The current required in the loop to experience the given torque is [tex]\boxed{6.366\times{{10}^2}\,{\text{A}}}[/tex] or [tex]\boxed{636.6\,{\text{A}}}[/tex] .
Further Explanation:
Given:
The diameter of the circular loop is [tex]20\,{\text{cm}}[/tex] .
The torque experienced by the circular loop is [tex]1.0\times{10^{-3}}\,{\text{N}}\cdot{\text{m}}[/tex] .
Concept:
Since the circular loop is kept in the effect of the Earth’s Magnetic field, it will experience a magnetic torque due to the magnetic lines of force passing through the area of cross-section of the loop.
The torque experienced by the loop is expressed as:
[tex]\boxed{\tau =BIA}[/tex]
Here, [tex]\tau[/tex] is the torque experienced, [tex]B[/tex] is the magnetic field, [tex]I[/tex] is the current in the loop and [tex]A[/tex] is the area of cross-section of the loop.
The strength of the Earth’s magnetic field is [tex]5\times{10^{-5}}\,{\text{T}}[/tex] .
Substitute the values in the above expression.
[tex]\begin{aligned}1.0\times{10^{-3}}&=\left({5\times{{10}^{-5}}}\right)\timesI\times\left({\pi \times{{\left({\frac{d}{2}}\right)}^2}}\right)\\I&=\frac{{1.0\times{{10}^{-3}}}}{{5\times{{10}^{-5}}\left({\pi {{\left({\frac{{0.20}}{2}}\right)}^2}}\right)}}\\&=6.366\times{10^2}\,{\text{A}}\\\end{aligned}[/tex]
The current required in the loop to experience the given torque is [tex]\boxed{6.366\times{{10}^2}\,{\text{A}}}[/tex] or [tex]\boxed{636.6\,{\text{A}}}[/tex] .
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Answer Details:
Grade: College
Subject: Physics
Chapter: Electromagnetism
Keywords:
Earth’s magnetic field, torque, maximum torque, maximum current, through the loop, experience a modest torque, T=BIA, 636 A, wire is oriented.
Making a pancake from batter is an example of a _____ change
What is the force of attraction between cations and anions?
Final answer:
The force of attraction between cations and anions is electrostatic attraction, which is fundamental to the formation of ionic bonds. The strength of this force depends on the charges of the ions and the distance between them, with stronger forces resulting from higher charges or shorter distances. The arrangement of ions in a crystal structure and the Madelung constant also play roles in the bond strength.
Explanation:
The force of attraction between cations and anions is known as electrostatic attraction. This is the principle underlying ionic bonds, which form when electrons are transferred from one atom to another, leading to the creation of oppositely charged ions that are held together by this force. According to Coulomb's law, the strength of the electrostatic force between two ions is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
A cation with a greater positive charge will form a stronger bond than one with a lesser charge. Conversely, larger ions result in weaker bonds due to the increased distance between the electrons of one ion and the nucleus of the other. Additionally, the orientation of ions in a crystal lattice affects the attractive forces. Salts such as NaF and NaCl are classic examples, where ions arrange themselves in a way to maximize attractive interactions and minimize repulsive ones.
The Madelung constant also influences the bond strength and depends on the type of crystal structure. The potential energy of an ionic bond can be quantitatively expressed using the formula involving Avogadro's number, Madelung constant, ion charges, the charge of an electron, and the ion radius.
People who have color vision deficiency typically lack one or more of the three cones that are sensitive to a particular wavelength.
true or false
People who have color vision deficiency typically lack one or more of the three cones that are sensitive to a particular wavelength is the true statement.
What is color vision deficiency?Color vision deficiency is the inability to distinguish certain shades of color. Color blindness is used to describe this visual condition, but very few people are completely color blind.
What are cones?Color vision is possible due to photoreceptors in the retina of the eye known as cones. These cones have light-sensitive pigments that enable us to recognize color.
Each cone is sensitive to either red, green or blue light. The cones recognize these lights based on their wavelengths.
The pigments inside the cones register different colors and send that information through the optic nerve to the brain.
Most people with color vision deficiency can see colors. The most common form of color deficiency is red-green. It does not mean people with this deficiency cannot see these colors altogether, they simply have a harder time differentiating between them, which can depend on the darkness or lightness of the colors.
Another form of color deficiency is blue-yellow. It is a rarer and more severe form of color vision loss than just red-green deficiency as people with blue-yellow deficiency frequently have red-green blindness, too. In both cases, people with color-vision deficiency often see neutral or gray areas where color should appear.
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A karate expert breaks a stack of bricks with his bare hand. If the force applied is 520 newtons and the impact time is 5.0 × 10-4 seconds, what is the value of impulse?
Final answer:
The impulse delivered by the karate expert's hand to the stack of bricks is 2.6 × 102 N·s, which can be calculated using the force of 520 newtons multiplied by the impact time of 5.0 × 10-4 seconds.
Explanation:
The student is asking about the concept of impulse in physics. The impulse experienced by an object is the product of the average force applied to the object and the time interval over which it is applied. According to the given information:
Force (F) = 520 newtonsImpact time (t) = 5.0 × 10-4 secondsThe impulse (J) can be calculated using the formula:
J = F × t
By substituting the given values:
J = 520 N × 5.0 × 10-4 s = 0.26 kg·m/s
To express it in scientific notation, we can write it as 2.6 × 102 N·s (Newtons second), which is the value of the impulse delivered by the karate expert's hand to the stack of bricks.
the speedometer in a car does not measure the cars velocity because the velocity is a...
The speedometer in a car does not measure velocity because velocity is a vector quantity, including both speed and direction, and the speedometer only provides information about speed (magnitude). So, the correct option is A, velocity is a vector quantity that includes both speed and direction.
Let's go into more detail:
Velocity:
- Velocity is a vector quantity that includes both speed and direction.
- Speed is the magnitude of velocity, representing how fast an object is moving.
- Direction is a crucial component of velocity; it indicates the path an object is taking.
Speed:
- Speed is a scalar quantity, representing only the magnitude of motion, or how fast an object is moving.
- It does not include information about the direction of motion.
Speedometer in a Car:
- The speedometer in a car measures the instantaneous speed of the vehicle.
- It provides information about how fast the car is moving at a given moment.
- However, the speedometer does not provide any information about the direction in which the car is moving.
- Since velocity includes both speed and direction, and the speedometer only measures speed, it does not directly measure velocity.
Correct Answer (A):
- The correct option is (A) because velocity is indeed a vector quantity, having both magnitude (speed) and direction.
- The speedometer, by measuring speed alone, does not account for the directional component of velocity.
Complete Question: The speedometer in a car does not measure the car's velocity because velocity is a
(A) vector quantity and has a direction associated with it
(B) vector quantity and does not have a direction associated with it
(C) scalar quantity and has a direction associated with it
(D) scalar quantity and does not have a direction associated with it
Janet jumps off a high diving platform with a horizontal velocity of 2.06 m/s and lands in the water 1.8 s later. How high is the platform? The acceleration of gravity is 9.8 m/s 2 .
Which two processes increase the motion of the molecules?
Final answer:
Increasing the temperature and decreasing the solvent density are two processes that increase the motion of molecules, facilitating increased diffusion rates.
Explanation:
The two processes that increase the motion of molecules are raising the temperature and decreasing the solvent density. When the temperature is increased, it provides more energy to the molecules, thus making them move faster and increasing the rate of diffusion. On the other hand, a lower solvent density means that the molecules have fewer obstructions to navigate through, allowing them to move more freely and thus increasing diffusion rate.
For instance, heating water can increase the kinetic energy of its molecules, leading to a faster spread of those molecules through the environment. Conversely, if water is very dense, such as saltwater compared to fresh water, molecules of a solute would diffuse more slowly due to the increased resistance.
The primary of a step-up transformer is connected across the terminals of a standard wall socket, and resistor 1 with a resistance r1 is connected across the secondary. the current in the resistor is then measured. next, resistor 2 with a resistance r2 is connected directly across the terminals of the wall socket (without the transformer). the current in this resistor is also measured and found to be the same as the current in resistor 1. how does the resistance r2 compare to the resistance r1? answers
The resistance [tex]\( r_2 \)[/tex] is greater than the resistance [tex]\( r_1 \)[/tex] by the square of the turns ratio of the transformer.
Let's denote the turns ratio of the step-up transformer as [tex]n[/tex], which is the ratio of the number of turns in the secondary winding [tex]\( N_s \)[/tex] to the number of turns in the primary winding [tex]\( N_p \)[/tex]. Therefore, [tex]\( n = \frac{N_s}{N_p} \).[/tex]
Since it is a step-up transformer, [tex]\( n > 1 \).[/tex]
The voltage across the secondary winding [tex]\( V_s \)[/tex] is equal to the voltage across the primary winding [tex]V_p[/tex] multiplied by the turns ratio [tex]n[/tex]. Thus, [tex]\( V_s = n \cdot V_p \).[/tex]
The current in the secondary winding [tex]\( I_s \)[/tex] is related to the current in the primary winding [tex]\( I_p \)[/tex] by the inverse of the turns ratio, due to the conservation of power in an ideal transformer (neglecting losses). Therefore, [tex]\( I_s = \frac{I_p}{n} \).[/tex]
The power delivered to both resistors must be the same because the current in both cases is measured to be the same, and power is the product of voltage and current. Hence, [tex]\( P = V_s \cdot I_s = V_p \cdot I_p \).[/tex]
Now, let's calculate the resistance of the resistors using Ohm's law, which states that [tex]\( V = I \cdot R \)[/tex], where [tex]V[/tex] is the voltage, [tex]I[/tex] is the current, and [tex]R[/tex] is the resistance.
For resistor 1 connected across the secondary:
[tex]\( R_1 = \frac{V_s}{I_s} \)[/tex]
Substituting [tex]\( V_s = n \cdot V_p \) and \( I_s = \frac{I_p}{n} \)[/tex] into the equation, we get:
[tex]\( R_1 = \frac{n \cdot V_p}{\frac{I_p}{n}} = n^2 \cdot \frac{V_p}{I_p} \)[/tex]
For resistor 2 connected directly across the wall socket:
[tex]\( R_2 = \frac{V_p}{I_p} \)[/tex]
Since the currents are the same [tex](\( I_s = I_p \))[/tex], we can equate the powers:
[tex]\( V_s \cdot I_s = V_p \cdot I_p \)[/tex]
Substituting [tex]\( V_s = n \cdot V_p \) and \( I_s = I_p \),[/tex] we get:
[tex]\( n \cdot V_p \cdot I_p = V_p \cdot I_p \)[/tex]
This simplifies to:
[tex]\( n = 1 \)[/tex]
However, this is not possible since [tex]\( n > 1 \)[/tex] for a step-up transformer. The mistake here is that we assumed [tex]\( I_s = I_p \)[/tex] without considering the turns ratio. The correct approach is to use the power equation:
[tex]\( P = V_s \cdot I_s = V_p \cdot I_p \)[/tex]
Since [tex]\( V_s = n \cdot V_p \) and \( I_s = \frac{I_p}{n} \),[/tex] we have:
[tex]\( n \cdot V_p \cdot \frac{I_p}{n} = V_p \cdot I_p \)[/tex]
This simplifies to:
[tex]\( V_p \cdot I_p = V_p \cdot I_p \)[/tex]
Now, using the resistance formula for both resistors, we have:
[tex]\( R_1 = \frac{V_s}{I_s} = \frac{n \cdot V_p}{\frac{I_p}{n}} = n^2 \cdot \frac{V_p}{I_p} \)[/tex]
[tex]\( R_2 = \frac{V_p}{I_p} \)[/tex]
Comparing [tex]\( R_1 \) and \( R_2 \), we find: \( R_1 = n^2 \cdot R_2 \)[/tex]
Since [tex]\( n > 1 \)[/tex], it follows that [tex]\( R_1 > R_2 \)[/tex]. However, we are asked how [tex]\( r_2 \)[/tex]compares to [tex]\( r_1 \)[/tex], which means we need to express [tex]\( R_2 \)[/tex] in terms of [tex]\( R_1 \)[/tex]:
[tex]\( R_2 = \frac{R_1}{n^2} \)[/tex]
Therefore, [tex]\( r_2 \) is less than \( r_1 \)[/tex] by a factor of [tex]\( n^2 \)[/tex],
mercury is 0.39 AU from the sun what is its distance from the sun in kilometers
Answer:The distance of Mercury from the Sun in kilometer is [tex]5.8344\times 10^7 km[/tex].
Explanation;
Distance between the Mercury and Sun = 0.39 AU
1 AU = [tex]1.496\times 10^8 km[/tex]
So, 0.39 AU = [tex]0.39\times 1.496\times 10^8 km=5.8344\times 10^7 km[/tex]
The distance of Mercury from the Sun in kilometer is [tex]5.8344\times 10^7 km[/tex].
Which of the following is not true about chemical changes? a. They form a new substance. b. They can be reversed by physical changes. c. They can be detected by changes such as color. d. They have different properties from their starting materials. Please select the best answer from the choices provided
Answer : The incorrect option is (b) They can be reversed by physical changes.
Explanation :
Chemical change : It is a change where changes occurs in the chemical composition and thus resulting in the formation of new compound or substance. It is an irreversible reaction.
The indication of chemical changes are :
Formation of gas bubbles.
Formation of precipitate.
Change in color.
Change in temperature.
Change in volume.
Change in smell or taste.
Evolution of heat, light and sound.
Physical change : It is a change in which shape and size of a substance changes. In this there is no change in the chemical composition of the substance and no new substance is forming. It is a reversible reaction.
The indication of chemical changes are :
Change in shape.
Change in form.
Change in size.
Change in phase.
From the given options we conclude that the option (b) is incorrect option while all the options are correct for chemical changes.
Hence, the incorrect option is (b)
If you hold a horizontal metal bar several centimeters above the ground and move it through grass, each leaf of grass bends out of the way.?
Slate is a metamorphosed rock made from the sedimentary rock _____. A. shale B. limestone C. sandstone D. conglomerate
Answer:
A. Shale
Explanation: Sedimentary rocks are converted into metamorphosed rocks under high temperature and pressure. Shale is a sedimentary rock which get converted into slate under high temperature and pressure. Shale is a sedimentary rock made up of volcanic ash or clay while slate is a fine- grained , homogeneous metamorphosed rock. Slate can be found in many colors such as- grey, green, pale to brown.
The de broglie wavelength of an electron is 8.7 Ã 10-11 m. the mass of an electron is 9.1 Ã 10-31 kg. the velocity of this electron is ________ m/s.
A car is skidding to a stop on a level stretch of road. you may want to review ( pages 115 - 117) . part a identify the number of the action/reaction pairs of forces between the car and the road surface.
When rust forms on a piece of iron, what evidence do you have that a chemical reaction has taken place?
Calculate the resultant force, fr, and the couple moment, mr,a. don't forget to include the appropriate signs with your numerical answers.
What is another word for change in motion?
Acceleration is another term for change in motion, referring to changes in velocity due to an applied external force.
Another word for change in motion is acceleration. This term refers to a change in velocity, which includes changes in speed, direction, or both. When an object experiences acceleration, it means there has been a non-zero net external force applied to it, as stated by Newton's first law of motion.
Acceleration is quantified as the rate of change of velocity over time and is observed in everyday phenomena such as the breaking of a car or the circular motion of a rotating wheel.
A kangaroo jumps to a vertical height of 2.3 m. how long was it in the air before returning to earth?
Two ice skaters stand at rest in the center of an ice rink. when they push off against one another the 45-kg skater acquires a speed of 0.62 m/s. if the speed of the other skater is 0.89 m/s, what is this skater's mass?
Answer:
mass of other skater is 31.3 kg
Explanation:
Here since we know that two skaters push each other so if we consider two skaters as system then there is no external force on the system.
hence we can say that momentum of the system is conserved
so here we have
[tex]P_i = P_f[/tex]
now we can say that initially both skaters are at rest so initial total momentum is ZERO for both
now we have
[tex]0 = m_1v_{1i} + m_2v_{2i}[/tex]
[tex]0 = 45(0.62) + m_2(-0.89)[/tex]
[tex]m_2 = 31.3 kg[/tex]
Based on the information given, the mass of the other skater will be 31.3 kg.
How to calculate the mass.From the information given, ice skaters stand at rest in the center of an ice rink. when they push off against one another the 45-kg skater acquires a speed of 0.62 m/s and the speed of the other skater is 0.89 m/s.
Therefore, the mass of the skater will be:
0 = 45(0.62) + (-0.89)m
m = 31.3kg
In conclusion, the correct option is 31.3kg.
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The automobile is originally at rest s = 0. if it then starts to increase its speed at v # = (0.05t 2) ft>s2, where t is in seconds, determine the magnitudes of its velocity and acceleration at s = 550 ft.
The velocity of the car at s = 550 ft is 2,904,166.67 ft/s and the acceleration at s = 550 ft is 1512.5 ft/s^2.
Explanation:The velocity of the car can be determined by finding the integral of the acceleration function with respect to time. In this case, the acceleration function is v' = 0.05t^2. Integrating this function gives the velocity function v = (0.05/3)t^3 + C, where C is the constant of integration. To find the value of C, we can use the fact that the car is originally at rest, so v(0) = 0. Plugging in the values, we get C = 0, so the velocity function is v = (0.05/3)t^3.
To find the magnitude of the velocity at t = 550 ft, we can plug in the value of t into the velocity function. So, v = (0.05/3)(550)^3 = 2,904,166.67 ft/s. Therefore, the magnitude of the velocity at s = 550 ft is 2,904,166.67 ft/s.
The acceleration can be determined by taking the derivative of the velocity function with respect to time. In this case, the velocity function is v = (0.05/3)t^3. Taking the derivative, we get a = (0.05)t^2. Plugging in the value of t = 550 ft, we get a = (0.05)(550)^2 = 1512.5 ft/s^2. Therefore, the magnitude of the acceleration at s = 550 ft is 1512.5 ft/s^2.
What evidence is there from your results that the characteristic color observed for each compound is due to the metal ion in each case? describe an additional test that could be done to confirm that the color is due to the metal ion?
The color in metal compounds is primarily due to the metal ion and how it interacts with light. This is evident in emission spectra and color patterns seen in flame tests. A flame test can specifically prove this by displaying characteristic colors for each metal ion.
Explanation:The color observed in metal compounds is often due to the metal ion involved in the compound - a phenomenon made apparent by changes in the relative energies of the electron orbitals. To illustrate, compounds of a variety of metals (including alkaline earth metals like calcium and strontium) produce different colors when exposed to flame - a feature of their emission spectrum. Furthermore, the color of coordination compounds, like the iron(II) complex [Fe(H₂O)6]SO4 that appears blue-green, depends on the specific ligands coordinated to the metal center, which influences the absorption of light.
A simple test to confirm that the color is due to the metal ion is to perform flame tests on the compounds. This test involves introducing the compound to a flame and observing the color of the flame. Each metal ion can produce a characteristic flame color; hence the flame test serves to confirm the presence of a specific metal ion in a compound.
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If a 4.5 kg object is dropped from a height of 6.0 m, what will be its velocity when it is halfway toward the ground? (Use g = 9.80 m/s2, and ignore air resistance.) 7.7 m/s 11 m/s 16 m/s 29 m/s
The velocity of object at halfway is 7.67 m/s.
Given data:
The mass of object is, m = 4.5 kg.
The height from the ground is, h = 6.0 m.
When an object falls or is dropped from rest it's initial velocity is zero.
(u = 0). Using the second kinematic equations for a motion, find the time it takes to reach 3.0 m down (half way).
x = ut - 1/2gt²
x = ut - 1/2 (9.8) t²
x = ut - 4.9t²
-3 = 0 - 4.9t²
-3/-4.9 = t²
0.6122 = t²
0.7825 sec = t
Now, apply the first kinematic equation of motion as,
v = u + (-g)t
v = 0 - 9.8(0.7825)
v = -7.67 m/s
the negative denotes downward direction.
Thus, we can conclude that the velocity of object at halfway is 7.67 m/s.
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Two conductors are made of the same material and have the same length. conductor a is a solid wire of diameter 1.3 mm. conductor b is a hollow tube of outside diameter 8.0 mm and inside diameter 7.0 mm. what is the resistance ratio ra/rb , measured between their ends?
A train rolls past a stationary observer. To him, the train is moving at a speed of 23 m/s west, and a woman on the train is moving at a speed of 22.4 m/s west. How long does it take the woman to move 13 m relative to the train?
Answer:
21.7 seconds
Explanation:
A person who climbs up something (e.g., a hill, a ladder, the stairs) from the ground gains potential energy. a person's weight (f = mg) is usually measured in pounds. for conversions, you may need to know that the weight of 1 pound is equal to 4.448 newtons. part a how many meters above the ground would a 240 lb person have to climb to gain 3 kilojoules (3000 joules) of potential energy?
We are given the following values:
weight w = 240 lb = 1,067.52 N
energy E = 3,000 J
The formula for potential energy is:
E = w h
where h is the height the person has to climb, therefore:
h = 3000 / 1067.52
h = 2.81 m
Therefore he has to climb 2.81 meters
A Honda Civic Hybrid weighs about 3200 lb .
Part A
Calculate the weight of the car in newtons. (Note: 0.22 lb =1N).
Answer:
14545 .45 N
Explanation:
The weight of given car is 3200 lb.
0.22 lb = 1 N (Given)
[tex]1 = \frac{1}{0.22}N/lb[/tex]
Therefore, the weight of the car in N can be calculated as follows:
[tex]3200 lb =3200 lb\times \frac{1}{0.22}N/lb=14545 .45 N[/tex]
The speed of sound in air is 344 m/s at room temperature. the lowest frequency of a large organ pipe is 30 s−1 and the highest frequency of a piccolo is 1.5×104s−1. part a find the difference in wavelength between these two sounds. express your answer using two significant figures. λ = 11 m
The formula for calculating wavelength ʎ is:
ʎ = s / f
where ʎ is wavelength, s is speed of sound, f is frequency
ʎ (large organ pipe) = (344 m/s) / (30 s-1) = 11.47 m
ʎ (piccolo) = (344 m/s) / (1.5x10^4 s-1) = 0.023 m
So the difference is:
11.47 – 0.023 = 11.45 m
Answer:
11.45 m
The difference in wavelength between the lowest frequency of a large organ pipe and the highest frequency of a piccolo, with the speed of sound at 344 m/s, is approximately 11 m.
Explanation:The question asks to calculate the wavelength difference between the lowest frequency of a large organ pipe and the highest frequency of a piccolo, given the speed of sound in air at room temperature. The speed of sound in air at 21°C is typically around 344 m/s. The frequency for the organ pipe is 30 s⁻¹ (30 Hz), and for the piccolo, it's 1.5×10⁴ s⁻¹ (15,000 Hz). To find the wavelengths, we use the formula λ = v/f, where λ is the wavelength, v is the speed of sound, and f is the frequency. Thus, for the organ pipe, the wavelength is λ = 344 m/s / 30 s⁻¹ = 11.47 m, and for the piccolo, λ = 344 m/s / 1.5×10⁴ s⁻¹ = 0.0229 m. The difference in wavelength, to two significant figures, is about 11 m.
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within what force will acar hit a tree if the car has a mass of 3,000 kg and it is accelerating at a rate of 2 m/s/s
Short-range forecasts tends to ________ longer-range forecasts.
Short-range forecasts are typically more accurate than longer-range forecasts because they use near future data and can provide detailed specifics about the weather, which is difficult to maintain over a longer time span.
Explanation:In weather forecasting, short-range forecasts usually tend to be more accurate than longer-range forecasts. This is because the short-range forecasts use models that are based on current and near-future atmospheric conditions, which predict the weather for 1 to 3 days. On the other hand, longer-range forecasts predict weather for a period of 3 to 7 days or even up to several months, and although they can give a general pattern of the weather to be expected, they can't provide detailed specifics like short-range forecasts do. Therefore, short-range forecasts are typically more reliable than longer-range forecasts due to the complexities and variabilities involved in predicting atmospheric conditions over a long time span.
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which of the following statement best describes the laws of conservation mass?
Mass is neither created or destroyed.