The refractive index of the glass material is approximately 1.4226.
To calculate the refractive index of the glass material for the fiber optic cable, you can use Snell's Law and the definition of the critical angle. The critical angle (θc) is the angle of incidence at which the angle of refraction is 90°. In this case, the critical angle is 25°.
Snell's Law: n1 * sin(θ1) = n2 * sin(θ2)
For the critical angle, θ1 = 25°, and θ2 = 90°. The refractive index of air (n1) is approximately 1.
Applying Snell's Law: 1 * sin(25°) = n2 * sin(90°)
Solving for the refractive index (n2) of the glass material:
n2 = sin(25°) / sin(90°)
n2 ≈ 0.4226 / 1
n2 ≈ 1.4226
The refractive index of the glass material is approximately 1.4226.
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A puck slides on a frictionless table hitting a block. in which scenario does the puck exert the most force on the block?
The force exerted by the puck on the block depends on the rate of change of momentum during the collision.
To determine the scenario in which the puck exerts the most force on the block, we need to consider the principles of conservation of momentum.
The momentum of an object is defined as the product of its mass and velocity.
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision, assuming no external forces are acting on the system.
Let's consider two scenarios:
Scenario 1: The puck approaches the block with a higher initial velocity.
Scenario 2: The puck approaches the block with a lower initial velocity.
In both scenarios, the mass of the puck and the block remains constant.
However, the difference lies in the initial velocity of the puck.
According to the conservation of momentum, the change in momentum of the puck must be equal and opposite to the change in momentum of the block.
If the initial momentum of the puck is greater in scenario 1 compared to scenario 2, the change in momentum will also be greater.
Since force is defined as the rate of change of momentum, a greater change in momentum implies a larger force.
Hence, in scenario 1 where the puck has a higher initial velocity, the puck will exert more force on the block during the collision.
To summarize, the puck exerts the most force on the block when it approaches the block with a higher initial velocity (scenario 1).
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A horizontal, uniform board of weight 125 n and length 4 m is supported by vertical chains at each ends. a person weighing 500 n is sitting on the board. the tension in the right chain is 125 n.what is the tension in the left chain
The tension in the left chain is 500 N, which is equal to the weight of the person on the board. Since the board is in equilibrium, the net force and net torque acting on the board must be zero.
Let's consider the forces acting on the board: the weight of the board (125 N) acts downward, the weight of the person (500 N) acts downward at the center of the board, and the tension in each chain acts upward.
Since the tension in the right chain is given to be 125 N, the total upward force acting on the board is 125 N + T (where T is the tension in the left chain).
Therefore, the net force on the board is 125 N + T - 625 N = 0 (where 625 N is the combined weight of the board and person).
Solving for T, we get T = 500 N, which is the tension in the left chain. So the tension in the left chain is 500 N, which is equal to the weight of the person on the board.
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Consider example 20. 15, what angle of deflection would you get if the electron gun distance as well as electron defelctor distance were to both double, with the electric fields staying as in the example?.
If the electron gun distance and electron deflection distance both double, while the electric fields stay the same, then the angle of deflection would also double.
This is because the electric field strength is directly proportional to the angle of deflection, and since the electric field strength is staying the same, the angle of deflection increases proportionally with the increase in distance.
The equation to determine the angle of deflection is as follows: θ = Vd/E, where θ is the angle of deflection, V is the velocity of the electron, d is the distance between the electron gun and deflection plate, and E is the strength of the electric field.
When the distance between the two plates doubles, the angle of deflection will also double. Therefore, if the electron gun and electron deflection plate are both doubled in distance, the angle of deflection would be double the original angle.
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The figure shows a 25-cm-long metal rod pulled along two frictionless, conducting rails at a constant speed of 3. 5 m/s. The rails have negligible resistance, but the rod has a resistance of 0. 65 Ω
The magnitude of the force required to keep the rod moving at a constant speed is 0.9065 N.
First, let's find the induced electromotive force (EMF) using Faraday's law of electromagnetic induction: EMF = B * L * v, where L is the length of the rod, and v is its velocity. Converting the length to meters: L = 0.25 m.
EMF = 1.4 T * 0.25 m * 3.7 m/s = 1.295 V
Next, let's find the induced current using Ohm's law: I = EMF / R, where R is the resistance of the rod.
I = 1.295 V / 0.50 Ω = 2.59 A
The current induced in the rod is 2.59 A.
Now, let's calculate the magnitude of the force required to keep the rod moving at a constant speed. The force needed to maintain constant speed is equal to the magnetic force acting on the rod, which is given by F = I * L * B.
F = 2.59 A * 0.25 m * 1.4 T = 0.9065 N
The magnitude of the force required to keep the rod moving at a constant speed is 0.9065 N.
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Complete question:
The figure shows a 25 cm -long metal rod pulled along two frictionless, conducting rails at a constant speed of 3.7 m/s . The rails have negligible resistance, but the rod has a resistance of 0.50 Ω .
B=1.4T
What is the current induced in the rod?
What is the magnitude of the force is required to keep the rod moving at a constant speed?
Bart has rubbed a balloon with wool to give it a charge of -1.0 x 10-6 c. he then acquires a plastic golf tube with a charge of +4.0 x 10-6 c localized at a given position. determine the distance between the golf tube and the balloon if the electrical force between the two is -1.0 x 10-5 n.
The distance between the golf tube and the balloon is approximately 53.9 millimeters.
To solve this problem, we can use Coulomb's Law, which states that the electrical force (F) between two charges (q1 and q2) is proportional to the product of their charges divided by the square of the distance (r) between them:
F = k * (q1 * q2) / r²
where k is Coulomb's constant, approximately 8.99 x 10^9 Nm²/C².
In this case, the electrical force (F) is -1.0 x 10^-5 N, the charge of the balloon (q1) is -1.0 x 10^-6 C, and the charge of the plastic golf tube (q2) is +4.0 x 10^-6 C. We want to find the distance (r) between them.
First, let's rearrange the formula to solve for r:
r = √(k * (q1 * q2) / F)
Now, substitute the given values into the equation:
r = √((8.99 x 10^9 Nm²/C²) * (-1.0 x 10^-6 C) * (4.0 x 10^-6 C) / (-1.0 x 10^-5 N))
Solve for r:
r ≈ 0.0539 meters or 53.9 millimeters
So, the distance between the golf tube and the balloon is approximately 53.9 millimeters.
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Hunter pushed a couch across the room. He did 800 J of work in 20 seconds.
The couch weighed 500 N. How much power did he have?
A. 40 W
B. 1. 6 W
C. 16,000 W
D. 800 W
SUBMIT
Hunter had a power of 40 watts when he pushed the couch across the room.
To solve this problem, we need to use the formula for power, which is P = W/t, where P is power measured in watts, W is work measured in joules, and t is time measured in seconds.
Given that Hunter did 800 J of work in 20 seconds, we can calculate his power as follows:
P = W/t
P = 800 J / 20 s
P = 40 W
Therefore, Hunter had a power of 40 watts when he pushed the couch across the room.
It's important to note that power is a measure of how quickly work is done. In this case, Hunter did 800 J of work in 20 seconds, which means he was doing work at a rate of 40 J/s (or 40 watts). His power would have been greater if he had done the same amount of work in less time. Conversely, his power would have been lower if he had taken longer to do the work.
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Question 6
Two ropes are attached to a tree, and forces of F₁ =2.01 +4.03 N and F₂=3.01+6.01 N
are applied. The forces are coplanar (in the same plane). Find the magnitude of the
net force.
15 N
The net force has a magnitude of C, 5.0 N.
How to determine magnitude?To find the net force, add the two forces vectorially. Break down each force into its x and y components:
F₁ = (2.01 N)î + (4.03 N)ĵ
F₂ = (3.01 N)î + (6.01 N)ĵ
To find the net force, add the components:
F_net = F₁ + F₂ = (2.01 N + 3.01 N)î + (4.03 N + 6.01 N)ĵ
F_net = 5.02î + 10.04ĵ
The magnitude of the net force is given by:
|F_net| = √((5.02 N)² + (10.04 N)²)
|F_net| = √(25.2004 N²)
|F_net| = 5.02 N (rounded to two decimal places)
Therefore, the magnitude of the net force is 5.0 N.
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During practice a soccer player kicks a ball and sends it rolling across the grass. Over a short distance the ball slows down and stops which two statements support the idea that energy is conserved in this example? Please Hurry
Energy cannot be created or destroyed, it can only be converted from one form to another. When the soccer player kicked the ball, they transferred their kinetic energy to the ball, causing it to move.
As the ball rolled across the grass, its kinetic energy was gradually converted into other forms of energy, such as frictional heat and sound energy, causing it to slow down and eventually stop.
The total amount of energy in a closed system remains constant. In this case, the system is the ball and the grass.
Even though the ball slowed down and stopped, the total amount of energy in the system remained the same, as the kinetic energy of the ball was converted into other forms of energy, such as heat and sound. Therefore, energy was conserved in this example.
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Which statement best describes what would happen if the current in the coil of an electromagnet were increased?
A. The electromagnet would stop working until the current became steady
B. The magnetic field would not change
C. The magnetic field would decrease
D. The magnetic field would increase
Answer:D. The magnetic field would increase.
Explanation:
Based on the text how might the surfing "purists" feel about the movement toward incorporating aerial moves into surfing competitions? Use evidence from the text to support your answer
Surfing purists dislike aerial moves in competitions, preferring traditional surfing. There is controversy over the emphasis on aerial moves, and diversity of opinion within the community.
The surfing "purists" are likely to be critical of the movement towards incorporating aerial moves into surfing competitions, as they are described as valuing "traditional" or "classic" surfing.
The text notes that these purists "feel that aerial moves represent a departure from classic surfing," and quotes a professional surfer who suggests that "real surfing is all about turns and the flow of the wave."
The article also notes that there is some controversy within the surfing community over the emphasis on aerial moves, with some feeling that it has become too dominant in competitions. This further suggests that there are those within the community who are resistant to this trend.
Overall, it seems that the surfing "purists" value a more traditional, flowing style of surfing and may view aerial moves as a departure from this style.
However, it is important to note that there is diversity of opinion within the surfing community, and not all surfers or fans may share this view.
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An object is being pulled along a rough table with a frictional force of 7N acting
upon the object. The object is being pulled along by a horizontal force of 18N and
weighs 30N.
To fathom this issue, we have to be utilize Newton's moment law of movement, which states that the net force acting on an question is equal to the item of its mass and increasing speed. Able to utilize this law to discover the speeding up of the object:
Net force= ma
where m is the mass of the object and a is its increasing speed.
What is the the net force of the object?In this case, the net force is the horizontal force of 18N short the frictional constrain of 7N:
Net constrain = 18N - 7N = 11N
The mass of the object is given as 30N, so we are able modify the condition to unravel for the speeding up:
a = Net force / m = 11N / 30N = 0.37 m/s^2
Hence, the object is accelerating at a rate of 0.37 m/s^2 along the table.
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Lab: Newton's Laws of Motion
Assignment: Lab Report
--------------
I finished and wanted to give my lab report if anyone had trouble or needed it :)
Thank you for offering your lab report to others! However, it's important to remember that sharing your work can lead to academic misconduct if others use your report as their own.
It's important for everyone to complete their assignments independently and to not share their work with others.
It's also important to understand the concepts behind Newton's Laws of Motion rather than relying solely on someone else's report.
That being said, if anyone is struggling with the lab, it's best to seek help from the instructor or a tutor. Good luck with your assignment!
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In which spectral class does a white dwarf with a temperature of 10,000 K belong?
Answer: A white dwarf with a temperature of 10,000 K belongs to the spectral class DA.
White dwarfs are classified based on their atmospheric composition and temperature. The DA spectral class refers to white dwarfs that have a hydrogen-dominated atmosphere. Their spectra exhibit strong hydrogen absorption lines.
The temperature of a white dwarf is a measure of its surface temperature and is related to its age and mass. A white dwarf with a temperature of 10,000 K is relatively hot, indicating that it is likely a young and massive white dwarf.
Explanation:
Identify the level of ecological organization referenced in this statement: The herd of elephants moved quickly. Question 9 options:
The level of ecological organization referenced in the statement "The herd of elephants moved quickly" is the population level.
This is because a population consists of individuals of the same species, in this case, elephants, living in the same area and interacting with one another.
In this particular statement, the focus is on a group of elephants, referred to as a herd. A herd is a group of individuals of the same species, in this case, elephants, that live and interact together. The movement of the herd as a collective entity implies the behavior and characteristics of the population as a whole.
At the population level of ecological organization, the emphasis is on understanding the dynamics, behaviors, and interactions of a group of individuals belonging to the same species in a particular area.
The population level provides insights into factors such as population size, population density, population growth, social dynamics, and reproductive patterns.
In the given statement, the mention of the herd of elephants moving quickly suggests a collective behavior and movement pattern observed in a population of elephants.
This observation would be relevant to understanding the ecological dynamics and behavioral characteristics specific to elephant populations, such as their migratory patterns, foraging strategies, or response to environmental changes.
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The rear defroster of your car operates on a current of 6. 00 A. If the voltage drop across it is 5. 00 V, how much electric power is it consuming as it melts the frost
The rear defroster is consuming 30.00 watts of electric power as it melts the frost. Electric power is the rate at which electrical energy is consumed or produced.
It is calculated by multiplying the voltage (V) across a device or component by the current (I) flowing through it.
To calculate the electric power consumed by the rear defroster, you can use the formula:
Power (P) = Voltage (V) × Current (I)
Given:
Current (I) = 6.00 A
Voltage (V) = 5.00 V
Substituting the values into the formula:
P = 5.00 V × 6.00 A
P = 30.00 W
Therefore, the rear defroster is consuming 30.00 watts of electric power as it melts the frost. The power indicates how quickly the defroster can generate heat and melt the frost on the rear window of the car.
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Can someone help me with questions 2 and 4 please ?
2. The angle of refraction of the material is 16.0°.
4. Index of refraction of the prism is n = 1.45.
How to determine angle and index of refraction?2. Using Snell's law:
n₁sinθ₁ = n₂sinθ₂
where n₁ = index of refraction of the first material (a), θ₁ = angle of incidence (13°), n₂ = index of refraction of the second material (1.60), and θ₂ = angle of refraction (unknown).
Plugging in the given values:
2.04sin13° = 1.60sinθ₂
θ₂ = sin⁻¹(2.04sin13°/1.60) = 16.0°
Therefore, the angle of refraction is θ = 16.0°.
4. Again, using Snell's law:
n₁sinθ₁ = n₂sinθ₂
where n₁ = index of refraction of water (1.33), θ₁ = angle of incidence (45°), n₂ = index of refraction of the prism (unknown), and θ₂ = angle of refraction (42°).
Plugging in the given values:
1.33sin45° = n₂sin42°
n₂ = sin45°/sin42° × 1.33 ≈ 1.45
Therefore, the index of refraction of the prism is n = 1.45.
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Two uniform solid spheres have the same mass, 1.75 kg, but one has a radius of 0.206 m while the other has a radius of 0.834 m. for each of the spheres, find the torque required to bring the sphere from rest to an angular velocity of 327 rad/s in 15.5 s. each sphere rotates about an axis through its center. torque on sphere with the smaller radius.
The torque required for the sphere with the smaller radius is approximately 0.622 N*m.
To find the torque required for each sphere, we need to first calculate the moment of inertia (I) for each sphere, and then use the formula for torque (τ) which is τ = I * α, where α is the angular acceleration.
The moment of inertia for a solid sphere is given by I = (2/5) * M * R^2, where M is the mass and R is the radius.
For the smaller sphere (radius = 0.206 m):
I₁ = (2/5) * 1.75 kg * (0.206 m)^2 ≈ 0.0295 kg*m^2
For the larger sphere (radius = 0.834 m):
I₂ = (2/5) * 1.75 kg * (0.834 m)^2 ≈ 0.5093 kg*m^2
Next, we need to find the angular acceleration (α) using the formula α = Δω/Δt, where Δω is the change in angular velocity and Δt is the time interval.
Δω = 327 rad/s (final angular velocity) - 0 rad/s (initial angular velocity) = 327 rad/s
Δt = 15.5 s
α = 327 rad/s / 15.5 s ≈ 21.1 rad/s^2
Now, we can find the torque (τ) for each sphere using τ = I * α.
Torque for smaller sphere:
τ₁ = 0.0295 kg*m^2 * 21.1 rad/s^2 ≈ 0.622 N*m
Torque for larger sphere:
τ₂ = 0.5093 kg*m^2 * 21.1 rad/s^2 ≈ 10.76 N*m
So, the torque required for the sphere with the smaller radius is approximately 0.622 N*m.
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In a vacuum, electromagnetic radiation of short wavelengths.
In a vacuum, electromagnetic radiation of short wavelengths refers to high-energy radiation. According to the electromagnetic spectrum, shorter wavelengths correspond to higher frequencies and higher energies.
At the short wavelength end of the spectrum, you have gamma rays, which have the shortest wavelengths and highest energy among all forms of electromagnetic radiation. Gamma rays have wavelengths less than 10 picometers (pm) or frequencies greater than 10 exahertz (EHz).
Gamma rays are highly energetic and can penetrate matter deeply. They are often produced in nuclear reactions, radioactive decay, and high-energy particle interactions.
It's important to note that in a vacuum, all forms of electromagnetic radiation, including gamma rays, travel at the speed of light. The properties of electromagnetic radiation, such as wavelength and frequency, are intrinsic characteristics that remain constant regardless of the medium through which they propagate.
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A drug tagged with 9943Tc (half-life = 6. 05 h) is prepared for a patient. If the original activity of the sample was 1. 0 ✕ 104 Bq, what is its activity (R) after it has been on the shelf for 1. 8 h?
After 1.8 hours on the shelf, the activity of the drug tagged with 99m43Tc is approximately 8147 Bq.
Step 1: Calculate the number of half-lives that have passed.
To do this, divide the elapsed time (1.8 h) by the half-life of the isotope (6.05 h).
Number of half-lives = 1.8 h / 6.05 h = 0.2975 half-lives
Step 2: Use the decay formula to calculate the remaining activity.
The decay formula is R = R₀ * (1/2)^(t/T), where R is the remaining activity, R₀ is the initial activity, t is the elapsed time, and T is the half-life.
Step 3: Plug in the values and solve for R.
R = (1.0 x 10^4 Bq) * (1/2)^(0.2975)
R ≈ 1.0 x 10^4 Bq * 0.8147
R ≈ 8147 Bq
So, after 1.8 hours on the shelf, the activity of the drug tagged with 99m43Tc is approximately 8147 Bq.
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Activity 3:
Direction: Read the sample weather bulletin.
Weather Bulletin: Tropical Cyclone Typhoon Rolly (GONI)
Sunday, 1 November, 2020 at 4:00 PM (DOST PAG-ASA 2020)
Location of Center
50 km South Southwest of Tayabas, Quezon
Coordinates
13. 6°N, 121. 40 E
Strength of the Winds
Maximum sustained winds of 165 km/h near
the center and gustiness of up to 230 km/h.
Movernent
Moving westward at 25 km/h
Forecast positions
(24 hours) Afternoon of November 2: 300 km
West of Iba, Zambales
15. 1° N, 117. 20 E
(48 hours) Afternoon of November 3: 665 km
West of Iba, Zambales
Outside PAR (15° N, 113. 8°E)
(72 hours) Afternoon of November 4: 935 km
West of Central Luzon
Outside PAR (14. 79 N, 111. 6° E)
Questions:
3.
What is the speed of the typhoon winds?
What is the velocity of the typhoon?
How does speed differ from velocity?
How important is knowing the velocity in determining the weather
forecast for the next hours?
4
Let Us Reflect
Based on the weather bulletin provided for Typhoon Rolly (GONI), the speed of the typhoon winds is 165 km/h with gustiness up to 230 km/h.
The velocity of the typhoon, which takes into account both the speed and direction, is moving westward at 25 km/h.
The main difference between speed and velocity is that speed only considers the magnitude of motion, while velocity includes both the magnitude and direction of motion.
Knowing the velocity of the typhoon is important in determining the weather forecast for the next hours, as it helps predict the movement and potential impact of the typhoon on specific areas.
This information can help authorities and individuals prepare and respond accordingly to ensure safety and minimize damages.
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Which observation supports a model of the nature of light in which light acts as a wave
The observation from the constructive interference supports the model of the wave nature of light. The correct option (A).
The observation of diffraction and interference lends weight to the idea that light behaves like a wave. When two or more waves interact with one another, interference occurs. It can be constructive (where the waves reinforce one another) or destructive (where the waves cancel one another out). When light waves from various sources overlap or pass through small gaps, this phenomenon can be seen.
Another property of waves, including light waves, is diffraction. When waves approach an obstruction or pass through an opening, they may bend or spread out. When light waves come into contact with sharp edges, slits, or other obstructions, diffraction patterns can be seen, and they are compatible with how waves behave.
Strong proof that light is a wave and that theories like the electromagnetic wave theory of light are correct can be found in the observations of interference and diffraction.
Hence, The observation from the constructive interference supports the model of the wave nature of light. The option is (A).
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Complete Question:
Which observation supports a model of the nature of light in which light acts as a wave?
A. Constructive interference
B. Temperature change
C. Blackbody radiation
D. Photoelectric effect
Technician a says that there is often more than one circuit being protected by each fuse. Technician b says that more than one circuit often shares a single ground connector. Which technician is correct?
a. Technician a.
b. Technician b.
c. Both technician a and b.
d. Neither technician a and b
The correct answer is c. Both Technician A and B are correct.
Technician A is correct because there is often more than one circuit being protected by each fuse. Fuses are used to protect electrical circuits from excessive current, which can cause damage or fire. It is common for multiple circuits to be connected to a single fuse, as it simplifies the electrical system and reduces the number of fuses needed.
Technician B is also correct because more than one circuit often shares a single ground connector. A ground connector provides a path for excess electrical energy to flow safely to the ground, preventing damage to components and electrical shock. By sharing a ground connector, multiple circuits can utilize a common grounding point, further simplifying the electrical system and reducing the need for additional connectors.
Overall Both technicians are correct, as multiple circuits can be protected by a single fuse, and multiple circuits can share a single ground connector.
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You add 50 mL of water at 20°C to 200 mL of water at 70°C. What is the most
likely final temperature of the mixture?
OA. 60°C
о B. 45°C
C. 30°C
о D. 50°C
Answer:
Option (a)
Explanation:
Let c be the specific heat of water.
According to the principle of caloriemetry.
Heat lost by hot water = heat gained by cold water
200 x c x (70 - T) = 50 x c x (T - 20)
280 - 4T = T - 20
300 = 5T
T = 60 C
Explanation:
In a case whereby You add 50 mL of water at 20°C to 200 mL of water at 70°C the most likely final temperature of the mixture is A. 60°C.
How can this be calculated?Specific heat is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius (or one Kelvin). Different substances have different specific heats, which means that they require different amounts of heat energy to achieve the same temperature change.
The specific heat of water can be represented as c, following the principle of caloriemetry. (Heat lost by hot water) =( heat gained by cold water), thjen we can substitute the values as ;
[200 x c x (70 - T)] = [50 x c x (T - 20)]
[280 - 4T] = [T - 20]
[300 = 5T]
T = 60 C
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Stephen rubbed one balloon on his hair for 10 seconds.
Then he grabbed another balloon and rubbed it on his hair for 10 seconds.
What will happen if he ties a string to each balloon and places them next to each other?
a The two balloons will repel.
b The two balloons will attract.
c The two balloons will do nothing since they are not charged.
Answer:
a. The two balloons will repel
Explanation:
when stephen rubs the balloon on his head, the balloon collects a negative charge. this will happen to both balloons and because the balloons are both negatively charged they will repel
A sound wave has a wavelength of 0. 96 m. How many times does this wave cause your eardrum to oscillate back and forth in 1 s?
A sound wave has a wavelength of 0. 96 m and this sound wave causes your eardrum to oscillate back and forth 357 times per second or 357 Hz.
The number of times a sound wave causes your eardrum to oscillate back and forth in one second is known as its frequency. We can calculate the frequency of a sound wave by dividing the speed of sound by its wavelength.
The speed of sound in air at room temperature is about 343 m/s.To calculate the frequency of a sound wave with a wavelength of 0.96 m, we can use the formula:
frequency = speed of sound/wavelength
frequency = 343 m/s / 0.96 m
frequency = 357 Hz
Therefore, this sound wave causes your eardrum to oscillate back and forth 357 times per second, or 357 Hz.
In summary, the frequency of a sound wave is the number of times it causes your eardrum to oscillate back and forth in one second. We can calculate the frequency of a sound wave by dividing the speed of sound by its wavelength. A sound wave with a wavelength of 0.96 m has a frequency of 357 Hz.
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. a tire 0.500 m in radius rotates at a constant rate of 200 revolutions per minute. find the speed and acceleration of a small stone lodged in the tread of the tire
The speed of the small stone lodged in the tire's tread is approximately 10.47 m/s, and its acceleration is approximately 219.35 m/s².
We need to find the speed and acceleration of a small stone lodged in the tread of a tire with a 0.500 m radius, rotating at 200 revolutions per minute.
First, let's convert the revolutions per minute (rpm) to radians per second (rad/s):
200 rpm * (2π radians/1 revolution) * (1 minute/60 seconds) ≈ 20.94 rad/s
Now, we can find the linear speed (v) of the stone using the formula:
v = rω, where r is the radius, and ω is the angular velocity in rad/s.
v = 0.500 m * 20.94 rad/s ≈ 10.47 m/s
Next, we'll find the centripetal acceleration (a_c) of the stone using the formula:
a_c = rω²
a_c = 0.500 m * (20.94 rad/s)² ≈ 219.35 m/s²
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Co-efficient of volume expansion of
aluminium
The coefficient of volume expansion of a material is a measure of how much its volume changes with a change in temperature. For aluminium, the coefficient of volume expansion is approximately [tex]7.1 \times 10^{-5}[/tex] per degree Celsius ([tex]K^{-1}[/tex]).
For aluminium, the coefficient of volume expansion is approximately [tex]23.1 \times 10^{-6}[/tex] per degree Celsius. This means that for every degree Celsius increase in temperature, the volume of aluminium will increase by approximately 23.1 parts per million (ppm).
This coefficient of volume expansion is an important property of aluminium, as it affects its behaviour in a variety of applications. For example, in the aerospace industry, aluminium is used extensively in the construction of aircraft because of its low weight and high strength-to-weight ratio. However, as the temperature of the aircraft changes during flight, the volume of the aluminium components will also change, potentially affecting the structural integrity of the aircraft.
Understanding the coefficient of volume expansion is therefore essential for engineers and designers working with aluminium in a variety of fields, from aerospace to construction to electronics.
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How does the freezing method work when separating engine oil from water?
The freezing method works by exploiting the difference in freezing points between engine oil and water. However, its effectiveness may vary depending on the properties and composition of the mixture.
The freezing method for separating engine oil from water is based on the difference in freezing points between the two substances. Water has a higher freezing point than most engine oils, which means that when a mixture of oil and water is cooled to a temperature below the freezing point of water, the water will freeze while the oil remains in liquid form.
To use this method, the mixture is first placed in a container and then put in a freezer or other cooling device. As the temperature drops, the water in the mixture will begin to freeze, forming ice crystals. These can then be removed by either skimming them off the surface or pouring off the liquid oil, which should be separated from the frozen water.
It's worth noting that this method is not always effective, as some engine oils may have a higher freezing point than water, making it difficult to separate them using this technique. Additionally, it may not be suitable for larger quantities of oil and water or for more complex mixtures containing other substances.
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Find the frequency of the 5th harmonic (h5) of a 5 hz fundamental
The frequency of the 5th harmonic of a 5 Hz fundamental is 25 Hz.
To find the frequency of the 5th harmonic (h₅) of a 5 Hz fundamental, you need to multiply the fundamental frequency (f₁) by the harmonic number (n). The formula is:
fₙ = n*f₁
where:
fₙ = frequency of the nth harmonic
f₁ = fundamental frequency
n = harmonic number
In this case, the fundamental frequency (f₁) is 5 Hz and the harmonic number (n) is 5. So, the frequency of the 5th harmonic (h₅) would be:
h₅ = 5 * 5
= 25 Hz
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In the figure, a horse pulls a barge along a canal by means of a rope. The force on the barge from the rope has a magnitude of 7890 N and is at the angle θ = 13° from the barge's motion, which is in the positive direction of an x axis extending along the canal. The mass of the barge is 9500 kg, and the magnitude of its acceleration is 0. 12 m/s2. What are (a) the magnitude and (b) the direction (measured from the positive direction of the x axis) of the force on the barge from the water? Give your answer for (b) in the range of (-180°, 180°]
A horse pulls a barge along a canal by means of a rope. The force on the barge from the rope has a magnitude of 7890 N and is at the angle θ = 13° from the barge's motion, which is in the positive direction of an x axis extending along the canal. The mass of the barge is 9500 kg, and the magnitude of its acceleration is 0. 12 m/[tex]s^{2}[/tex]. 7890 N is the magnitude of the force and its direction (measured from the positive direction of the x axis) is 103°.
a. To solve this problem, we need to use Newton's second law, which states that the net force acting on an object is equal to the product of its mass and acceleration
Fnet = m*a.
We can start by finding the net force acting on the barge, which is the force of the rope pulling it forward minus the force of the water pushing against it. Since the barge is moving at a constant speed, the net force must be zero. Thus, we have
Frope - Fwater = 0
Solving for Fwater, we get
Fwater = Frope = 7890 N
This is the magnitude of the force on the barge from the water.
b. To find the direction of this force, we need to use trigonometry. Let's call the angle between the force of the rope and the positive x axis φ. Then we have
φ = 90° - θ = 90° - 13° = 77°
This means that the force of the rope makes an angle of 77° with the negative x axis. Since the net force is zero, the force of the water must make an angle of 180° - 77° = 103° with the negative x axis.
Therefore, the magnitude of the force on the barge from the water is 7890 N and its direction (measured from the positive direction of the x axis) is 103°.
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