnitude of the force per meter of length on the wire is 3.77 N/m when the angle between the wire and field is 34.5∘.
The magnitude of the force per meter of length on a straight wire carrying a 7.30 a current when perpendicular to a 0.90 T uniform magnetic field can be calculated using the formula:
F = B * I * L
where F is the force, B is the magnetic field, I is the current, and L is the length of the wire.
Since we want to calculate the force per meter of length, L = 1 meter.
F = 0.90 T * 7.30 A * 1 m = 6.57 N/m
If the angle between the wire and field is 34.5°, we need to use the formula:
F = B * I * L * sin(θ)
where θ is the angle between the wire and the magnetic field.
F = 0.90 T * 7.30 A * 1 m * sin(34.5°) = 6.57 N/m * sin(34.5°) ≈ 3.77 N/m
So, the magnitude of the force per meter of length is 6.57 N/m when perpendicular, and 3.77 N/m when the angle is 34.5°.
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at some distance away from a long, straight current carrying wire, in what direction does the magnetic field point?
At some distance away from a long, straight current carrying wire, the magnetic field points perpendicular to the wire. This is known as the right-hand rule, which is used to determine the direction of the magnetic field in relation to the direction of the current flow.
A long, straight current-carrying wire produces a magnetic field, and the direction of the field is determined by the right-hand rule. This rule states that if you wrap your right hand around the wire in such a way that your thumb points in the direction of the current, your fingers will point in the direction of the magnetic field.
The direction of the magnetic field can also be determined by the direction of the current flow. The field is perpendicular to the wire and circular around the wire. This means that the field lines of the magnetic field are circular around the wire, and they point in the direction of the current flow.
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a piston expands against an external pressure of 2.35 atm. if the initial volume is 0.455 l and the final volume is 1.318 l, then how much work (in joules) is done?
The work done by the piston in expanding against an external pressure of 2.35 atm is 545 J.
The work done by a piston can be calculated using the formula: work = -PΔV, where P is the external pressure, ΔV is the change in volume, and the negative sign indicates that work is done by the system (the piston) on the surroundings (the external pressure).
In this case, the external pressure is 2.35 atm, the initial volume is 0.455 L, and the final volume is 1.318 L. Therefore, the change in volume is:
ΔV = final volume - initial volume
ΔV = 1.318 L - 0.455 L
ΔV = 0.863 L
Substituting the values into the formula, we get:
work = -PΔV
work = -(2.35 atm)(0.863 L)
work = -2.025 J
Since the work done is negative, it means that the system loses energy as it expands against the external pressure. To obtain the absolute value of the work done, we take the magnitude of the negative work, giving: work = 2.025 J
Therefore, the work done by the piston in expanding against an external pressure of 2.35 atm is 545 J (rounded to three significant figures).
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A student places a transparent semicircular block on a sheet of paper and draws
around the block. She directs a ray of light at the centre of the flat edge of the block.
Figure 1 shows the path of the ray through the block.
Figure 1
incident ray
centre of the flat
edge of the block
transparent
semicircular block
emergent ray \ sheet of paper
[foya}(4] State why the emergent ray does not change direction as it leaves the block.
[1 mark]
Answer:incidence
Explanation: Because it depends on incident
Which situations show examples of work occurring? Check all that apply
Examples of work taking place include options 1, 2, and 3.
Work is said to be done when a force causes a displacement in an object in the direction of the force. The following situations are examples of work occurring:
Lifting a box off the ground: The force of lifting the box causes a displacement in the box in the upward direction, which is the same direction as the force applied. Therefore, work is done on the box.
Pushing a car up a hill: The force of pushing the car causes a displacement in the car in the direction of the hill, which is the same direction as the force applied. Therefore, work is done on the car.
Carrying a backpack: Although the backpack may not be moving, work is still being done because the force of carrying the backpack causes a displacement in the person's body in the upward direction.
Holding a heavy object: If a person is holding a heavy object, but not moving it, no work is being done on the object because there is no displacement. However, the person's muscles are still working to maintain the position, which is an example of isometric work.
Therefore, options 1, 2, and 3 are examples of work occurring. Option 4 is not an example of work being done on the object, but it is an example of work being done by the person's muscles.
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is the impulse delivered to the superball during its collision with the scale greater than, less than, or equal to the impulse delivered to the clay during its collision with the scale?
The impulse delivered to superball is greater than the impulse delivered to the clay.
The impulse delivered to superball is equal to the impulse delivered to the clay.
The impulse delivered to superball is less than the impulse delivered to the clay.
The impulse delivered to the superball is greater than the impulse delivered to the clay.
Impulse refers to the change in momentum of an object when a force is applied to it over a certain period of time. Impulse (J) is given by the equation:
J = F × Δt
J = Δp
Where: J is the impulse,
F is the force applied to the object, and
Δt is the time interval over which the force acts.
Δp is the change in momentum
So, the change in momentum for the clay takes a larger time than for the superball. Thus for the same force, a larger impulse has to be imparted to superball than clay.
Therefore, the impulse delivered to the superball is greater than the impulse delivered to the clay.
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one end of a 3.0-m rope is tied to a tree; the other end is tied to a car stuck in the mud. the motorist pulls sideways on the midpoint of the rope, displacing it a distance of 0.25 m. if he exerts a force of 200.0 n under these conditions, determine the force exerted on the car.
The force exerted on the car when motorist is pulling on the midpoint of the 3.0-m rope is 400 N.
The question involves the determination of the force exerted on the car when one end of a 3.0-m rope is tied to a tree; the other end is tied to a car stuck in the mud.
The motorist pulls sideways on the midpoint of the rope, displacing it a distance of 0.25 m. If he exerts a force of 200.0 N. Under these conditions, the force exerted on the car can be calculated as follows;
Since the displacement of the rope is perpendicular to the direction of the applied force, the component of the force perpendicular to the rope's direction must be considered. We can calculate the force perpendicular to the direction of the applied force as follows;
F_perpendicular = F x sinθ
where, F is the force exerted, and θ is the angle between the force and the direction of the rope (90°).
Therefore,
F_perpendicular = 200 x sin(90°) = 200 x 1 = 200 N
The force acting on the car is the force in the direction of the rope, which is equal to two times the force perpendicular to the rope direction. Therefore,
F_car = 2 x F_perpendicular
F_car = 2 x 200 N = 400 N
Therefore, the force exerted on the car is 400 N.
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Defferentiate between vector and scalar quantity giving relevannt example in case
A scalar quantity is a quantity that just has magnitude and no direction. Scalars include things like length, mass, speed. But a physical quantity is referred to as a vector quantity if it includes both magnitude and direction.
A number of physical quantities that each express a unique meaning and significance in that context can be used to explain each scientific explanation. A physical quantity is a measurable, quantifiable physical property that carries specific information, according to the definition. Physical quantities can be divided into the scalar and vector categories depending on how dependent they are on direction. These two numbers are used to depict an object's motion.To know more about scalar quantity
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calculate the force of gravity a newborn baby of mass 3.6 kg and the obstetrician of mass 100.0 kg exert on each other when the distance between them is 0.5 m .
Answer:
F=Gm1m2/r^2
Explanation:
the term we use to generally describe the total incoming solar energy from the sun to the earth is called
The term we use to generally describe the total incoming solar energy from the sun to the Earth is called solar radiation or solar insolation.
This refers to the electromagnetic radiation emitted by the sun, which includes visible light, ultraviolet (UV) radiation, and infrared (IR) radiation, among others. Solar radiation is the primary source of energy that drives many Earth systems, such as the atmosphere, oceans, and land surface. It is responsible for warming the Earth's surface and fuels photosynthesis in plants, among other important processes. The amount and distribution of solar radiation that reaches the Earth's surface depend on various factors, including latitude, time of day, season, and atmospheric conditions.
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---The complete question is, the term we use to generally describe the total incoming solar energy from the sun to the earth is called ___________.------
15. The diagram shows an electric circuit including a photocell.
The photocell contains a metal plate X that is exposed to
electromagnetic radiation. Photoelectrons emitted from the
surface of the metal are accelerated towards the positive
electrode Y. A sensitive ammeter measures the current in the
circuit due to the photoelectrons emitted by the metal plate
X. The metal plate X has a work function of 2.2 eV. The
maximum kinetic energy of an emitted photoelectron from
this plate is 0.3eV.
5
KE/10-19 J
4
2
a) Calculate the energy of a single photon in eV and in joules.
b) Calculate the frequency of the incident electromagnetic radiation.
c) Deduce the effect on the current if the radiation has the same intensity, but the frequency is
greater than in (b).
16. A negatively charged metal plate is exposed to electromagnetic radiation of frequency (f). The
diagram below shows the variation with (f) of the maximum kinetic energy KEmax of the
photoelectrons emitted from the surface.
1
0-
0
2
6
a) Define the threshold frequency of a metal.
b)
+
8
Electroma
10
radiation
vacuum
12
f/10¹4 Hz
14
i. Explain how the graph shows that the threshold frequency of this metal is
5.0 x 10¹4 Hz.
ii. Calculate the work function of this metal in joules.
Answer:
15.
a) The energy of a single photon can be calculated using the equation: E = hf, where h is Planck's constant (6.63 x 10^-34 J s) and f is the frequency of the radiation. Thus, E = (6.63 x 10^-34 J s)(c/λ), where c is the speed of light (3.00 x 10^8 m/s) and λ is the wavelength of the radiation. Using the maximum kinetic energy of an emitted photoelectron (0.3 eV) and the work function of the metal plate (2.2 eV), we can find the energy of a single photon: E = 2.5 eV = 4.0 x 10^-19 J.
b) The maximum kinetic energy of a photoelectron can be related to the frequency of the radiation by the equation: KEmax = hf - Φ, where Φ is the work function. Thus, f = (KEmax + Φ)/h. Substituting the given values, we get: f = (0.3 + 2.2) eV/(6.63 x 10^-34 J s) = 3.4 x 10^14 Hz.
c) If the frequency of the radiation is increased, more photoelectrons will be emitted per unit time, so the current in the circuit will increase.
16. a) The threshold frequency of a metal is the minimum frequency of radiation required to emit photoelectrons from the surface of the metal.
i. The graph shows that the kinetic energy of the emitted photoelectrons is zero for frequencies below 5.0 x 10^14 Hz. This means that the photoelectrons are not emitted below this frequency, indicating that the threshold frequency is 5.0 x 10^14 Hz.
ii. The work function of the metal can be calculated using the equation: Φ = hf - KEmax, where h is Planck's constant and KEmax is the maximum kinetic energy of the emitted photoelectrons. At the threshold frequency, KEmax is zero, so Φ = hf. Substituting the given values, we get: Φ = (6.63 x 10^-34 J s)(5.0 x 10^14 Hz) = 3.32 x 10^-19 J.
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what is the current through a long straight wire if the magnetic field at a point 3.70 cm away is 1.70 t?
The current through the long straight wire is 45.7 A.
The magnetic field produced by a long straight wire carrying a current is given by the formula B = (μ0I)/(2πr), where B is the magnetic field, μ0 is the permeability of free space, I is the current, and r is the distance from the wire. Rearranging the formula to solve for I, we get I = (2πrB)/μ0.
Substituting the given values, we have B = 1.70 T and r = 0.0370 m. The permeability of free space μ0 is a constant equal to 4π × 10⁻⁷ T·m/A. Thus, we can calculate the current I as I = (2π0.0370 m1.70 T)/(4π × 10⁻⁷ T·m/A) = 45.7 A.
Therefore, the current through the long straight wire is 45.7 A.
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you use the doppler method to discover a planet around a nearby star that is very similar to the sun; the velocity curve that has a period of 6 months. what can you conclude about the planet's orbital distance?
The Doppler method is used to discover a planet around a nearby star that is similar to the Sun; the velocity curve has a period of 6 months. We can conclude that the planet's orbital distance is 1 AU.
The Doppler method is a technique for discovering planets that orbit other stars. The Doppler method, also known as the radial velocity method, involves measuring the movement of a star towards or away from the observer. As a planet orbits a star, it pulls the star in a small, regular circle around the center of mass of the planet-star system.The period of the velocity curve can be used to determine the planet's orbital period and distance.
If the velocity curve has a period of 6 months, the planet's orbital period is also 6 months. Kepler's third law can then be used to determine the planet's orbital distance.
According to Kepler's third law, the square of a planet's orbital period is proportional to the cube of its orbital distance. P² α a³ where P is the orbital period and a is the orbital distance.
Thus, a² ∝ P²/3a² = 1 AU (since P = 6 months).
Therefore, we can conclude that the planet's orbital distance is 1 AU.
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The electric field in a region of space is Ex = -1000 xV/m, where x is in meters. What is the potential difference between xi = −30cm and xf = 60cm? I got -900 but it is wrong.
The potential difference between xi = -30 cm and xf = 60 cm for the given electric field is -135 V.
To find the potential difference follow these steps:
1. Convert the given positions from centimeters to meters: xi = -0.3 m and xf = 0.6 m.
2. Calculate the potential difference using the formula ΔV = -∫(E(x) dx) over the interval [xi, xf].
3. Integrate the electric field function, Ex = -1000 x, with respect to x: ∫(-1000 x dx) = -500 x² + C, where C is the integration constant.
4. Find the potential difference by evaluating the integral at the given points: ΔV = -500 (xf² - xi^2) = -500 (0.6² - (-0.3)^2) = -500 (0.36 - 0.09) = -500 (0.27).
5. Calculate the result: ΔV = -500 * 0.27 = -135 V.
The potential difference between xi = -30 cm and xf = 60 cm for the given electric field is -135 V.
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A horse can produce 60,000 W of power when he pulls a wagon. The horse pulls with
20,000 N of force for a time of 80 s. What is the distance traveled by the horse.
Answer:
The horse traveled 240 meters
Explanation:
In this example we are given power, the applied/resultant force, and time.
We can use the following equations to evaluate the distance.
[tex]\boxed{\sf Work=Power\cdot Time}[/tex]
[tex]\boxed{\sf Work=Force\cdot Distance}[/tex]
We can set them equal to each other.
[tex]\sf Force \cdot Distance=Power\cdot Time[/tex]
We can isolate Distance by dividing both sides of the equation by Force.
[tex]\sf Distance=\dfrac{Power\cdot Time}{Force}[/tex]
Now we have an equation to evaluate the distance.
Numerical Evaluation
In this example we are given
[tex]\sf Power=60000 \\Time=80\\Force=20000[/tex]
Substituting our values into our equation for Distance yields
[tex]\sf Distance=\dfrac{60000\cdot 80}{20000}[/tex]
[tex]\sf Distance=\dfrac{4800000}{20000}[/tex]
[tex]\sf Distance=240[/tex]
Lets figure out what unit we end up with.
When you multiply watts by seconds, you get the unit of energy, which is joules (J). When you divide joules by newtons, you get the unit of distance, which is meters (m).
a 50 g ball of clay is thrown at 10 m/s tangent to the edge of a 2.0 kg, 30 cm diameter disk that can turn on a frictionless axle. the clay hits the edge of the disk and sticks. if the disk was initially at rest, what is the angular velocity in rpm, after the collision?
The final angular velocity of the disk-clay system after the collision is approximately 1.67 rpm.
To find the angular velocity in rpm after the collision, we can use the principle of conservation of angular momentum.
Since the disk is initially at rest, the initial angular momentum is zero. After the clay sticks to the edge of the disk, the system will be a combination of the clay and the disk, which will rotate together with some final angular velocity.
The angular momentum of the system is given by the formula:
L = Iω
where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
Since the system is rotating about an axis perpendicular to the disk, the moment of inertia of the system can be calculated as:
[tex]I = I_{disk} + I_{clay}[/tex]
where I_disk is the moment of inertia of the disk and I_clay is the moment of inertia of the clay. The moment of inertia of a solid disk rotating about an axis through its center is given by:
[tex]I_{disk} = (\frac{1}{2} )MR^2[/tex]
where M is the mass of the disk and R is the radius of the disk. Substituting the given values, we get:
[tex]I_{disk }= (\frac{1}{2} )(2.0 kg)(0.15 m)^2 = 0.0225 kg m^2[/tex]
The moment of inertia of the clay can be approximated as that of a solid sphere rotating about an axis through its center, given by:
[tex]I_{clay} = (\frac{2}{5} )MR^2[/tex]
where M is the mass of the clay and R is its radius. Substituting the given values, we get:
[tex]I_{clay} = (\frac{2}{5} )(0.050 kg)(0.05 m)^2 = 0.000125 kg m^2[/tex]
Therefore, the total moment of inertia of the system is:
[tex]I = I_{disk} + I_{clay} = 0.0225 kgm^2 + 0.000125 kgm^2 = 0.022625 kgm^2[/tex]
The final angular momentum of the system is:
L = Iω
where ω is the final angular velocity of the system. Before the collision, the clay is moving tangent to the disk, so its velocity is perpendicular to the line joining its center and the centre of the disk.
Therefore, the angular momentum of the clay is zero. After the collision, the clay sticks to the edge of the disk, which acquires the angular momentum of the clay. Therefore, the angular momentum of the system after the collision is:
[tex]L = I\omega = (0.000125 kgm^2)(10 m/s) = 0.00125 kgm^2/s[/tex]
Setting the initial and final angular momenta equal, we can solve for the final angular velocity:
L_initial = L_final
[tex]0 = (0.022625 kg m^2) \times 0 + (0.000125 kgm^2 + 0.0225 kgm^2) \times \omega[/tex]
Solving for ω, we get:
ω = 0.00556 rad/s
Finally, we can convert the angular velocity to rpm:
[tex]\omega_{rpm} = \frac{\omega \times 60}{2\pi} = \frac{0.00556 rad/s \times 60}{2\pi} \approx 1.67 rpm[/tex]
The angular velocity in rpm, after the collision is 1.67 rpm.
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carefully examine the view in the sky chart. which of the inner planets has the most eccentric orbit?
Of the four inner planets, Mercury has the most eccentric orbit, with an eccentricity of 0.21. The inner planets of our solar system - Mercury, Venus, Earth, and Mars - have nearly circular orbits around the sun.
Their eccentricities (the degree to which their orbits deviate from perfect circles) are relatively low compared to the outer planets. This means that its orbit is more elliptical than the orbits of the other inner planets, which have eccentricities ranging from 0.0068 (Venus) to 0.0934 (Mars).
Mercury's highly eccentric orbit means that its distance from the Sun varies greatly throughout its year, which leads to extreme temperature variations on its surface. Conversely, Venus has nearly circular orbit and experiences relatively stable temperatures as a result.
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