The ultraviolet catastrophe is good evidence for the (B).wave nature of quanta is correct option.
The ultraviolet catastrophe was a problem in classical physics that arose when attempting to explain the spectral distribution of blackbody radiation. According to classical physics, the energy of radiation should increase without limit as the frequency of the radiation increases. However, experiments showed that this was not the case, and there was a maximum frequency beyond which the energy decreased.
This problem was resolved by Max Planck in 1900, who proposed that energy is quantized and can only exist in discrete packets or "quanta". This led to the development of quantum mechanics, which describes the behavior of matter and energy at the atomic and subatomic level.
The wave-particle duality is a fundamental concept in quantum mechanics that describes the dual nature of particles, which can exhibit both wave-like and particle-like behavior depending on the experimental setup. However, the ultraviolet catastrophe is specifically related to the wave nature of quanta, as it was the wave-like behavior of energy that led to the resolution of the problem.
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During the course of a hot, summer day the temperature of the wooden beam slowly increases from 15°C at night to a final temperature of 35°C during the day. Calculate the amount of heat transferred to the wooden beam if it has mass 60kg
The amount of heat transferred to the wooden beam is 2,040,000 Joules.
During the course of a hot, summer day, the temperature of the wooden beam slowly increases from 15°C at night to a final temperature of 35°C during the day.
To calculate the amount of heat transferred to the wooden beam with a mass of 60kg, follow these steps:
Step 1: Determine the temperature change (∆T)
∆T = [tex]T_{final} - T_{initial}[/tex]
∆T = 35°C - 15°C
∆T = 20°C
Step 2: Find the specific heat capacity (c) of the wooden beam
The specific heat capacity of wood varies depending on its type. For this example, let's use an average specific heat capacity of wood, which is approximately 1700 J/(kg·K).
Step 3: Calculate the amount of heat transferred (Q) using the formula:
Q = mc∆T
where
m is the mass of the wooden beam,
c is the specific heat capacity of wood, and
∆T is the temperature change.
Step 4: Plug in the values and solve for Q
Q = (60 kg)(1700 J/(kg·K))(20 K)
Q = 2,040,000 J
Therefore, the amount of heat transferred to the wooden beam is 2,040,000 Joules.
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27. A bicycle wheel on a repair bench can be
accelerated either by pulling on the chain that
is on the gear or by pulling on a string wrapped
around the tire. The tire's radius is 0. 38 m, while
the radius of the gear is 0. 14 m. What force would
you need to pull on the string to produce the
same acceleration you obtained with a force of
15 N on the chain?
You would need to pull on the string with a force of 5.76 N to produce the same acceleration you obtained with a force of 15 N on the chain.
To calculate the force needed to produce the same acceleration as a force of 15 N on the chain, we need to use the formula:
force = mass × acceleration
First, we need to calculate the acceleration of the bicycle wheel when a force of 15 N is applied to the chain. We can use the formula:
acceleration = [tex]\frac{acceleration}{mass}[/tex]
Assuming the mass of the wheel is negligible, we can simplify this to:
acceleration = [tex]=\frac{force}{0.38}[/tex] = [tex]\frac{15N}{0.38}[/tex]=39.47 N/m
Now we can calculate the force needed to produce the same acceleration when pulling on the string wrapped around the tire. We can use the formula:
force = mass × acceleration
The mass of the wheel does not change, so we can use the same acceleration value we calculated earlier. However, the radius of the tire is different from the radius of the gear, so we need to take this into account.
The circumference of the tire is 2π(0.38 m) = 2.39 m, while the circumference of the gear is 2π(0.14 m) = 0.88 m.
This means that the force needed to produce the same acceleration when pulling on the string is:
force = mass × acceleration × [tex](\frac{radius of the gear}{radius of the tire} )[/tex]
= 0.38 kg x 39.47 N/m x [tex](\frac{0.14 m}{0.38 m} )[/tex]
= 5.76 N
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young's double-slit experiment is performed with 568-nm light and a distance of 2.00 m between the slits and the screen. the tenth interference minimum is observed 7.08 mm from the central maximum. determine the spacing of the slits.
Answer:
yes
Explanation:
Some machines will have a body constructed around a frame for_____
Some machines will have a body constructed around a frame for added structural support and stability.
This design approach ensures that the machine can withstand various forces, stresses, and vibrations that it may encounter during operation. The frame acts as a skeleton, providing a solid foundation for the machine's various components, such as motors, gears, and electronic systems, to be mounted securely.
By constructing the body around the frame, the machine's weight is evenly distributed, helping to prevent any undue strain on individual parts. This structural design can also facilitate easier maintenance, as components can be accessed and replaced more easily.
Additionally, the frame may be designed with specific materials, such as steel or aluminum, to enhance durability and resist corrosion. In summary, constructing a machine's body around a frame provides numerous benefits, including enhanced structural support, improved stability, and easier maintenance.
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Do the Pressure vs. Depth Lab (record Describe how the distance the water
your activity)
•When will the water flow out the farthest: when the water is nearly full, half-full, or nearly empty?
•Hold the bottle over the bucket so that the water will flow out the hole into the bucket and loosen the bottle cap.
Observe the flow of water. PUT THE CAP BACK ON!
•Describe how the distance the water flowed out changed as the depth of the water changed.
fill in the blanks
•The pressure of a fluid _____ as depth increases. So pressure and depth are _____ proportional.
This can be written as _____
Pressure vs. Depth Lab:
The water will flow out the farthest when the bottle is nearly full.As the depth of the water increased, the distance the water flowed out also increased.The pressure of a fluid increases as depth increases. So pressure and depth are directly proportional.This can be written as P ∝ d, where P is pressure and d is depth.What is pressure?Pressure is defined as the force per unit area applied on an object. It is a scalar quantity, which means it only has magnitude and no specific direction.
It is often measured in units of Pascals (Pa), which is equivalent to one Newton of force per square meter of area. Pressure can be caused by the weight of an object, the force applied by a fluid, or the collision of particles with a surface.
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A force compresses a bone by 1. 0 mm. A second bone has the same cross-sectional area but twice the length as the first. By how much would the same force compress this second bone
The second bone has the same cross-sectional area and material as the first bone, the same force would create the same stress in both bones.
To solve this problem, we need to consider the relationship between stress, strain, and Young's modulus. Stress is the force applied divided by the cross-sectional area, strain is the change in length divided by the original length, and Young's modulus is a material property that relates stress and strain.
1. Calculate stress (σ) for the first bone:
σ = Force / Cross-sectional area
2. Calculate strain (ε) for the first bone:
ε = Compression / Original Length
ε = 1.0 mm / Original Length
3. Find Young's modulus (Y) for the bone material:
Y = σ / ε
4. Calculate the strain (ε') on the second bone, using the same force and Young's modulus:
ε' = σ / Y
5. Calculate the compression (ΔL) of the second bone, given that its length is twice the first bone:
ΔL = ε' * (2 * Original Length)
However, since the second bone is twice as long, it would experience a greater strain and, as a result, a larger compression. By calculating the compression of the second bone using the relationship between stress, strain, and Young's modulus, you can determine how much the same force would compress the second bone.
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in the diagram below are shown snapshots of the changing electric and magnetic field that make up a beam of light. each frame has a time stamp, given in terms of the period of oscillation of the fields. in what direction is the beam of light moving?
Answer:
yes
Explanation:
45 N
15 N
Net Force:
Is it balanced or unbalanced?
net force: 60( not sure)
I would say it's unbalanced because these forces are not of the same magnitude.
One form of energy that exists in every system but is difficult to quantify is heat. Think about how we formulated our spring resonance model. Did we account for the heat energy in the medium? why do we need to?.
No, our spring resonance model did not account for the heat energy in the medium. Heat energy is generated due to the friction between the spring and the medium during the oscillation of the spring.
This energy is dissipated into the medium in the form of thermal energy, causing the amplitude of the oscillation to decrease over time.
In order to develop an accurate and complete model of the spring resonance, we need to account for the heat energy generated during the oscillation.
This is important because the amount of heat generated depends on the mechanical properties of the medium and the frequency and amplitude of the oscillation, and can have a significant impact on the behavior of the system.
By accounting for heat energy, we can better understand the dynamics of the system and predict how it will behave over time.
This can be particularly important in practical applications, such as in engineering and design, where we need to know how a system will perform under different conditions and over long periods of time.
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A concrete column has a diameter of 350m and length of 2m. If the density (mass/volume) of the concrete is 2. 45mg/m^3 determine the weight of column in pounds
The weight of the concrete column with a diameter of 350mm and a length of 2m, having a density of 2.45 Mg/m³, is: approximately 1042 pounds.
To determine the weight of the concrete column with a diameter of 350mm and a length of 2m, we first need to calculate its volume. Since the column is cylindrical, we can use the formula for the volume of a cylinder: V = πr²h, where V is the volume, r is the radius, and h is the height.
The radius of the column is half of the diameter, so r = 350mm / 2 = 175mm, which is equivalent to 0.175m. The height is 2m. Plugging these values into the formula, we get:
V = π(0.175m)²(2m) ≈ 0.193m³
Now that we have the volume, we can use the given density of concrete, which is 2.45 Mg/m³, to determine the mass. The mass can be calculated using the formula: mass = density × volume.
Mass = 2.45 Mg/m³ × 0.193m³ ≈ 0.473 Mg
Next, we need to convert the mass from Mg (megagrams) to kg (kilograms) since 1 Mg = 1000 kg:
Mass = 0.473 Mg × 1000 kg/Mg = 473 kg
Now, to find the weight, we'll use the formula: weight = mass × gravity. The gravitational force is approximately 9.81 m/s².
Weight = 473 kg × 9.81 m/s² ≈ 4638.93 N (Newtons)
Finally, we'll convert the weight from Newtons to pounds using the given conversion factor: 1 pound = 4.4482 N.
Weight = 4638.93 N × (1 pound / 4.4482 N) ≈ 1042 pounds
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Complete question:
A concrete column has a diameter of 350mm and a length of 2m. If the density (mass/volume) of concrete is 2.45 Mg/m3 determine the weight of the column in pounds. 1 pound = 4.4482 N
a 1.90-m-long wire having a mass of 0.100 kg is fixed at both ends. the tension in the wire is maintained at 21.0 n.
The fundamental frequency of the 1.90-m-long wire with a mass of 0.100 kg and tension of 21.0 N is approximately 5.24 Hz.
Given the information provided, we have a 1.90-m-long wire with a mass of 0.100 kg that is fixed at both ends and has a tension of 21.0 N.
To find the linear mass density (µ) of the wire, we can use the following formula:
µ = mass/length
Using the given values, we can calculate µ as follows:
µ = 0.100 kg / 1.90 m = 0.05263 kg/m
Now that we have the linear mass density, we can find the fundamental frequency (f) using the formula:
f = (1 / 2L) × √(T / µ)
Where:
f = fundamental frequency
L = length of the wire
T = tension
µ = linear mass density
Substituting the values we found earlier, we get:
f = (1 / 2 × 1.90 m) × √(21.0 N / 0.05263 kg/m)
f ≈ 0.263 × √(399.2) ≈ 5.24 Hz
So, the fundamental frequency of the 1.90-m-long wire with a mass of 0.100 kg and a tension of 21.0 N is approximately
5.24 Hz.
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If three crests pass Pin in one second, the wavelength is?
The wavelength of the wave as we have it is 3m
What is the wavelength of a wave?A wave's wavelength is the separation between two successive locations on the wave that are in phase, or at the same stage of their cycle. In other terms, it is the separation between two wave crests or troughs.
We know that the wavelength = Number of crests = 3m
Wave speed = 3 m/s
We would then have that;
v = λf
v = wave speed
f = frequency
λ = wavelength
Thus since there are three crests then the wavelength must be 3m
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What is the absolute index of refraction of medium x?
The refractive index of the wave in medium X is 0.577.
What is the refractive index?The refractive index of a substance or medium measures how much light can bend through it. The difference between the speed of light in an object or medium and the speed of light in a vacuum (or in air) is how it is defined. Usually, the letter n is used to denote the refractive index.
The refractive index of a substance or medium is a critical property that determines how light will behave when it passes through it.
We know that the refractive index can be obtained as;
n = sin i/sinr
Thus we have that;
sin i = sin 30
sin r = sin 60
n = sin 30/sin 60
n = 0.577
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A typical color television draws about 2. 5 A
when connected to an 89 V source.
What is the effective resistance of the T. V.
set?
Answer in units of Ω
The effective resistance of the TV set is 35.6 ohms (Ω).
To find the effective resistance of the TV set, we can use Ohm's Law, which states that Voltage (V) = Current (I) × Resistance (R). We need to rearrange the formula to solve for resistance: R = V / I.
Given the information in your question:
Current (I) = 2.5 A
Voltage (V) = 89 V
Now we can calculate the resistance (R):
R = V / I
R = 89 V / 2.5 A
R = 35.6 Ω
The effective resistance of the TV set is 35.6 ohms (Ω).
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« A 100 kg stunt woman falls from a three-story
building that is 9. 9 m high. If she falls into a net,
which slows her down over the course of 1 s,
what force did she experience while landing?
The stunt woman experienced a force of 1393 N while landing in the net.
A 100 kg stunt woman falls from a 9.9 m high building and is slowed down by a net over the course of 1 s. To calculate the force she experienced while landing, we first need to determine her velocity when hitting the net.
We can use the formula: v^2 = u^2 + 2as
where v is the final velocity, u is the initial velocity (0 m/s), a is the acceleration due to gravity (9.81 m/s^2), and s is the distance fallen (9.9 m).
v^2 = 0 + 2(9.81)(9.9)
v^2 = 194.118
v = √194.118 ≈ 13.93 m/s
Now, we can use the impulse-momentum theorem to find the force: Ft = mv - mu
where F is the force, t is the time taken to slow down (1 s), m is the mass (100 kg), and v and u are the final and initial velocities, respectively.
F(1) = (100)(13.93) - (100)(0)
F = 1393 N
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Josh pushes a table with a force of 80. N at an angle of 30°
to the table. If he pushes the table 5 meters, how much
work has he done? Joules
Josh pushes a table with a force of 80. N at an angle of 30° to the table. If he pushes the table 5 meters then Josh has done 346.41 Joules of work on the table.
To calculate the work done by Josh on the table, we can use the formula:
[tex]W = F \times d \times cos(\theta)[/tex]
where W is the work done, F is the force applied, d is the distance moved, and theta is the angle between the force and the direction of motion.
Substituting the given values, we get:
[tex]W = 80 N \times 5 m \times cos(30^{\circ})[/tex]
W = 346.41 J
Therefore, Josh has done 346.41 Joules of work on the table. To understand the concept of work, it is important to note that work is done when a force is applied to an object and it causes it to move.
In this case, Josh applies a force of 80 N at an angle of 30° to the table, causing it to move 5 meters. The work done is calculated by multiplying the force, distance, and cosine of the angle between them.
In summary, to calculate the work done by Josh on the table, we use the formula [tex]W = F \times d \times cos(\theta)[/tex] , where W is the work done, F is the force applied, d is the distance moved, and theta is the angle between the force and the direction of motion.
By substituting the given values, we find that Josh has done 346.41 Joules of work on the table.
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Which statement describes what the hand shows?
A-When the current flows down the wire, the magnetic
field flows out on the left side of the wire and in on the
right side of the wire.
B-When the current flows up the wire, the magnetic field
flows out on the left side of the wire and in on the right
side of the wire.
C-When the current flows down the wire, the magnetic
field flows in on the left side of the wire and out on the
right side of the wire.
D-When the current flows up the wire, the magnetic field
flows in on the left side of the wire and out on the right
side of the wire.
When the current flows up the wire, the magnetic field flows in on the left side of the wire and out on the right side of the wire.
Right hand ruleThe right-hand rule is a method for determining the direction of the force experienced by a current-carrying conductor in a magnetic field or the direction of the magnetic field created by the conductor.
The direction of the magnetic field created by the current is indicated by the way your fingers curl. This is the statement of the right hand rule as shown in the image.
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NEED HELP FAST!!!! Please answer both questions
Answer:
1. 0.102 mol/kg.
2. 0.444 mol/kg.
Explanation:
Work on 1.To calculate molality, we need to know the moles of solute (NaCl) and the mass of the solvent (water) in kilograms. First, we need to convert the mass of NaCl to moles by dividing by its molar mass. Then we convert the mass of water to kilograms. Molality (m) is equal to moles of solute divided by kilograms of solvent.
Work on 2.
First, we need to convert the mass of glucose to moles by dividing by its molar mass. Then we convert the volume of water to kilograms. Molality (m) is equal to moles of solute divided by kilograms of solvent. Finally, we need to round the answer to three significant figures.
Day 58
1. Developing decision-making skills is a vital aspect that occurs during which stage of adolescent development?
social development
physical development
emotional development
intellectual development
4
Answer:
Developing decision-making skills is a vital aspect that occurs during the stage of intellectual development in adolescent development.
Explanation:
During adolescence, individuals undergo significant changes in their cognitive abilities, including an increase in abstract thinking, reasoning, and problem-solving skills. These changes allow adolescents to start thinking critically and independently, weigh options, and make more informed decisions about their lives.
As adolescents develop their intellectual abilities, they also gain more control over their lives and begin to make decisions about their education, career paths, relationships, and other important aspects of their lives. This is a critical time for developing decision-making skills, as the decisions made during adolescence can have significant and long-lasting effects on individuals' lives.
While other aspects of adolescent development, such as social, emotional, and physical development, are also important, intellectual development plays a crucial role in helping adolescents navigate the complex and challenging decisions they face as they transition to adulthood.
which is a form of potential energy
A ball bounces off the floor elastically as shown. The direction of the change in momentum of the ball is.
The direction of the change in momentum of the ball is in the opposite direction of its original momentum. This is because when the ball bounces off the floor, it experiences an equal and opposite force, which causes its momentum to change direction.
This is known as an elastic collision, and the change in momentum is equal in magnitude to the original momentum but in the opposite direction. This is because the total momentum is conserved in the collision. This means that the sum of the momentum of the ball after the collision is equal to the sum of the momentum of the ball before the collision.
Since the ball has no external forces acting on it, the only way for the momentum to remain the same is for the momentum to change direction. Therefore, the direction of the change in momentum of the ball is in the opposite direction of its original momentum.
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which one of the following is the correct order of the electromagnetic spectrum from low to high frequencies? select one: a. radio waves, uv, x-rays, microwaves, infrared, visible, gamma rays b. radio waves, infrared, microwaves, uv, visible, x-rays, gamma rays c. radio waves, microwaves, infrared, visible, uv, x-rays, gamma rays d. radio waves, infrared, x-rays, microwaves, uv, visible, gamma rays
The correct order of the electromagnetic spectrum from low to high frequencies is: radio waves, microwaves, infrared, visible, UV, X-rays, gamma rays. Option C is correct.
The electromagnetic spectrum is the range of all types of electromagnetic radiation, from low-frequency radio waves to high-frequency gamma rays. Radio waves have the longest wavelengths and lowest frequencies, followed by microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays, which have the shortest wavelengths and highest frequencies.
This order is based on the different ways in which electromagnetic radiation interacts with matter, with longer wavelengths being less energetic and shorter wavelengths being more energetic. It is important to note that while this order is generally accepted, there can be some overlap and variation depending on context and source. Option C is correct.
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imagine that you have a vehicle traveling on mars. the shortest distance between earth and mars is 56 * 106 km; the longest is 400 * 106 km. what is the delay time for the signal that you send to mars from earth? can you use radio signals to give commands to the vehicle?
The delay time for the signal that you send to mars from earth is 22.4 minutes.
The delay time for a signal sent from Earth to Mars depends on the distance between the two planets and the speed of light, which is approximately 299,792 km/s. Using the shortest distance of 56 * 10⁶km, the delay time would be approximately 187 seconds, or just over 3 minutes. Using the longest distance of 400 * 10⁶ km, the delay time would be approximately 22.4 minutes. Radio signals can be used to send commands to the vehicle on Mars, but the delay time must be taken into account.
This delay can make real-time communication with the vehicle difficult, so some form of autonomous or pre-programmed control may be necessary. Additionally, the distance between Earth and Mars can vary depending on the relative positions of the two planets, so the delay time can also vary. However, despite these challenges, radio communication remains a vital tool for sending commands and receiving data from spacecraft on Mars and other distant locations in the solar system.
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Help me!
in your own words, describe how the marble-jar experiment explains newton's law of inertia.
The marble-jar experiment is a classic demonstration of Newton's Law of Inertia. The experiment consists of a jar filled with marbles and a card covering the jar's opening.
When the jar is inverted quickly, the card falls, and the marbles remain in place.
According to Newton's Law of Inertia, an object at rest will remain at rest, and an object in motion will continue to move in a straight line at a constant velocity unless acted upon by an external force.
In this experiment, the marbles' inertia keeps them in place when the jar is inverted, while the card falls due to the external force of gravity.
This experiment provides a simple and tangible way to understand Newton's Law of Inertia.
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Help urgent- Two waves travel through the air: wave
A, at 680 Hz, and wave B, at 1760 Hz.
Which wave will travel faster? Why?
The speed of a wave in a medium depends on the properties of that medium, such as its density and elasticity. The frequency of the wave, or the number of cycles it completes in a second, does not affect its speed.
Therefore, both wave A and wave B will travel through the air at the same speed, which is approximately 343 meters per second at room temperature and atmospheric pressure.
However, the wavelength of a wave is inversely proportional to its frequency, so wave B will have a shorter wavelength than wave A.
This means that wave B will have a higher energy and be more directional than wave A, but it will not travel faster through the air.
In summary, the frequency of a wave does not affect its speed in a given medium, and both wave A and wave B will travel through the air at the same speed of approximately 343 meters per second.
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A 0.050 kg bullet strikes a 5.0 wooden block and embeds itself
A tourist follows a passage which takes her 160 m west, then 180 m at an angle of 45. 0∘ south of east and finally 250 m at an angle 35. 0∘ north of east. The total journey takes 12 minutes.
a. Calculate the magnitude of her displacement from her original position. (4)
b. She measures the distance she has walked to a precision of 5%. She times her total journey to ±20 s.
(i) What is her average speed?
(ii) What is the absolute uncertainty on her absolute speed?
The three components of the journey's vector is 267.7 m, the displacement by the time taken is 22.3 m/min, the average speed is 23 m/min and the average speed with a precision of ±5% and ±20 s is 21.9 m/min to 23 m/min.
What is magnitude?Magnitude is a measure of the size or intensity of something. It is usually a numerical quantity or value, such as size, energy, power, intensity, brightness, strength, or speed. Magnitude is a mathematical concept that is used to compare and evaluate different values.
Using this theorem, we can find the magnitude of the displacement (d) by taking the square root of the sum of the squares of the three components of the journey's vector.
d = √(160² + (180*cos45)² + (250*cos35)²)
d = √(25600 + 25600 + 20625)
d = √71725
d ≈ 267.7 m
To calculate the average speed, we need to divide the magnitude of the displacement by the time taken.
Average Speed = d/t
Average Speed = 267.7 m/12 min
Average Speed = 22.3 m/min
To account for the precision of ±5%, we can add or subtract 5% of the displacement, and ±20 s of the time taken.
Using the new values, we can calculate the average speed as follows:
Average Speed = (267.7 ± 13.4 m)/(12 min ± 20 s)
Average Speed = (254.3 m - 281.1 m)/(11 min 40 s - 12 min 20 s)
Average Speed = (254.3 m/11 min 40 s) - (281.1 m/12 min 20 s)
Average Speed = 21.9 m/min - 23 m/min
Therefore, the average speed with a precision of ±5% and ±20 s is 21.9 m/min to 23 m/min.
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a weight lifter must expert of force to lift a set of barbells off the ground
It should be noted that the statement regarding the weightlifter is true.
How to explain the informationA weightlifter must apply a certain amount of force to lift a set of barbells off the ground. This force is known as the lifting force and it must be greater than the weight of the barbells in order to overcome the force of gravity and lift the barbells.
The amount of lifting force required will depend on the weight of the barbells and the strength of the weightlifter's muscles. The weightlifter can increase their lifting force by improving their strength and technique through training and practice.
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A weight lifter must be expert of force to lift a set of barbells off the ground
true or false
The maximum allowable resistance for an underwater cable is one hundredth of an ohm per
meter and the resistivity of copper is 1. 54 x 10-80m.
a) Calculate the smallest cross sectional area of copper cable that could be used.
The copper cable's smallest possible cross-sectional area is 1.54 x 10-6 square meters.
To calculate the smallest cross-sectional area of the copper cable, we can use the formula for resistance:
R = ρ(L/A),
where R is the resistance (in ohms), ρ is the resistivity of the material (in ohm meters), L is the length of the conductor (in meters), and A is the cross-sectional area (in square meters).
Given the maximum allowable resistance (R) is 0.01 ohms per meter (one-hundredth of an ohm per meter) and the resistivity of copper (ρ) is 1.54 x 10^-8 ohm meters. Let's calculate the smallest cross-sectional area (A) that can be used.
First, we'll rewrite the formula for A:
A = ρ(L/R).
Since R is given as ohms per meter, we can set L to 1 meter for simplicity, and the formula becomes:
A = ρ(1/R).
Now, we can plug in the given values:
A = (1.54 x 10^-8)/(0.01).
A = 1.54 x 10^-6 square meters.
So, the smallest cross-sectional area of the copper cable that could be used is 1.54 x 10^-6 square meters.
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A 1345-kg car moving east at 15. 7m/s is struck by a 1923-kg car moving north. They stick together and move with a velocity of 14. 5m / s at theta = 63. 5 degrees Was the north-moving car exceeding the 20. 1 m/s speed limit?
We need to first calculate the final velocity of the two cars after the collision. We can do this using the conservation of momentum principle, which states that the total momentum of a system remains constant if no external forces act on it.
Initially, the east-moving car has a momentum of (1345 kg) x (15.7 m/s) = 21136.5 kg m/s in the east direction, while the north-moving car has a momentum of (1923 kg) x (v) in the north direction, where v is the velocity of the north-moving car.
After the collision, the two cars stick together and move with a velocity of 14.5 m/s at an angle of 63.5 degrees. To find the velocity in the x-direction (east), we can use the cosine function:
cos(63.5 degrees) = x / 14.5 m/s
x = cos(63.5 degrees) x 14.5 m/s = 6.25 m/s
Similarly, to find the velocity in the y-direction (north), we can use the sine function:
sin(63.5 degrees) = y / 14.5 m/s
y = sin(63.5 degrees) x 14.5 m/s = 13.12 m/s
Therefore, the final velocity of the two cars is (6.25 m/s) east + (13.12 m/s) north = 14.5 m/s at 63.5 degrees.
To determine if the north-moving car exceeded the 20.1 m/s speed limit, we need to compare its initial velocity with the speed limit. The initial velocity of the north-moving car is not given in the problem, so we cannot determine whether it exceeded the speed limit or not.
In summary, the final velocity of the two cars after the collision is 14.5 m/s at 63.5 degrees. However, we cannot determine whether the north-moving car exceeded the 20.1 m/s speed limit without additional information.
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