The change in velocity of the tip of the second's hand in 15 seconds is: [tex]\pi /(30\sqrt2) cm/s[/tex]. The correct option is B.
To determine the change in velocity of the tip of the second's hand, we need to consider that the hand moves in a circular path with a radius of 1 cm. In 15 seconds, the angle covered is (15/60) × 360 = 90 degrees, or π/2 radians.
The initial velocity can be represented as (v1 = rω1) and the final velocity as (v2 = rω2), where r is the radius (1 cm) and ω is the angular velocity. Since the second's hand moves at a constant speed, the angular velocities are equal, and the change in velocity (∆v) can be calculated using the formula:
∆v = √(v1² + v2² - 2*v1*v2cos(π/2))
Since cos(π/2) = 0, the formula simplifies to:
∆v = √(v1² + v2²)
As v1 = v2 = rω,
∆v = √(2(rω)²) = rω√2 = (1cm)(π/30 rad/s)√2 = π/(30√2) cm/s
So, the change in velocity of the tip of the second's hand in 15 seconds is π/(30√2) cm/s. The correct option is B.
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Complete question:
The length of speed's hand of watch is 1cm the change in velocity of is tip in 15 sec
A. zero
B. π/(30√2)
C. π/30
D. 2π/(30√2)
Vocabulary: electron volt, frequency, photoelectric effect, photon, photon flux, voltage, wavelength, work function Prior Knowledge Questions (Do these BEFORE using the Gizmo. ) 1. Suppose you went bowling, but instead of a bowling ball you rolled a ping pong ball down the alley. What do you think would happen? 2. Suppose you rolled a lot of ping pong balls at the bowling pins. Do you think that would change the results of your experiment? Explain. Gizmo Warm-up The photoelectric effect occurs when tiny packets of light, called photons, knock electrons away from a metal surface. Only photons with enough energy are able to dislodge electrons. In the Photoelectric Effect Gizmo, check that the Wavelength is 500 nm, the Photon flux is 5 γ/ms, the Voltage is 0. 0 volts, and Potassium is selected. Click Flash the light to send photons of light (green arrows) toward a metal plate encased in a vacuum tube. 1. The blue dots on the metal plate are electrons. What happens when the photons hit the electrons? 2. What happens when the electrons reach the light bulb? _________________________________________________________________________ When electrons reach the light bulb they complete a circuit, causing the bulb to glow briefly
In this scenario, you are experimenting with the photoelectric effect, which occurs when photons (tiny packets of light) knock electrons away from a metal surface. Only photons with enough energy can dislodge electrons.
1. When the photons hit the electrons on the metal plate, if the photons have enough energy (determined by their frequency and wavelength), they can dislodge the electrons from the metal surface. This process demonstrates the photoelectric effect.
2. When the dislodged electrons reach the light bulb, they complete an electrical circuit, allowing the light bulb to glow briefly. This occurs due to the flow of electrons, which is influenced by the photon flux, electron volt, and voltage in the system.
The work function of the metal (in this case, potassium) also plays a role in the photoelectric effect, as it represents the minimum energy required to remove an electron from the metal surface.
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3) if tom cruise (red bike rider) is more massive than the other actor, which person has more momentum in mid-air? explain.
4) if the total momentum of both riders added together is 2400 kgm/s before they collide, what is their total momentum after they collide? explain how you know that?
5) is this collision elastic or inelastic? explain how you know.
6) if tom is more massive and stronger than the other actor, compare the forces that they exert on each other when they collide. explain.
7) what would this scene look like if it were done in space? what would be the same? what would be different? be sure to answer using the appropriate physics word (see top of page)
1) If Tom Cruise (the red bike rider) is more massive than the other actor, then Tom Cruise has more momentum in mid-air because momentum is equal to mass times velocity, and Tom Cruise has more mass.
What is momentum?Momentum is a physical concept used to describe the movement and direction of an object in motion. It is calculated by multiplying the mass of an object by its velocity. Momentum can be both linear and angular, depending on the force applied. When an object has momentum, it has a tendency to continue in the same direction due to the force applied.
2) Momentum is a vector quantity, so the direction of their motion will also affect their momentum.
3) If Tom Cruise is more massive than the other actor, then he will have more momentum in mid-air.
4) The total momentum of both riders after they collide would be 0 kgm/s.
5) This collision is inelastic because some of the kinetic energy of the riders is lost in the form of heat, sound, and deformation of the bike.
6) When the two riders collide, Tom Cruise will exert a greater force on the other actor than the other actor will exert on Tom Cruise.
7) If this scene were done in space, the riders would continue to move in the same direction they were travelling in before they collided.
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An individual receives frequent injections of drugs, which are administered in a small examination room at a clinic. The drug itself causes increased heart rate but after several trips to the clinic, simply being in a small room causes an increased heart rate
The repeated association of the drug injection with the small examination room has led to classical conditioning, resulting in an increased heart rate response to just being in the room.
This phenomenon can be explained through classical conditioning. Classical conditioning is a type of learning in which an organism learns to associate two stimuli together, resulting in a change in behavior.
In this case, the drug injection is the unconditioned stimulus (UCS) that naturally elicits an unconditioned response (UCR) of an increased heart rate.
However, over time, the small examination room has become a conditioned stimulus (CS) that has been associated with the drug injection and now elicits a conditioned response (CR) of an increased heart rate. This means that just the sight or thought of the examination room triggers the same physiological response as the drug itself.
This type of classical conditioning can have both positive and negative effects. On one hand, it can be beneficial for patients who are receiving treatment, as it can help them to anticipate and prepare for the effects of the drug.
On the other hand, it can also lead to a heightened anxiety or fear response in patients who may associate the examination room with negative experiences.
In summary, the repeated association of the drug injection with the small examination room has led to classical conditioning, resulting in an increased heart rate response to just being in the room.
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A fly accumulates 3.0 x 10-10 c of positive charge as it flies through the air. what is the
magnitude and direction of the electric field at a location 2.0 cm away from the fly?
The magnitude of the electric field at a location 2.0 cm away from the fly with 3.0 x 10^-10 C of positive charge is 5.39 x 10^(-2) N/C. The direction of the electric field is radially outward from the fly.
To find the magnitude and direction of the electric field at a location 2.0 cm away from the fly, we need to use the formula for the electric field due to a point charge:
E = k * Q / r^2
where E is the electric field, k is the electrostatic constant (8.99 x 10^9 N m^2/C^2), Q is the charge of the fly (3.0 x 10^-10 C), and r is the distance from the charge (2.0 cm or 0.02 m).
Step 1: Convert distance to meters: 2.0 cm = 0.02 m
Step 2: Plug in the values into the formula:
E = (8.99 x 10^9 N m^2/C^2) * (3.0 x 10^-10 C) / (0.02 m)^2
Step 3: Calculate the electric field magnitude:
E = 5.39 x 10^(-2) N/C
Since the fly has a positive charge, the electric field will be directed radially outward from the fly. This means that at any point 2.0 cm away from the fly, the electric field will be pointing away from the fly in a direction perpendicular to the line connecting the fly and the point.
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two similar razor blades were placed on a wooden block and the other on an iron block. it was observed that the razor blade on the wooden block is attracted by the magnet while that on the iron block was not. explain
The soft iron is a magnetic material hence it became an induced magnet and attracted the blade.What is a magnetic substance?The term magnetic substances is a substance that can be attracted b a magnet. Now we know that the soft iron is amagnetic material hence it became an induced magnet and attracted the blade.Recall that a magnetic substance is a substance that can be attracted by a magnet. Wood can not be attracted by a magnet but soft iron cash attracted by a magnet hence it is a magnetic substance.This is not possible in the case of thewooden block since it is not magnetic as such the the razor blade on the wooden block was attracted to the magnet while the other on the soft iron was not.
Identify what is being described in each sentence
Conductor, solar energy, power, solid wire, nonconductor or insulator power supply unit, stranded, conductor, fuse, LED , switch, may being described in each sentence.
Material with resistance to electricity, heat and sound.Device that requires energy to operate.Energy generating object that cannot dissipate energy.Type of wire made up of a single piece of metal.Material that allows the flow of electrical current, heat and sound.Computer hardware responsible for supplying power.Conductor made up of multiple small strands.Safety device used to protect an electrical circuit from excessive current.Semiconductor that illuminates with electrical charge.Device used to interrupt and transfer electric current.The complete question is ,
Direction: Identify what is being described in each sentence. Write your answer on a separate sheet of paper. 1. It resists electricity, heat and sound. 2. It requires a source of energy for its operation.
3. It generates energy but can't dissipate energy.
4. It is a type of wire assembled in a single piece of metal.
5. It permits electrical current, heat and sound to flow freely.
6. It is a computer hardware responsible in supplying power.
7. It is made up of multiple small strands that make-up a single conductor
8. It is a safety device used to protect an electrical circuit from cxcessive current. 9. It is a semiconductor that illuminates when an electrical charge passes through it.
10. It is a device used to break an electric current and transfer it to another conductor.
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15. True or flase: Condensation is the change of state from a liquid to a gas.._______
16. For a gas to become a liquid, large numbers of particles must clump together.
Particles clump together when the attraction between thm overcomes their_________
Scenario: You place a cold metal sphere in a container of hot water.
(a) Type(s) of energy transfer:
(b) Where will each form of transfer occur?
(c) What will happen and why?
4. Scenario: You place a piece of hot rock into a metal container, and then remove all the
air from the container.
(a) Type(s) of energy transfer:
(b) Where will each form of transfer occur?
(c) What will happen and why?
In the first scenario, heat transfers from hot water to a cold metal sphere until they reach thermal equilibrium. In the second scenario, heat and radiation occur from a hot rock to a metal container with no air until they reach thermal equilibrium.
For the scenario where a cold metal sphere is placed in hot water:
(a) The type of energy transfer is heat transfer.
(b) The transfer will occur from the hot water to the cold metal sphere, resulting in a decrease in the temperature of the water and an increase in the temperature of the sphere.
(c) The heat energy from the water will flow to the sphere until the two objects reach a state of thermal equilibrium, meaning they are at the same temperature. This occurs because heat naturally flows from hotter objects to cooler ones.
For the scenario where a hot rock is placed in a metal container with all the air removed:
(a) The type of energy transfer is both heat transfer and radiation.
(b) Heat transfer will occur from the hot rock to the metal container, while radiation will occur from the rock to the surrounding environment.
(c) The hot rock will lose heat energy to the metal container until they reach thermal equilibrium. Additionally, as the rock cools, it will emit electromagnetic radiation in the form of infrared waves. Because there is no air in the container, convection, another form of heat transfer, cannot occur.
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Maintenance of military defense and the national parks system that must be renewed every year falls under which type of government spending
The maintenance of military defense and the national parks system that must be renewed every year falls under the category of government current spending, also known as government consumption.
Government current spending refers to the expenses incurred by the government on the day-to-day activities of providing public goods and services, such as education, healthcare, defense, and infrastructure maintenance.
This spending is financed through taxes and other forms of revenue collected by the government.
Government current spending is different from government capital spending, which involves investment in infrastructure, such as roads, bridges, and buildings.
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In the arrangement of the first figure, we gradually pull the block from x = 0 to x = +3. 0 cm, where it is stationary. The second figure gives the work that our force does on the block. The scale of the figure's vertical axis is set by Ws = 1. 0 J. We then pull the block out to x = +5. 0 cm and release it from rest. How much work does the spring do on the block when the block moves from xi = +5. 0 cm to (a) x = +3. 0 cm, (b) x = -1. 0 cm, and (c) x = -5. 0 cm?
To determine the work done by the spring on the block as it moves to different positions, we need to consider the displacement of the block and the potential energy stored in the spring.
Given:
Initial position of the block, xi = +5.0 cm
Final positions: (a) x = +3.0 cm, (b) x = -1.0 cm, (c) x = -5.0 cm
We'll calculate the work done by the spring separately for each position:
(a) From x = +5.0 cm to x = +3.0 cm:
In this case, the block is moving in the positive x-direction, compressing the spring. The work done by the spring is equal to the change in potential energy stored in the spring.
The change in potential energy can be calculated using the formula:
ΔPE = (1/2)k(Δx)^2.Here, k is the spring constant and Δx is the displacement of the block.
(b) From x = +5.0 cm to x = -1.0 cm:
In this case, the block is moving in the negative x-direction, stretching the spring. The work done by the spring is again equal to the change in potential energy stored in the spring.
(c) From x = +5.0 cm to x = -5.0 cm:
In this case, the block is moving in the negative x-direction, stretching the spring further. The work done by the spring is equal to the change in potential energy stored in the spring.
Note: To calculate the values, we need the spring constant (k) and the displacement (Δx) for each case. Without specific values or additional information, it is not possible to determine the exact numerical values of the work done by the spring in each scenario.
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Jake wants to prove the theorem that says that the measure of the quadrilateral's opposite angles add to 180°
Jake wants to prove the theorem that states that the measure of the opposite angles of a quadrilateral add up to 180 degrees.
This theorem is also known as the "opposite angles theorem." To prove this, Jake could use several methods, including the use of geometric proofs, algebraic proofs, or even visual aids such as diagrams or sketches.
One way to approach the proof would be to divide the quadrilateral into two triangles and show that the sum of the angles in each triangle equals 180 degrees.
Jake could then use this information to prove that the opposite angles of the quadrilateral add up to 180 degrees as well. Another approach would be to use the properties of parallel lines and transversals to show that the opposite angles are supplementary (i.e., add up to 180 degrees).
Regardless of the method used, the opposite angles theorem is a fundamental concept in geometry that is used to solve a variety of problems involving quadrilaterals.
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A candy distributor needs to mix a 20% fat-content chocolate with a 60% fat-content chocolate to create 100 kilograms of a 52% fat-content chocolate. How many kilograms of each kind of chocolate must they use?
By using, the system of equations, the candy distributor must use: 20 kilograms of the 20% fat-content chocolate and 80 kilograms of the 60% fat-content chocolate to create 100 kilograms of a 52% fat-content chocolate.
To create 100 kilograms of a 52% fat-content chocolate, the distributor needs to mix a 20% fat-content chocolate with a 60% fat-content chocolate. Let's use the variables x and y to represent the amounts of the 20% and 60% chocolates, respectively.
The sum of the two chocolates must equal 100 kilograms:
x + y = 100
The fat-content percentage must equal 52%:
0.20x + 0.60y = 0.52 * 100
Now, we'll solve the system of equations. From the first equation, we can express y as:
y = 100 - x
Substitute this expression for y in the second equation:
0.20x + 0.60(100 - x) = 52
Expand and simplify:
0.20x + 60 - 0.60x = 52
Combine like terms:
-0.40x = -8
Divide by -0.40 to find x:
x = 20
Now that we have x, we can find y:
y = 100 - 20 = 80
So, the candy distributor must use 20 kilograms of the 20% fat-content chocolate and 80 kilograms of the 60% fat-content chocolate to create 100 kilograms of a 52% fat-content chocolate.
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A gasoline engine takes in 1. 61 10 J of heat and delivers 3700 J of work per cycle. The heat is obtained by burning gasoline with a heat of combustion of 4. 60 10 J/g. (a) What is the thermal efficiency? (b) How much heat is discarded in each cycle? (c) What mass of fuel is burned in each cycle? (d) If the engine goes through 60. 0 cycles per second, what is its power output in kilowatts? In horsepower?
(a). The thermal efficiency is approximately 22.9%.
(b). The heat discarded in each cycle is approximately 1.6063 × [tex]10^6[/tex] J.
(c). The mass of fuel burned in each cycle is approximately 0.035 kg.
(d). The engine's power output is approximately 222 kW or 297.6 hp.
To solve this problem, let's use the following formulas and conversions:
Thermal efficiency (η) = (Useful work output / Heat input) * 100%Heat input = Heat of combustion * Mass of fuel burnedPower output (P) = Work done per cycle * Number of cycles per second1 kilowatt (kW) = 1000 watts (W)1 horsepower (hp) = 745.7 watts (W)Given:
Heat input (Qin) = 1.61 × [tex]10^6[/tex]J
Work done per cycle (W) = 3700 J
Heat of combustion of gasoline (H) = 4.60 × [tex]10^7[/tex] J/kg
Cycles per second (f) = 60.0 cycles/s
(a) To calculate the thermal efficiency:
Thermal efficiency (η) = (Useful work output / Heat input) * 100%
η = (W / Qin) * 100%
η = (3700 J / 1.61 × 10^6 J) * 100%
η ≈ 0.229 * 100%
η ≈ 22.9%
(b) To calculate the heat discarded in each cycle:
Heat discarded = Heat input - Useful work output
Heat discarded = Qin - W
Heat discarded = 1.61 × [tex]10^6[/tex] J - 3700 J
Heat discarded ≈ 1.6063 × [tex]10^6[/tex] J
(c) To calculate the mass of fuel burned in each cycle:
Heat input = Heat of combustion * Mass of fuel burned
Mass of fuel burned = Heat input / Heat of combustion
Mass of fuel burned = 1.61 × [tex]10^6[/tex] J / 4.60 × [tex]10^7[/tex] J/kg
Mass of fuel burned ≈ 0.035 kg
(d) To calculate the power output in kilowatts and horsepower:
Power output (P) = Work done per cycle * Number of cycles per second
P = W * f
P = 3700 J * 60.0 cycles/s
P = 2.22 × [tex]10^5[/tex] J/s
Power output in kilowatts:
P(kW) = P / 1000
P(kW) ≈ 2.22 × [tex]10^5[/tex] J/s / 1000
P(kW) ≈ 222 kW
Power output in horsepower:
P(hp) = P / 745.7
P(hp) ≈ 2.22 × [tex]10^5[/tex] J/s / 745.7
P(hp) ≈ 297.6 hp
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How far do you have to lift a 10kg bag of salt to do 250j of work?
You have to lift the 10kg bag of salt approximately 2.55 meters to do 250J of work.
To determine how far you have to lift a 10kg bag of salt to do 250J of work, we need to use the work-energy theorem and the formula for gravitational potential energy. The work-energy theorem states that the work done on an object is equal to the change in its potential energy. The formula for gravitational potential energy is:
PE = m * g * h
where PE is the potential energy, m is the mass (10kg), g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height the object is lifted.
Since the work done is 250J, we can set the potential energy equal to the work done:
250J = 10kg * 9.8 m/s² * h
Now, we need to solve for h:
250J = 98 kg*m/s² * h
h = 250J / 98 kg*m/s²
h ≈ 2.55 meters
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How much heat, in joules, is transferred into a system when its internal energy decreases by 125 J while it was performing 30. 5 J of work
94.5 J of heat was transferred out of the system. The first law of thermodynamics states that the change in the internal energy of a system is equal to the heat added to the system minus the work done by the system.
Mathematically, ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.
Given that the internal energy decreases by 125 J while performing 30.5 J of work, we can find the heat transferred into the system as follows:
ΔU = Q - W
-125 J = Q - 30.5 J
Q = -125 J + 30.5 J
Q = -94.5 J
The negative sign indicates that heat was transferred out of the system. Therefore, 94.5 J of heat was transferred out of the system.
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Estimate the lowest possible kinetic energy of a neutron contained in a typical nucleus of radius 1. 2×10−15m. Use the radius as the uncertainty in position for the neutron. [Hint: Assume a particle can have a kinetic energy as large as its uncertainty. ]
The uncertainty principle can be used to estimate the minimum kinetic energy of a neutron in a nucleus of a certain size. The resulting minimum energy is around [tex]10^{-24}[/tex] joules.
The uncertainty principle states that the product of the uncertainty in the position and momentum of a particle must be greater than or equal to Planck's constant divided by 4π.
Therefore, using the given radius of the nucleus as the uncertainty in position, we can calculate the minimum kinetic energy of a neutron in the nucleus by assuming it has an uncertainty in momentum equal to its uncertainty in position.
Using this approach, we have:
[tex]\Delta x = 1.2 \times 10 - 15 m[/tex] (uncertainty in position)
[tex]\Delta p = \Delta mv = \Delta m(\Delta x/\Delta t) = \Delta m(2\pi \Delta f \Delta x)[/tex] (uncertainty in momentum)
where Δm is the uncertainty in mass, Δf is the frequency of the neutron, and Δt is the time interval over which the position is measured.
Assuming a typical frequency of [tex]10^{21} Hz[/tex] and a mass uncertainty of 1 atomic mass unit [tex](1.67 \times 10^{-27} kg)[/tex], we obtain a minimum kinetic energy of approximately [tex]10^{-24} \;joules[/tex].
In summary, the minimum kinetic energy of a neutron contained in a typical nucleus of radius [tex]1.2 \times 10^{-15} m[/tex] can be estimated using the uncertainty principle.
This approach involves assuming an uncertainty in momentum equal to the uncertainty in position and using typical values for the frequency and mass uncertainty of the neutron. The resulting minimum kinetic energy is on the order of [tex]10^{-24} \;joules[/tex].
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A beam of light travels into a new denser medium causing the speed of light to change to 2. 5 x 10 8 m/s. What is the index of refraction for the new medium?
The index of refraction for the new medium is 1.2. The index of refraction is a measure of how much the speed of light is slowed down as it passes through a material.
It is defined as the ratio of the speed of light in a vacuum to the speed of light in the material. The formula for the index of refraction is:
n = c/v
where n is the index of refraction, c is the speed of light in a vacuum (approximately 3 x [tex]10^{8}[/tex] m/s), and v is the speed of light in the material.
In this case, we are told that the speed of light in the new medium is 2.5 x [tex]10^{8}[/tex] m/s. Plugging this into the formula, we get:
n = c/v
n = 3 x [tex]10^{8}[/tex] m/s / 2.5 x [tex]10^{8}[/tex] m/s
n = 1.2
Therefore, the index of refraction for the new medium is 1.2.
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Using what you learned from this lab describe how you receive colors from the various object observed in our world. discuss how we receive colors from objects to omit light such as tvs, objects i don’t emit light such as colored paper, and how filters on our eyes work such as sunglasses. keywords: phototons, wavelength, and colors that just red, green, and blue.
Color perception is determined by wavelengths of light, red, green, and blue make colors for objects that emit light. The color we see for objects not emitting light is based on reflected light. Sunglasses and filters change perceived colors by blocking certain wavelengths of light.
Color perception is a complex phenomenon that involves the interaction between light and objects in our environment. The colors that we see are determined by the wavelengths of photons that are reflected or emitted by objects. When light hits an object, some photons are absorbed while others are reflected, and the reflected photons are what we see as color.
For objects that emit light, such as TVs and computer screens, the colors are created by combining just three primary colors: red, green, and blue. By varying the intensity of these three colors, the screen can create a wide range of hues and shades.
For objects that do not emit light, such as colored paper, the color that we see is determined by the wavelengths of light that are reflected by the object. For example, a red piece of paper appears red because it reflects red light and absorbs other wavelengths.
Filters, such as sunglasses, work by selectively blocking certain wavelengths of light. This changes the colors that we perceive, as some colors are absorbed while others are allowed through.
In summary, color perception is based on the wavelengths of photons reflected or emitted by objects. For objects that emit light, colors are created by combining red, green, and blue.
For objects that do not emit light, the color that we see is determined by the wavelengths of light that are reflected. Filters, such as sunglasses, work by selectively blocking certain wavelengths of light to change the colors that we perceive.
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To cause sunburn on human skin by breaking a chemical bond within a skin cell, a photon with about
3.5 eV of energy is required. What is the required wavelength?
What is the wavelength?
The required wavelength to cause sunburn on human skin by breaking a chemical bond is 3.56 x 10⁻⁷ meters
How to calculate wavelength?Use the equation E=hc/λ, where E is the energy of the photon, h is Planck's constant, c is the speed of light, and λ is the wavelength.
First, convert the energy of the photon to joules (J) from electron volts (eV):
3.5 eV x 1.602 x 10⁻¹⁹ J/eV = 5.61 x 10⁻¹⁹ J
Next, substitute the values into the equation:
5.61 x 10¹⁹ J = (6.626 x 10⁻³⁴ J s)(3.0 x 10⁸ m/s)/λ
Solving for λ:
λ = (6.626 x 10⁻³⁴ J s)(3.0 x 10⁸ m/s)/(5.61 x 10⁻¹⁹ J) = 3.56 x 10⁻⁷ m
Therefore, the required wavelength is approximately 3.56 x 10⁻⁷ meters (or 356 nanometers), which falls in the ultraviolet (UV) region of the electromagnetic spectrum.
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A shell that is initially at rest explodes into two fragments, one fragment 25 times heavier than the other. If any gas from the explosion has negligible mass, then:.
The larger fragment moves at 1/25th the velocity of the smaller fragment.
By conservation of momentum, the total momentum of the system before and after the explosion must be equal. Since the shell is initially at rest, the total initial momentum is zero. After the explosion, the two fragments move in opposite directions with different velocities. Let the mass of the smaller fragment be m and the mass of the larger fragment be 25m. Then, by conservation of momentum:
0 = mv + (25m)(-v')
0 = v - 25v'
where v and v' are the velocities of the smaller and larger fragments, respectively, after the explosion. Solving for v', we get:
v' = v/25
Since the total kinetic energy of the system is also conserved, we can use the conservation of energy equation to solve for the velocities of the two fragments. Let E be the total kinetic energy of the system after the explosion. Then:
E = (1/2)mv^2 + (1/2)(25m)(v/25)^2
E = (1/2)mv^2 + (1/2)mv^2
E = mv^2
Therefore, the kinetic energy of the system after the explosion is equal to the kinetic energy of the smaller fragment before the explosion. Using this, we can solve for the velocity of the smaller fragment:
E = (1/2)mv^2
v = sqrt(2E/m)
And the velocity of the larger fragment is:
v' = v/25 = sqrt(2E/m)/25
So, the ratio of the velocities of the two fragments is:
v'/v = (sqrt(2E/m)/25) / sqrt(2E/m) = 1/25
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A 66-kg skier speeds down a trail, as shown in (Figure 1). The surface is smooth and inclined at an angle of 22 ∘ with the horizontal.
A)Complete the free-body diagram by adding the forces that act on the skier.
Draw the vectors with their tails at the black dot.
B)Determine the normal force acting on the skier. Express your answer in newtons.
(a) The free body diagram consist of three forces, normal force, weight of skier, and force of friction.
(b) The normal force acting on the skier is approximately 600 N.
What are the forces acting on the skier?The forces that act on the skier are:
Gravitational force or weight (W) acting vertically downward with a magnitude of W = mg.Normal force (N) acting perpendicular to the surface of the slope, with a magnitude equal to the component of the gravitational force perpendicular to the slope.Frictional force (F) acting parallel to the surface of the slope, opposing the motion of the skier.B) To determine the normal force acting on the skier, we need to find the component of the gravitational force perpendicular to the slope. This can be calculated using trigonometry:
N = mg cos(θ)
where;
θ is the angle of inclination of the slope with respect to the horizontal.Substituting the given values, we get:
N = (66 kg) x (9.8 m/s^2) x cos(22°)
N ≈ 600 N
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Waves in a lake are 5 meters in length and pass an anchored boat 2 seconds apart. What is the speed of the waves?
The speed of the waves passing the anchored boat can be calculated using the formula Speed = Wavelength / Period. With a wavelength of 5 meters and a period of 2 seconds, the speed of the waves is 2.5 meters per second.
The speed of the waves can be determined by the formula:
Speed = Wavelength / Period
Where wavelength is the distance between two consecutive wave crests, and period is the time it takes for two consecutive wave crests to pass a fixed point (in this case, the anchored boat).
We know that the wavelength of the waves is 5 meters. We also know that the period is 2 seconds. Therefore:
Speed = 5 meters / 2 seconds = 2.5 meters/second
So the speed of the waves is 2.5 meters per second.
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Compare and contrast compounds and mixtures (select all that are true):
Compounds are pure substances, but mixtures are not.
When two elements bond together into a compound they have new properties.
o When two substances are mixed together in a mixture, they keep their individual properties.
Compounds are physically combined.
O Mixtures are chemically combinded.
Compounds are chemically combined pure substances with new properties, while mixtures are physically combined substances that retain their individual properties.
Compare and contrast compounds and mixtures (select all that are true):
1. Compounds are pure substances, but mixtures are not.
This statement is true. Compounds are pure substances formed by the chemical combination of two or more elements in a fixed ratio, while mixtures are combinations of two or more substances that are not chemically combined and can be physically separated.
2. When two elements bond together into a compound they have new properties.
This statement is true.
When elements chemically bond to form a compound, they create a substance with unique properties different from the individual elements.
3. When two substances are mixed together in a mixture, they keep their individual properties.
This statement is true.
In a mixture, the substances retain their individual properties because they are not chemically combined.
4. Compounds are physically combined.
This statement is false.
Compounds are chemically combined, as elements form chemical bonds to create a compound with new properties.
5. Mixtures are chemically combined.
This statement is false.
Mixtures are physically combined, as the substances in a mixture are not chemically bonded and retain their individual properties.
In summary, compounds are chemically combined pure substances with new properties, while mixtures are physically combined substances that retain their individual properties.
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When training for muscular endurance, how should the athlete alter the number of repetitions he or she performs in an
exercise?
O More reps should be executed.
O Fewer reps should be executed.
O Raising or lowering the number should depend on the exercise and goals.
O The number of reps should not be changed.
Deployment Worksheet 2b - Work 1. A 1400 N force is applied parallel to a horizontal surface. It pushes an 80 kg box 2 m across the surface. What work is done
The work done in pushing the 80 kg box 2 meters across the surface with a 1400 N force applied parallel to the surface is 2800 Joules.
To find the work done, we need to consider the force applied, the displacement, and the angle between them.
In this case, the force (F) applied is 1400 N, the displacement (d) is 2 meters, and since the force is applied parallel to the horizontal surface, the angle (θ) between the force and the displacement is 0 degrees. The formula to calculate work (W) is:
W = F × d × cos(θ)
Now, let's substitute the given values:
W = 1400 N × 2 m × cos(0°)
Since cos(0°) = 1, the equation becomes:
W = 1400 N × 2 m × 1
W = 2800 J (Joules)
So, the work done in pushing the 80 kg box 2 meters across the surface with a 1400 N force applied parallel to the surface is 2800 Joules.
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Object A is traveling at half the speed of light colliding with object B that is stationary. How does object A experience time in comparison to object B and how does object B experience time in comparison to object A before there collision?
Object A will experience time passing slower than Object B due to its velocity, while Object B will experience time passing at its normal rate. As the objects approach each other, their perception of time will start to converge.
According to the theory of relativity, time appears to be different for two observers in relative motion. In this scenario, Object A is traveling at half the speed of light, while Object B is stationary.
From Object A's perspective, time appears to be moving slower for Object B, while for Object B, time appears to be moving at its normal rate. This is due to the time dilation effect, which is a consequence of special relativity.
As Object A approaches Object B, both objects will experience a different perception of time. Object A will perceive time to be passing more slowly, while Object B will perceive time to be passing at its normal rate. However, this difference will be negligible due to the low relative velocity of the objects.
In summary, Object A will experience time passing slower than Object B due to its velocity, while Object B will experience time passing at its normal rate. As the objects approach each other, their perception of time will start to converge.
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Which characteristic of the moon made it the best choice for the first manned space missions instead another celestial body like mars?.
Here are some reasons why the Moon was chosen for the first manned space missions:
The moon's proximity to Earth and its relatively low gravity made it the best choice for the first manned space missions, as it was a more feasible target to reach and return from compared to other celestial bodies like Mars.
Additionally, the moon's lack of atmosphere and magnetic field meant that it presented fewer technical challenges for spacecraft to land and operate on its surface.
The characteristic of the Moon that made it the best choice for the first manned space missions, such as the Apollo missions, was its relative proximity to Earth. Compared to other celestial bodies in our solar system, the Moon is the closest and most accessible.
1. Proximity: The Moon is located at an average distance of about 384,400 kilometers (238,900 miles) from Earth. This relatively short distance made it feasible for manned missions using the available technology at the time. Sending astronauts to Mars or other distant celestial bodies would have required significantly more time, resources, and technological advancements.
2. Exploration and Preparation: Before attempting manned missions to more distant destinations, such as Mars, it was important to gain experience and knowledge about human space travel. The Moon provided a relatively nearby and manageable target for astronauts to explore, learn about spaceflight operations, and conduct experiments. It served as a stepping stone for future space exploration endeavors.
3. Safety and Communication: The Moon's proximity to Earth allowed for more straightforward communication and a shorter travel duration. In case of emergencies or technical difficulties during the missions, direct communication and potential rescue operations were more feasible compared to missions to more distant locations like Mars.
4. Scientific Value: The Moon also presented scientific value in terms of studying its geology, lunar samples, and the potential for resource utilization. By conducting manned missions to the Moon, scientists and researchers were able to gather valuable data about the Moon's composition, formation, and potential for future exploration and scientific research.
It's important to note that while the Moon was a logical choice for the first manned space missions, the desire to explore and study other celestial bodies, including Mars, remains a significant goal for future space exploration endeavors.
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5. The planet Mars has a mass about one-tenth the mass of Earth. Even though Mars has two moons, their tidal forces have a much weaker effect on Mars than Earth's moon does on Earth. Why do you think this is ? Use the data in the tables to support your prediction
This is supported by the data in the tables, which show that the moon of Mars has a much smaller tidal force (0.2 m/s²) than the moon of Earth (2.2 m/s²).
Why is Mars unique from Earth?
The diameter of Earth is about twice that of Mars. Mars would be the size of a ping-pong ball if Earth were a baseball. While Mars has no liquid water, nearly 70% of Earth does. The surface of the Earth receives more than 100 degrees Fahrenheit of solar heating.
The difference in mass between Mars and Earth is a significant factor in the difference between the tidal forces each planet experiences. Since Mars is much less massive than Earth, it has much less gravity and therefore a weaker pull on its moons. This means that the moons of Mars are much less able to exert a tidal force on the planet. This is supported by the data in the tables, which show that the moon of Mars has a much smaller tidal force (0.2 m/s²) than the moon of Earth (2.2 m/s²).
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(b)
(iii) Explain in terms of photons what effect, if any, increasing the
intensity of this radiation would have on the number of electrons
ejected per second, and on their maximum kinetic energy.
[3]
In 1902, Einstein's equation: Exmax hf- was revolutionary because it gave
strong evidence for light behaving as particles. Explain why this theory was
controversial in 1902, but is now accepted as standard pre-university physics.
[4]
Answer:
(iii) Increasing the intensity of radiation would increase the number of photons hitting the surface per second. As a result, the number of electrons ejected per second would also increase, as the photoelectric effect is a stochastic process. However, the maximum kinetic energy of the ejected electrons would not change, as it depends solely on the frequency of the incident photons.
In terms of photons, increasing the intensity of radiation would mean an increase in the number of photons per unit area per second. This would increase the probability of a photon interacting with an electron and causing ejection.
(iv) Einstein's theory that light behaved as particles, or photons, was controversial in 1902 because it contradicted the established wave theory of light. Many physicists at the time believed that light waves were similar to sound waves, and that they propagated through a medium called the "luminiferous ether." Einstein's theory challenged this idea by suggesting that light was made up of discrete particles, or photons, with specific energies.
However, Einstein's theory was later supported by experiments such as the photoelectric effect, which demonstrated that light could indeed behave like particles. Furthermore, the theory of quantum mechanics developed in the early 20th century provided a more complete understanding of the dual nature of light, which can behave as both particles and waves. Today, the particle nature of light is widely accepted and is a standard concept in pre-university physics.
Instruction: Answer all questions Time: 1. 5hrs An electron is placed in a uniform electric field with field strength of 150kvm Calculate the duration for it to travel 30mm from its stationary Position Give an explanation for your answer.
The duration for the electron to travel 30 mm in a uniform electric field with a field strength of 150 kV/m is approximately 6.37 x 10⁻⁸ seconds.
What is acceleration?The rate at which velocity changes with respect to time.
To solve this problem, we can use the equation for the acceleration of an electron in an electric field:
a = F/m = qE/m
where a is the acceleration, F is the force, m is the mass of the electron, q is the charge of the electron, and E is the electric field strength.
We can rearrange this equation to solve for the time it takes for the electron to travel a certain distance:
t = √(2d/a)
where d is the distance traveled.
Plugging in the given values, we get:
a = (1.602 x 10⁻¹⁹ C)(150 x 10³ V/m)/(9.109 x 10⁻³¹ kg) = 2.62 x 10¹⁴ m/s²
d = 30 mm = 0.03 m
t = √(2 x 0.03 m / 2.62 x 10¹⁴ m/s²) = 6.37 x 10⁻⁸ s
Therefore, the duration for the electron to travel 30 mm in a uniform electric field with a field strength of 150 kV/m is approximately 6.37 x 10⁻⁸ seconds.
Explanation: The acceleration of the electron in the electric field is independent of its initial velocity. Hence, the electron will continue to accelerate at a constant rate until it reaches the end of the distance. Once it reaches the end, it will have attained a maximum velocity and will continue to move at a constant velocity if there are no other forces acting on it. Therefore, the time taken to travel the distance depends only on the acceleration and the distance traveled.
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