The rate at which the bullets are fired is 200 bullets/min, or 3.33 bullets/s. The magnitude of the average force on Superman's chest from the stream of bullets is approximately 78,299 N.
To calculate the magnitude of the average force on Superman's chest from the stream of bullets, we can use the equation for impulse:
I = FΔt
where I is the impulse, F is the force, and Δt is the time interval over which the force is applied.
Assuming that the bullets rebound straight back with no change in speed, the time interval over which each bullet is in contact with Superman's chest is given by:
Δt = 2l/v
where l is the thickness of Superman's chest, and v is the velocity of the bullet.
Substituting the given values, we get:
Δt = 2(0.1 m)/(680 m/s)
= 2.94 × 10^-4 s
The total impulse delivered to Superman's chest by each bullet is equal to its momentum change, which is given by:
I = Δp = 2mv
where m is the mass of the bullet, and v is its velocity.
Substituting the given values, we get:
I = 2(5.1 × 10^-3 kg)(680 m/s)
= 6.92 Ns
The rate at which the bullets are fired is 200 bullets/min, or 3.33 bullets/s. Therefore, the total impulse delivered to Superman's chest per second is:
I_tot = 3.33 bullets/s × 6.92 Ns/bullet
= 23.04 Ns/s
The average force on Superman's chest can be calculated by dividing the total impulse by the time interval over which it is delivered:
F_avg = I_tot/Δt
= 23.04 Ns/s / 2.94 × 10^-4 s
= 78,299 N
This is an enormous amount of force, far greater than any normal human could withstand. However, since Superman is a fictional character with superhuman strength and invulnerability, he can withstand this force without harm.
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What type of water is most of the water on the earth?
A.
saltwater
B.
groundwater
C.
lake water
D.
freshwater
Answer:
Saltwater
Explanation:
Because of the oceans.
Answer:
A: Saltwater
Explanation:
97% of all water on earth is saltwater.
an object with mass m is suspended at rest from a spring with a spring constant of 200 n/m . the length of the spring is 5.0 cm longer than its unstretched length l, as shown above. a person then exerts a force on the object and stretches the spring an additional 5.0 cm. what is the total energy stored in the spring at the new stretched length?
The total energy stored in the spring at the new stretched length is 2.25 Joules.
The potential energy stored in a spring is given by the formula:
U = (1/2) k x²
where U is the potential energy, k is the spring constant, and x is the displacement from the equilibrium position. Initially, the spring was stretched by 5.0 cm, so its displacement from the equilibrium position is x = 0.05 m + 0.05 m = 0.10 m.
The force applied to stretch the spring is given by Hooke's law, F = kx, where F is the force applied, k is the spring constant, and x is the displacement from the equilibrium position. The force applied to stretch the spring by an additional 5.0 cm is,
F = kx = (200 N/m)(0.05 m) = 10 N
The total displacement of the spring is now x = 0.10 m + 0.05 m = 0.15 m. The total potential energy stored in the spring is:
U = (1/2) k x² = (1/2)(200 N/m)(0.15 m)² = 2.25 J
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a 10-kg dog is runnng with a speed of 5.0 m/s. what is the minimum work required to stop the dog in 2.40 seconds? group of answer choices 125 j 75 j 50 j 100 j
The minimum work required to stop a 10-kg dog running with a speed of 5.0 m/s in 2.40 seconds is 125 J .
We are given that a 10-kg dog is running with a speed of 5.0 m/s. We need to find the minimum work required to stop the dog in 2.40 seconds. Work done to stop the dog = change in kinetic energy of the dog.
Let the initial velocity of the dog be u = 5.0 m/s.
The final velocity of the dog when it is stopped is v = 0 m/s.
The mass of the dog is m = 10 kg. Work done = 1/2 × m × (v² - u²).
Work done = 1/2 × 10 × (0² - 5.0²)Work done = 1/2 × 10 × (-25)
Work done = -125 J.
We get a negative value for the work done because the direction of work is opposite to the direction of motion of the dog. Therefore, the minimum work required to stop the dog in 2.40 seconds is 125 J.
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HELP PLS URGENT
(b) Three forces of magnitude 6 N, 2 N, and 3 N act on a small object in directions North, South, and West respectively. Find the direction and magnitude of the resultant force. If the object is free to move and its mass is 0.2 kg calculate the initial acceleration.
Answer:
The net force in the North-South direction is 6 N - 2 N = 4 N towards the North. The net force in the East-West direction is 3 N towards the West. The magnitude of the resultant force can be found using the Pythagorean theorem: sqrt(4^2 + 3^2) = 5 N.
The direction of the resultant force can be found using trigonometry: tan(θ) = 3/4, so θ = arctan(3/4) = 36.87° West of North.
The acceleration of the object can be found using Newton’s second law: F = ma, so a = F/m = (5 N)/(0.2 kg) = 25 m/s^2.
So, the initial acceleration of the object is 25 m/s^2 in the direction
Explanation:
36.87° West of North.
What is the initial energy for the scenario below? You and a bike have a combined mass of 100 kg and are going 5 m/s. You then go up a hill as far as you can before coming to a stop.
The initial energy of the system is 1250 J, which is the kinetic energy of the bike and rider before they start going up the hill. This energy is then converted to potential energy as the bike and rider move up the hill and come to a stop at the top.
To calculate the initial energy, we need to use the kinetic energy formula:
KE = 0.5 * m * v²
where KE is the kinetic energy, m is the mass, and v is the velocity.
Substituting the given values, we get:
KE = 0.5 * 100 kg * (5 m/s)²
= 0.5 * 100 kg * 25 m²/s²
= 1250 J
Therefore, the initial energy of the system is 1250 joules.
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what types of exoplanets are easiest to detect with the transit method? group of answer choices large planets far from their host stars hot planets far from their host stars large planets close to their host stars hot planets close to their host stars
The types of exoplanets that are easiest to detect with the transit method are: large planets close to their host stars and hot planets close to their host stars.
What is an exoplanet, An exoplanet or extrasolar planet is a planet that orbits a star outside of the Solar System's planetary system. It is detected indirectly by measuring its gravitational influence on its host star, its thermal or other radiation, or the effects of its atmosphere on the light from its host star as it passes through it.
What is the transit method, The transit method is one of the ways that exoplanets can be detected. It entails detecting a dip in a star's brightness when an exoplanet passes in front of it. A change in the star's apparent brightness is caused by the decrease in the amount of light reaching the observer due to the exoplanet being in the way.
What types of exoplanets are easiest to detect with the transit method, The transit method is most effective for detecting large planets close to their host stars or hot planets close to their host stars. This is due to the fact that such exoplanets are more likely to cause a significant decrease in their host star's brightness when they transit. As a result, smaller exoplanets or those far from their host stars may be difficult to detect with this technique.
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how does the number of lines in the emission spectrum for element compare with the number of lines in the absorption spectrum ?
The number of lines in the emission spectrum for an element compares with the number of lines in the absorption spectrum in that they are generally equal. When an element is heated, it emits light at specific wavelengths, creating an emission spectrum. Conversely, when light passes through a cool gas of that element, the same wavelengths of light are absorbed, creating an absorption spectrum.
1. An element is heated, and its electrons gain energy and move to higher energy levels.
2. The heated element emits light at specific wavelengths, creating an emission spectrum with distinct lines.
3. When light passes through a cool gas of the same element, electrons absorb the energy from the light and move to higher energy levels.
4. The absorbed wavelengths of light create an absorption spectrum with distinct lines.
5. The emission and absorption spectra for a given element have the same number of lines, as they represent the same energy level transitions within the element's electrons.
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if two objects in space are moved to a distance of 7 times further from each other than they were before, by what factor has the gravitational force changed? (hint: it should be a factor less than 1.
The gravitational force has changed by a factor less than 1, which is 1/49 or approximately 0.0204.
When two objects in space are moved to a distance of 7 times further from each other than they were before, the gravitational force has changed by a factor less than 1. Gravity is a natural phenomenon that arises due to the attraction between two objects with mass.
Gravity is directly proportional to the mass of the objects and inversely proportional to the square of the distance between them. The formula for the gravitational force is given by:Fg = (G x m1 x m2) / r2where, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.
In the given case, if two objects in space are moved to a distance of 7 times further from each other than they were before, then their distance will become 7r. Hence, the new gravitational force will be given by:F'g = (G x m1 x m2) / (7r)2Simplifying the above expression:F'g = Fg/49.
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forces and motion until test for physical science eginuity credit recovery ????
Forces and motion are fundamental concepts in physics that help us understand the behavior of objects in motion. Forces can cause objects to accelerate, change direction, or stop moving altogether.
The three laws of motion proposed by Sir Isaac Newton provide a framework for understanding how forces affect motion. The first law states that an object at rest will stay at rest, and an object in motion will stay in motion, unless acted upon by an external force. The second law states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. The third law states that every action has an equal and opposite reaction. To test these concepts in physical science, experiments can be designed to measure the effects of forces on motion, such as the acceleration of objects on inclined planes, the motion of objects in free fall, or the forces involved in collisions.
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The complete question is
Forces and motion until test for physical science eginuity credit recovery ?
question 11 pts which of the following statements about inductors is correct? group of answer choices inductors store energy by building up charge. when an inductor and a resistor are connected in series with a dc battery, the current in the circuit is reduced to zero in one time constant. when it is connected in a circuit, an inductor always resists having current flow through it. when an inductor and a resistor are connected in series with a dc battery, the current in the circuit is zero after a very long time. an inductor always resists any change in the current through it.
An inductor always resists any change in the current through it. The correct statement about inductors is D.
This is due to the property of inductance, which is the ability of an inductor to generate a voltage that opposes any change in the current through it. This is described by Faraday's law of electromagnetic induction. As a result, inductors are commonly used in circuits to smooth out changes in current, and also to filter out high-frequency signals.
Option A is incorrect because inductors store energy in a magnetic field, not by building up charge. Option B is incorrect because an inductor allows current to flow through it, but opposes changes in the current. Option C is incorrect because the current in the circuit will eventually become steady, but not zero. Hence option D is correct.
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why parachutist travel at constant velocity for the last part of his drop
Explanation:
Air friction finally builds up and equals the magnitude of his weight.
The drag force resists the downward movement of gravity.
Eventually, they reach an equilibrium where acceleration = 0 and velocity remains constant.
Question 12 (1 point)
Jared has been running in the park on a hot day when he feels his legs begin
spasming in an unusual way. He feels shaky. He thinks back to what he learned in
fitness class about heat emergencies for what to do. What should Jared do FIRST?
Run home to take a cold shower.
Find a cool place to rest.
Begin stretching carefully.
Buy a sports drink with electrolytes.
Find a cool place to rest. It is important for Jared to get out of the heat and lower his body temperature as quickly as possible.
What is temperature?Temperature is a physical property of matter that is a measure of the average kinetic energy of the particles in a substance. It is the measure of hot and cold, and is usually expressed in terms of the Celsius, Fahrenheit, or Kelvin scale. Temperature affects the state of matter, and can be used to determine whether a substance is solid, liquid, or gas. Additionally, temperature affects the rate of chemical reactions, and can be used as a metric in which to measure the amount of energy being released or absorbed. Temperature is very important to all forms of life, as living organisms rely on temperature to survive and thrive.
Taking a cold shower, stretching and replenishing electrolytes can all happen after he finds a cool place to rest.
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a basketball has a diameter of about 25 cm (0.25 meters). if i measure the apparent angular diameter of a basketball to be 357 arc seconds, what is its distance from me in meters?
A basketball has a diameter of about 25 cm (0.25 meters). if i measure the apparent angular diameter of a basketball to be 357 arc seconds: the basketball is about 2.52 meters away from you.
To solve this problem, we can use the small angle formula which relates the angular size of an object, the actual size of the object, and its distance from the observer:
angular size = actual size / distance
First, we need to convert 357 arc seconds to radians:
1 arc second = 1/60 arc minute
1 arc minute = 1/60 degree
1 degree = π/180 radians
Therefore:
357 arc seconds = (357/60) arc minutes = 5.95 arc minutes
5.95 arc minutes = 5.95/60 degrees = 0.0992 radians
Now we can use the small angle formula:
0.0992 radians = 0.25 meters / distance
Solving for distance, we get:
distance = 0.25 meters / 0.0992 radians
distance = 2.52 meters
Therefore, the basketball is about 2.52 meters away from you.
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a mass of 0.150 kg is attached to a spring with a force constant of 3.58 n/m and undergoes simple harmonic oscillations with an amplitude of 7.50 cm. what is the total mechanical energy of the system?
The full Mechanical energy of the machine is 0.01 J.
Mass of the cart, m = 0.15 kg
The force constant of the spring, K = 3.58 N/m
The amplitude of the oscillations, A = 7.5 cm = 0.075 m
[tex]E=\frac{1}{2} KA^2[/tex]
[tex]E= \frac{1}{2} *3.58*(0.075)^2\\E= 0.01J[/tex]
Mechanical energy is a form of energy associated with the motion and position of objects. It is the sum of two components: kinetic energy and potential energy. Kinetic energy is the energy possessed by an object due to its motion and is dependent on the mass of the object and its velocity. Potential energy is the energy an object possesses due to its position or state, and it is dependent on the height of an object above a reference point and its mass.
Mechanical energy is conserved in an isolated system where no external forces act on it. This means that the total mechanical energy of the system remains constant, even if the kinetic and potential energy of individual objects within the system change. Mechanical energy plays a crucial role in many aspects of physics, from the study of mechanics to the understanding of thermodynamics and electromagnetism.
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which type of scale has all the properties of an interval scale with the additional attribute of representing absolute quantities, characterized by a meaningful absolute zero?
The type of scale that has all the properties of an interval scale with the additional attribute of representing absolute quantities, characterized by a meaningful absolute zero, is a ratio scale.
The type of scale that has all the properties of an interval scale with the additional attribute of representing absolute quantities, characterized by a meaningful absolute zero is a ratio scale. In a ratio scale, the values not only have an order and equal intervals but also a true, non-arbitrary zero point.
This means that ratios of values are meaningful, and one can meaningfully say that a value is, for example, twice or half of another value. Examples of ratio scales include measurements of weight, length, time, temperature in Kelvin, and counts of discrete objects. Ratio scales provide the most precise and informative type of measurement and are widely used in scientific and statistical analysis.
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a particle of mass m is embedded at a distance r/4 from the center of a massless circular disc of radius r which can roll without slipping down a plane inclined at an angle a with the horizontal. Use the Lagrangian method to write the dif- ferential equation of motion for the system
The differential equation of motion for the system using the Lagrangian method is D²θ/Dt² + (g/[(19/8) r]sin α)θ = 0.
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The differential equation of motion for the system is given by the Lagrangian method when a particle of mass m is embedded at a distance r/4 from the center of a massless circular disc of radius r that can roll without slipping down a plane inclined at an angle a with the horizontal. Using the Lagrangian method, the differential equation of motion for
the system is given as follows:L = T - VL = [1/2 m(r² + (r/4)²)ω² + 1/2 Iω²] - mgrsin(α)r/4Here, I = [1/2 m(r/2)²] + m(r/4)²I = [1/2 m(r²/4 + r²/16)] + m(r²/16)I = m(r²/8)Therefore, I = mr²/4Then, the expression of Lagrangian can be given as:L = [1/2 m(r² + r²/16)ω² + 1/2 (mr²/4)ω²] - mgrsin(α)r/4L = [1/2 m(17r²/16)ω² + (1/8)mω²] - mgrsin(α)r/4L = [1/8 mω²(17r² + 2r²) - mgrsin(α)r/4]L = [1/8 mω²(19r²) - mgrsin(α)r/4]So, the Lagrangian equation of motion for the system is given as:D²θ/Dt² + (g/[(19/8) r]sin α)θ = 0
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the diagram below illustrates the geometry of lunar phases with the moon shown in 8 positions in its orbit. which numbered position with a first quarter moon?
The diagram you are referring to demonstrates the various Lunar phases as the Moon orbits Earth. To identify the numbered position representing the first quarter moon, let's understand the different lunar phases.
The primary lunar phases are:
1. New Moon
2. First Quarter
3. Full Moon
4. Last Quarter
These phases occur as the Moon orbits Earth, with the illuminated side of the Moon (the side facing the Sun) changing based on its position relative to Earth.
In the case of the first quarter moon, it occurs when the Moon has completed one-quarter of its orbit around Earth since the new moon. During this phase, half of the Moon's illuminated side is visible from Earth, making it appear as a semicircle in the sky.
Now, let's consider the numbered positions in the diagram:
1. New Moon - Moon is between Earth and the Sun, and its illuminated side is facing away from Earth.
2. Waxing Crescent - A small part of the illuminated side is visible, as the Moon moves away from the New Moon position.
3. First Quarter - The Moon has completed one-quarter of its orbit, and half of the illuminated side is visible from Earth.
4-7. Waxing Gibbous, Full Moon, Waning Gibbous, and Last Quarter - Other positions/phases as the Moon continues its orbit.
8. Waning Crescent - The Moon is almost back to its New Moon position.
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reflections from a thin layer of air between two glass plates cause constructive interference for a particular wavelength of light l. by how much must the thickness of this layer be increased for the interference to be destructive?
To achieve destructive interference, the thickness of the air layer must be increased by a distance of (m + 1/4) times the wavelength of the light.
2t = mλ
2t = (m + 1/2)λ
To find the difference in the thickness required for destructive interference, we can subtract the two equations:
2t - 2t' = (m + 1/2)λ - mλ
Simplifying this equation, we get:
t' = (m + 1/4)λ
Interference refers to the phenomenon where two or more waves overlap and interact with each other. When waves of the same frequency and amplitude meet, they can either add up or cancel out, depending on their relative phase. This phenomenon is known as constructive interference and destructive interference, respectively.
Constructive interference occurs when two waves are in phase with each other, meaning that their peaks and troughs line up, resulting in a wave with a larger amplitude. Destructive interference, on the other hand, occurs when two waves are out of phase with each other, meaning that their peaks and troughs are offset, resulting in a wave with a smaller amplitude. Interference is a fundamental concept in many areas of physics, including optics, acoustics, and quantum mechanics.
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the north pole of a magnet is moved toward a copper loop, as shown below. if you are looking at the loop from above the magnet, will you say the induced current is circulating clockwise, counterclockwise, or is equal to 0?
When the north pole of a magnet is moved toward a copper loop, if you are looking at the loop from above the magnet, you will say the induced current is circulating counter clockwise.
An induced current is a current that is generated when a magnetic field moves through a conductor or wire loop. When the magnetic field lines cut across a wire loop or conductor, it generates a voltage across the loop, causing an electric current to flow through it, which is known as an induced current.
The direction of the induced current is dependent on the polarity and direction of the magnetic field lines and the direction of motion of the magnetic field relative to the wire loop.
To determine the direction of the induced current, we must use the right-hand rule, which states that if the thumb of your right hand points in the direction of the magnetic field line, and your fingers wrap around the wire loop in the direction of motion of the magnetic field,
then the direction of the induced current in the wire loop is determined by the direction of your extended fingers.
In this case, the north pole of the magnet is moving toward the copper loop, which generates a magnetic field in the wire loop in the opposite direction to that of the north pole of the magnet. As a result, the induced current will circulate counterclockwise through the copper loop if you are looking at it from above the magnet.
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a 32-kg child decides to make a raft out of empty 1.0-l water bottles and duct tape. neglecting the mass of the duct tape and plastic in the bottles, what minimum number of water bottles will the child need to be able to stay dry on the raft?
Ignoring the mass of duct tape and plastic in the bottles, a child will need at least 4 water bottles to stay dry on the raft. The child will need at least four water bottles to stay dry on the raft.
The buoyancy force exerted by the water on the raft must be greater than or equal to the weight of the child to keep the child afloat and dry on the raft. The buoyancy force is given by Archimedes' principle, which states that it is equal to the weight of the water displaced by the raft.
The volume of each 1.0 L water bottle is 0.001 m^3. The density of water is approximately 1000 kg/m^3. Therefore, each water bottle has a buoyant force of:
Buoyant force = Volume of water displaced x Density of water x Acceleration due to gravity
Buoyant force = 0.001 m^3 x 1000 kg/m^3 x 9.81 m/s^2
Buoyant force = 9.81 N
To find the minimum number of water bottles needed to keep the child afloat, we need to divide the weight of the child by the buoyant force of one water bottle:
Minimum number of water bottles = Weight of child / Buoyant force per bottle
Minimum number of water bottles = 32 kg / 9.81 N
Minimum number of water bottles = 3.26 (rounded up to 4)
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7. (a) How much heat energy would be required to convert 2.5kg of ice at 10 °C to steam at 100 °C?
Answer:
the answer up top is correct
A 14.0 kg stone slides down a snow-covered hill (the figure (
Figure 1)), leaving point A with a speed of 12.0 m/s. There is
no friction on the hill between points A and B, but there is friction
on the level ground at the bottom of the hill, between B and the
wall. After entering the rough horizontal region, the stone travels
100 m and then runs into a very long, light spring with force
constant 2.10 N/m. The coefficients of kinetic and static friction
between the stone and the horizontal ground are 0.20 and 0.80,
respectively.
how far will the stone compress the spring?
You will pilot your drone through a series of obstacles. While doing so one of your rescue team members will document the time it takes you to fly from one obstacle to the next. That data will be populated in the following table:
My data table
(position) (distance) (time) (type of maneuver)
(Start to obstacle 1) (13’6”) (9 seconds) (around)
(obstacle 1 to obstacle 2) (31’1”) (20 seconds) (under)
(Obstacle 2 to obstacle 3) (27’3”) (38 seconds) (Precision landing)
(Obstacle 3 to End) (35’6”) (13 seconds) (Precision landing)
You will now present your data using three visual tools. You may create these illustrations using any tools you like Import pictures of your work into this performance task.
I only need someone to do me a graph for Position - Velocity Graph
The graph will be such that a blue line represents the position of the drone over time, while the orange line represents its velocity.
How to explain the graphA position-velocity graph, also known as a PV graph or a phase space plot, is a graphical representation of an object's position and velocity over time. It is a two-dimensional graph where the x-axis represents position and the y-axis represents velocity.
As you can see, the drone starts off relatively slow, then accelerates quickly to reach its maximum velocity during the second maneuver, before slowing down again for the final two maneuvers.
This graph gives a visual representation of how the drone's position and velocity change over time during the course of the obstacles.
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light from a slit passes through a transmission diffraction grating of 400 lines/mm, which is located 2.9 m from a screen. what are the distances on the screen (from the unscattered slit image) of the three brightest visible (first-order) hydrogen lines?
Distances on the screen from the central maximum to the first-order maximum for the three brightest visible hydrogen lines are:
y1 = 0.487 m, y2 = 0.357 m and y3 = 0.319 m.
How to determine Distances?The distance on the screen from the central maximum (unscattered slit image) to the first-order maximum can be found using the formula:
d sin θ = mλ
where d is the spacing between adjacent lines on the diffraction grating, θ is the angle between the incident beam and the diffracted beam, m is the order of the maximum, and λ is the wavelength of the light. For the first-order maximum, m = 1.
The spacing between adjacent lines on the diffraction grating is:
d = 1/400 mm/line
= 2.5 × 10⁻⁶ m/line
For hydrogen, the wavelengths of the three brightest visible lines in the Balmer series are:
λ1 = 656.3 nm
λ2 = 486.1 nm
λ3 = 434.0 nm
To find the angles θ for each of these wavelengths, we rearrange the equation:
θ = sin⁻¹ (mλ/d)
For m = 1 and λ = λ1:
θ1 = sin⁻¹ (1 × 656.3 × 10⁻⁹m / (2.5 × 10⁻⁶m)) = 0.168 radians
The distance on the screen from the central maximum to the first-order maximum for this wavelength is:
y1 = θ1 L = (0.168 radians) (2.9 m) = 0.487 m
Similarly, for m = 1 and λ = λ2:
θ2 = sin⁻¹ (1 × 486.1 × 10⁻⁹ m / (2.5 × 10⁻⁶m))
= 0.123 radians
y2 = θ2 L = (0.123 radians) (2.9 m) = 0.357 m
And for m = 1 and λ = λ3:
θ3 = sin⁻¹ (1 × 434.0 × 10⁻⁹m / (2.5 × 10⁻⁶m)) = 0.110 radians
y3 = θ3 L = (0.110 radians) (2.9 m) = 0.319 m
Therefore, the distances on the screen from the central maximum to the first-order maximum for the three brightest visible hydrogen lines are:
y1 = 0.487 m
y2 = 0.357 m
y3 = 0.319 m
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Which one is greater among 40°C, 40°F and 40K?
Answer:
To compare these temperatures, we need to convert them to the same unit of temperature.
To convert Celsius (°C) to Kelvin (K), we add 273.15 to the Celsius value.
40°C + 273.15 = 313.15 K
To convert Fahrenheit (°F) to Celsius (°C), we can use the formula:
°C = (°F - 32) * 5/9
So,
40°F = (40 - 32) * 5/9 = 4.44°C
Now, we can convert 4.44°C to Kelvin using the formula:
4.44°C + 273.15 = 277.59 K
So the order from smallest to largest temperature is:
40°F < 4.44°C < 40°C < 277.59 K
Therefore, 40K is the greatest temperature among the three.
which of the following is not a form of kinetic energy a. thermal energy b. mechanical energy c. elastic energy d. sound energy
c. Elastic energy is not a form of kinetic energy.
What is kinetic energy?
Kinetic energy is the energy generated by an object's movement or motion. It's the energy stored in moving objects, and it's dependent on the object's mass and speed. As the object's mass and velocity rise, so does the amount of kinetic energy it possesses.
Types of kinetic energy include:
Mechanical energy: The total energy stored in a moving object's position and motion is known as mechanical energy.
Thermal energy: Thermal energy is the energy that results from the motion of particles in a substance. The greater the speed of the particles, the greater the thermal energy.
Sound energy: The energy created by the vibration of an object is known as sound energy. It travels in the form of waves through the air.
Elastic energy: Elastic energy is the energy kept in an object when it is compressed or extended. For instance, when you extend a rubber band or compress a spring, the energy stored in them is elastic energy.
Therefore, from the given options, elastic energy is not a type of kinetic energy.
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imagine that radar had never been invented and that we instead had to rely on a less reliable method of measuring distances in our solar system. if that method led us to underestimate the earth-sun distance by 10%, how would it affect other measurements in the distance chain?
Underestimating the Earth-Sun distance by 10% would lead to a 10% error in all other measurements in the distance chain within our solar system, which would significantly impact our understanding of the size and scale of our solar system.
If radar had never been invented and we relied on a less reliable method of measuring distances in our solar system, underestimating the Earth-Sun distance by 10% would significantly affect other measurements in the distance chain.
Step 1: Determine the underestimated Earth-Sun distance
The actual Earth-Sun distance, also known as 1 astronomical unit (AU), is approximately 149.6 million kilometres. If we underestimated this distance by 10%, the measured distance would be:
149.6 million km * 0.9 = 134.64 million km
Step 2: Understand the impact on other measurements
Distances within our solar system are often measured using astronomical units (AU). If our measurement of 1 AU is off by 10%, then all other distance measurements based on this unit will also be off by 10%. This would impact our understanding of the size and scale of our solar system.
Step 3: Apply the error to other distance measurements
For example, the distance between Earth and Mars, on average, is about 225 million kilometers, or 1.52 AU. If our measurement of 1 AU was 10% less, we would underestimate the Earth-Mars distance as well:
1.52 AU * 134.64 million km = 204.656 million km (incorrect measurement)
The actual Earth-Mars distance would still be 225 million km, but our underestimated measurements would make us believe that it is only 204.656 million km.
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A 0.7 kg mass is attached to an ideal spring with a constant of 86 N/m. The mass is initially held at rest so that the spring is at its unextended length of 0.95 m. The mass is then released. What is the maximum distance the mass will fall?
Since the mass is attached to an ideal spring, the system will undergo simple harmonic motion. The maximum distance the mass will fall is equal to the amplitude of the oscillation.
The period of oscillation can be calculated as:
T = 2π√(m/k)
where m is the mass and k is the spring constant.
Substituting the given values, we get:
T = 2π√(0.7 kg / 86 N/m) ≈ 0.887 s
The maximum distance the mass will fall is equal to half the amplitude of the oscillation, which can be calculated using the equation:
x = A cos(2πt/T)
where x is the displacement of the mass from its equilibrium position at time t, and A is the amplitude of oscillation.
At the maximum displacement, cos(2πt/T) will be equal to -1. Therefore,
A = -x
The velocity of the mass at the maximum displacement will be zero. Therefore, the total energy of the system will be equal to the potential energy at the maximum displacement:
1/2 k A^2 = m g A
where g is the acceleration due to gravity.
Solving for A, we get:
A = (m g / k) = (0.7 kg x 9.81 m/s^2) / 86 N/m ≈ 0.0807 m
Therefore, the maximum distance the mass will fall is approximately 0.0807 m.
an 80.0 kg skydiver jumps out of a balloon at an altitude of 1000 m and opens the parachute at an altitude of 200.0m (A). Assuming that the total resisting force on the driver is constant at 50.0 N with the parachute closed and constant at 3 600 N with the parachute open, what is the speed of the driver when he lands on the ground?(B) do you think the skydiver will get hurt? explain(C) At what height should the parachute be opened so that the final speed of the skydiver when he hits the ground in 5.00 m/s?(d) how realistic is the assumption that the total resisting force is constant? explain
ANSWERS:
A. 38.3 m/s
B. Yes. 38.3 m/s is a very high speed and could potentially cause serious injury or death
C. 656.1 m
D. Not very realistic. The resisting force depends on the speed of the skydiver.
EXPLANATIONS:
(A) To solve for the speed of the skydiver when he lands on the ground, we can use conservation of energy. The initial potential energy of the skydiver is equal to the final kinetic energy plus the final potential energy.
Initial potential energy = mgh1 = 80.0 kg x 9.8 m/s^2 x 1000 m = 784000 J
Final potential energy = mgh2 = 80.0 kg x 9.8 m/s^2 x 200.0 m = 156800 J
With the parachute closed, the total resisting force is 50.0 N, so we can use the work-energy principle to find the final kinetic energy:
Work done by resisting force = Fd = 50.0 N x (1000 m - 200 m) = 40000 J
Final kinetic energy = Initial potential energy - Work done by resisting force - Final potential energy
Final kinetic energy = 784000 J - 40000 J - 156800 J = 587200 J
Finally, we can solve for the speed using the equation for kinetic energy:
Final kinetic energy = (1/2)mv^2
587200 J = (1/2)(80.0 kg)v^2
v = sqrt(1468 m^2/s^2) = 38.3 m/s
Therefore, the speed of the skydiver when he lands on the ground is 38.3 m/s.
(B) It's difficult to say whether the skydiver will get hurt based solely on the speed of impact. However, 38.3 m/s is a very high speed and could potentially cause serious injury or death. Other factors, such as the angle of impact and the condition of the ground, would also affect the outcome.
(C) We can use the same conservation of energy equation as in part (A), but solve for the height at which the parachute should be opened to achieve a final speed of 5.00 m/s.
Initial potential energy = mgh1 = 80.0 kg x 9.8 m/s^2 x h1
Final potential energy = mgh2 = 80.0 kg x 9.8 m/s^2 x 0
With the parachute open, the total resisting force is 3600 N, so we can use the work-energy principle to find the work done by the resisting force:
Work done by resisting force = Fd = 3600 N x (h1 - 0) = 3600h1 J
Then we can solve for the height using the equation:
Initial potential energy - Work done by resisting force = Final kinetic energy + Final potential energy
mgh1 - 3600h1 = (1/2)mv^2 + 0
Simplifying and solving for h1:
h1 = (v^2)/(2g) + 3600/g = (5.00 m/s)^2 / (2 x 9.8 m/s^2) + 3600/9.8 = 656.1 m
Therefore, the parachute should be opened at a height of 656.1 m to achieve a final speed of 5.00 m/s.
(D) The assumption that the total resisting force is constant is not very realistic because the resisting force depends on the speed of the skydiver. As the skydiver falls faster, the resisting force will increase due to air resistance. Therefore, the actual speed of the skydiver with the parachute closed and the actual speed with the parachute open would not be constant.
A second pendulum made of brass keeps correct time at 10°C. How many seconds will it lose or gain per Day when the temperature of its surroundings rises to 35°C?
The brass pendulum will lose or gain approximately 0.0015 seconds per day when the temperature of its surroundings rises from 10°C to 35°C
Calculation on the pendulumThe time period of a pendulum is given by the formula:
T = 2π√(L/g)
where T is the time period, L is the length of the pendulum, and g is the acceleration due to gravity.
Since both pendulums have the same length and are located in the same gravitational field, their time periods are equal. Therefore, the time gained or lost by the brass pendulum due to the change in temperature can be calculated using the following formula:
ΔT = T × α × ΔT
where ΔT is the change in temperature, α is the coefficient of linear expansion of brass, and T is the original time period.
The coefficient of linear expansion of brass is approximately 19 × 10^-6 /°C.
Substituting the values given in the problem, we get:
ΔT = T × α × ΔT
= (2π√(L/g)) × (19 × 10^-6 /°C) × (35 - 10) °C
= 2π√(L/g) × (0.000019) × (25) °C
= 2π√(L/g) × 0.000475
Assuming a standard pendulum length of 1 meter, the time gained or lost by the brass pendulum can be calculated as follows:
ΔT = 2π√(L/g) × 0.000475
= 2π√(1/9.81) × 0.000475
≈ 0.0015 seconds
Therefore, the brass pendulum will lose or gain approximately 0.0015 seconds per day when the temperature of its surroundings rises from 10°C to 35°C.
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