The radius of the bowling ball is approximately 7.65 inches.
We can use the formula for the surface area of a sphere to find the radius of the bowling ball:
Surface area of a sphere = 4πr²
where r is the radius of the sphere.
In this problem, we are given the surface area of a bowling ball, which is 232 square inches. We can use this information and the formula for surface area of a sphere to solve for the radius of the ball. Plugging this value into the formula, we get:
232 = 4πr²
Dividing both sides by 4π, we get:
r² = 58.5
Taking the square root of both sides, we get:
r ≈ 7.65 inches
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if a red giant appears the same brightness as a red main sequence star, which one is further away
If a red giant appears the same brightness as a red main sequence star, it is most likely that the red giant is further away.
Here's a step-by-step explanation:
1) Red giants and red main sequence stars are both types of stars that are similar in color, but they have different sizes and luminosities.
2) Red giants are much larger and more luminous than red main sequence stars. They are formed when a star like the sun runs out of fuel and begins to expand and cool.
3)Red main sequence stars, on the other hand, are smaller and less luminous than red giants. They are stars that are still burning hydrogen fuel in their cores.
4) The apparent brightness of a star depends on both its intrinsic luminosity and its distance from Earth. The farther away a star is, the dimmer it appears to us on Earth.
5) If a red giant appears the same brightness as a red main sequence star, this means that the red giant must be much farther away from Earth than the red main sequence star.
6) This is because the red giant is intrinsically much more luminous than the red main sequence star. If both stars were at the same distance from Earth, the red giant would appear much brighter than the red main sequence star.
7) However, since the red giant appears the same brightness as the red main sequence star, this means that the red giant must be much farther away from Earth and therefore appears dimmer.
Overall, by comparing the apparent brightness of a red giant and a red main sequence star, we can determine which star is farther away.
If the red giant appears the same brightness as the red main sequence star, then the red giant is likely to be much farther away.
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at a given instant in time, an 8-kg rock that has been dropped from a high cliff, experiences an upward force of air resistance of 12 n.note: this is a multi-part question. once an answer is submitted, you will be unable to return to this part.what is the gravitational force on the rock? use g
The gravitational force on the rock is 78.4 Newtons.
At the given instant, the 8-kg rock experiences a gravitational force which can be calculated using the formula:
F_gravity = m * g
where m is the mass of the rock (8 kg) and g is the acceleration due to gravity (approximately 9.8 m/s²).
F_gravity = 8 kg * 9.8 m/s² = 78.4 N
So, the gravitational force on the rock is 78.4 Newtons.his net force causes the rock to accelerate downwards.
The concept of gravitational force is an important one in physics, as it plays a significant role in many natural phenomena. The force of gravity is responsible for the motion of celestial bodies, and it is also a key factor in determining the weight of objects on earth.
Understanding the principles of gravitational force can help us understand the behavior of objects in motion and can also help us develop technologies that are based on these principles.
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the speedometer of my car reads v = 45 m/s. is this … group of answer choices instantaneous speed? average speed?
The speedometer of your car reading v = 45 m/s indicates the instantaneous speed of your car at that particular moment in time.
Instantaneous speed is the speed of an object at a specific moment in time and is often represented as the magnitude of the instantaneous velocity vector. In the context of your car's speedometer, the reading of 45 m/s indicates the speed of your car at the exact moment the reading was taken.
In contrast, the average speed is the total distance travelled by an object divided by the time it took to travel that distance. It represents the average rate at which the object covered the distance, and does not provide information about the object's speed at any particular moment in time.
Therefore, the reading on your car's speedometer represents instantaneous speed, not average speed.
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The speedometer of your car reading v = 45 m/s is the instantaneous speed of the car.
Instantaneous speed is the speed of an object at a particular moment in time, without taking into account any previous or future motion. In this case, the speedometer is providing a real-time reading of the car's speed at that moment.
The speedometer measures the speed of the car through a device called a speed sensor.
The sensor measures the rotation of the wheels and converts it into an electrical signal, which is then used to calculate the speed of the car.
The speedometer then displays this speed in m/s or mph on the dashboard of the car.
It's important to note that instantaneous speed can change rapidly as the car accelerates, decelerates, or changes direction. This means that the speedometer reading will change as the car's speed changes.
In contrast, average speed is calculated by dividing the total distance traveled by the total time taken to travel that distance.
It provides an average value of the speed over a period of time, such as the entire trip or journey.
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if interstellar dust makes an rr lyrae variable star look 5 magnitudes fainter than the star should, by how much will you over- or underestimate its distance?
The distance to the RR Lyrae variable star will be underestimated by a factor of 10 due to the effect of interstellar dust.
The distance to an astronomical object can be determined using the inverse square law, which states that the apparent brightness of an object decreases as the square of the distance increases.
The apparent magnitude of an object is a measure of its brightness as seen from Earth. The lower the magnitude, the brighter the object.
If interstellar dust makes an RR Lyrae variable star look 5 magnitudes fainter than it should, then the apparent magnitude of the star as observed from Earth is 5 magnitudes greater than its true apparent magnitude.
Using the inverse square law, we can write:
Apparent brightness ~ 1 / (distance[tex])^2[/tex]
If the apparent brightness is 5 magnitudes fainter than it should be, we can express the distance to the star as:
distance = sqrt(100^(0.4 * 5)) x true distance
where 0.4 is the conversion factor from magnitudes to brightness ratios, and 100 is the ratio of the brightness of the star as observed from Earth to its true brightness.
Simplifying this expression, we get:
distance = 100^(0.5) x true distance
distance = 10 x true distance
Therefore, the distance to the RR Lyrae variable star will be underestimated by a factor of 10 due to the effect of interstellar dust.
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Describe what happens as the hair dryer takes in cool air from one end and blows out warm air from other end TYYYY
When the hair dryer is turned on, it draws in cool air from its back end and passes it over a heating element, which increases the temperature of the air.
What happens when a hair dryer intakes cool air from one end and expels warm air from the other?Cool air is taken in and is heated using a heating element as described. The heated air is then forced out through the front end of the dryer by a fan. As the warm air blows over the hair, it causes the water molecules in the hair to evaporate, thus drying the hair. The hair dryer also helps to style hair by blowing it in different directions, causing it to move and create volume.
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after the train passed, the pitch of the train whistle became lower. this change in sound would be represented by what change in the diagram below?
The change in sound of the train whistle from a higher pitch to a lower pitch after the train passes can be explained by the Doppler Effect.
Here is a step-by-step explanation:
1) The Doppler Effect is the change in frequency or pitch of a sound wave due to the relative motion of the sound source and the observer.
2) When the train is approaching the observer, the sound waves from the train are compressed and the frequency or pitch of the sound wave appears higher.
3) As the train passes the observer, the sound waves from the train are stretched and the frequency or pitch of the sound wave appears lower.
4) This change in frequency or pitch can be explained by the relative motion of the train and the observer.
When the train is approaching the observer, the sound waves from the train are "bunched up" and appear closer together, resulting in a higher frequency or pitch.
When the train is moving away from the observer, the sound waves are "stretched out" and appear further apart, resulting in a lower frequency or pitch.
5) The change in frequency or pitch of the train whistle can be represented by a graph showing the frequency of the sound wave over time.
Before the train passes, the frequency of the sound wave gradually increases as the train approaches the observer.
After the train passes, the frequency of the sound wave gradually decreases as the train moves away from the observer.
6) The change in frequency or pitch of the train whistle can also be calculated using the Doppler Effect equation, which relates the frequency of the sound wave, the speed of the sound wave, and the relative velocity of the train and the observer.
In summary, the change in sound of the train whistle from a higher pitch to a lower pitch after the train passes is due to the Doppler Effect, which is caused by the relative motion of the train and the observer.
The change in frequency or pitch can be represented by a graph or calculated using the Doppler Effect equation.
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type 1 cable consists of ? twisted pairs, each individually shielded with foil, with a braided outer shield surrounding the entire cable core and covered with a jacket.
Type 1 cable consists of a braided outer shield surrounding the entire cable core and covered with a jacket, the correct answer is c.
Type 1 cable is commonly used in high-frequency applications where signal interference is a concern. The braided shield provides excellent protection against electromagnetic interference (EMI) and radio frequency interference (RFI). It also helps to reduce signal loss and attenuation by keeping the signal within the cable and preventing it from escaping.
The jacket provides an additional layer of protection against environmental factors such as moisture, abrasion, and temperature extremes. Type 1 cable is a reliable and effective option for applications where signal integrity and protection against interference are critical factors, the correct answer is c.
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The complete question is:
Type 1 cable consists of ?
a. twisted pairs
b. each individually shielded with foil
c. with a braided outer shield surrounding the entire cable core and covered with a jacket.
the geocentric model of the universe that was widely accepted in scientific and religious circles until the 16th century was that of
The geocentric model of the universe that was widely accepted in scientific and religious circles until the 16th century was that of Ptolemy, also known as the Ptolemaic system.
The geocentric model of the universe, widely accepted in scientific and religious circles until the 16th century, was based on the idea that Earth was at the center of the cosmos.
This model, also known as the Ptolemaic system, was developed by the ancient Greek astronomer Claudius Ptolemy in the 2nd century AD. According to this model, all celestial objects, including the Sun, Moon, and stars, revolved around the Earth in circular or epicyclical paths.
The geocentric model was dominant for over a thousand years due to its alignment with religious beliefs and its ability to explain astronomical observations.
However, the 16th-century work of Nicolaus Copernicus and later astronomers led to the acceptance of the heliocentric model, which placed the Sun at the center of the solar system and was a more accurate representation of the cosmos.
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. a horizontal force of 200 n is applied to a 55 kg cart across a 10-m level surface. if the cart accelerates at 2.0 m/s2 , then what is the work done by the force of friction as it acts to impede the motion of the cart?
The first step to solving this problem is to calculate the net force acting on the cart. To do this, we need to use Newton's second law, which states that the net force is equal to the mass of the object multiplied by its acceleration. So, in this case, the net force on the cart is:
Net force = (55 kg)(2.0 m/s^2) = 110 N
Next, we need to determine the force of friction acting on the cart. We know that it is acting in the opposite direction to the applied force, so it is equal in magnitude to the net force but in the opposite direction. Therefore, the force of friction is:
Force of friction = -110 N
Finally, we can use the formula for work, which is:
Work = force x distance x cos(theta)
where theta is the angle between the force and the direction of motion. In this case, the force of friction is acting opposite to the direction of motion, so theta is 180 degrees and cos(theta) is -1.
The distance traveled by the cart is 10 m, so we can plug in the values and get:
Work = (-110 N)(10 m)(-1) = 1100 J
Therefore, the work done by the force of friction as it acts to impede the motion of the cart is 1100 J.
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duc 1. Define the term 'element. 2. If you break down each of the following, how many different atoms would you be able to recover? a) Mercury b) Sodium chloride c) Water d) Carbon dioxide e) Oxygen
part a.
An element is described as a pure substance that is composed of only one type of atom. Each element is characterized by a unique atomic number, which corresponds to the number of protons in the nucleus of its atoms.
part b.
a) Mercury - breaking down mercury would yield only mercury atoms.
b) Sodium chloride - Breaking down sodium chloride would yield sodium and chlorine atoms in their respective ratios.
c) Water -Breaking down water would yield hydrogen and oxygen atoms in their respective ratios.
d) Carbon dioxide : Breaking down carbon dioxide would yield carbon and oxygen atoms in their respective ratios.
e) Oxygen - breaking oxygen down would yield only oxygen atoms.
More about Elements?Some facts about elements includes;
Elements found on Earth and Mars are exactly the same.Hydrogen is the most common element found in the universe. Isotopes are atoms of the same element, with different numbers of neutrons.In ancient times the elements referred to fire, earth, water, and air.Learn more about elements at: https://brainly.com/question/20096027
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question 34 pts how do ambient sounds differ from sound effects?how are foley sounds different from sound effects?
The differences between ambient sounds, sound effects, and Foley sounds.
Ambient sounds, also known as background sounds or atmospheric sounds, are the continuous, subtle noises that help create a sense of atmosphere or location in a scene. They differ from sound effects in that sound effects are distinct, purposeful sounds added to emphasize specific actions or events in a scene.
Foley sounds, on the other hand, are a type of sound effect created manually by a Foley artist to match and enhance the actions happening on-screen. They are different from regular sound effects because they are typically recorded live in a studio using various objects and materials to create realistic, synchronized sounds for actions such as footsteps, clothing rustles, and object handling.
In summary:
1. Ambient sounds create a sense of atmosphere or location and are continuous and subtle.
2. Sound effects are distinct, purposeful sounds added to emphasize specific actions or events.
3. Foley sounds are a type of sound effect created manually by a Foley artist to match on-screen actions.
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suppose the horns of all cars emitted sound at the same pitch or frequency. what would be the change in the frequency of the horn of a car moving toward ou? away from you?
The frequency of the horn of a car moving towards you would increase, while the frequency of a car moving away from you would decrease due to the Doppler effect.
The frequency of the sound waves an automobile makes will rise as it approaches you. This is due to the sound waves compression as the automobile draws closer to you, which causes them to have a shorter wavelength and a higher frequency. The Doppler effect is the name for this rise in frequency.
On the other hand, when an automobile pulls away from you, the sound waves' frequency will drop because they stretch, leading to a longer wavelength and a lower frequency. As a result, if all vehicles produce sound at the same frequency, you would hear a frequency rise for a vehicle travelling in your direction and a frequency drop for a vehicle driving away from you.
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If the car is moving towards you, the frequency of the horn will increase,moving away from you, the frequency will decrease
If the horns of all cars emitted sound at the same pitch or frequency, the frequency of the horn of a car moving toward you would appear to increase, as the sound waves are compressed and the wavelength is shortened due to the Doppler effect. Conversely, the frequency of the horn of a car moving away from you would appear to decrease, as the sound waves are stretched and the wavelength is lengthened due to the Doppler effect. This is because the observer perceives a higher frequency when the source is approaching and a lower frequency when the source is moving away.
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After a person has made a change in their life, relapse is common.
A. True
B. False
Answer:
A true
Explanation:
because it is talking about drugs and alcohol
A system consists of two charges,
and 109. The force exerted on charge q has a magnitude
of F. Does the force exerted on the charge 10 q have a
magnitude that is greater than, less than or equal to F?
Explain.
The force exerted on the charge 10q has a magnitude that is greater than F.
The force between two charged particles is given by Coulomb's law:
F = k * q1 * q2 / r^2
If we consider the system of two charges, q and 10q, and assume that they are at the same distance from the test charge:
[tex]F = k * q * qtest / r^2[/tex]
where qtest is the charge of the test charge.
Similarly, the force on the test charge due to 10q is given by:
F' = k * (10q) * qtest / r^2
Dividing second equation by the first, we get:
F' / F =[tex](10q * qtest) / (q * qtest)[/tex] = 10
So the force exerted on the charge 10q has a magnitude that is greater than the force exerted on the charge q by a factor of 10.
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at what speed, in m/s , would a moving clock lose 2.7 ns in 1.0 day according to experimenters on the ground? hint: use the binomial approximation.
The clock must be moving at a velocity of approximately 4.53 m/s relative to the observers on the ground in order to experience a time dilation of 2.7 ns over the course of one day.
According to Einstein's theory of relativity, time dilation occurs when an object moves at a constant velocity relative to an observer. This means that time appears to pass more slowly for an object in motion than for an observer at rest. The amount of time dilation depends on the relative velocity between the two objects.
In this problem, we are given that a clock moving at some velocity loses 2.7 nanoseconds (ns) over the course of one day, as measured by observers on the ground. We want to determine the velocity of the clock.
We can use the formula for time dilation, which states that the observed time interval (Δt') is related to the proper time interval (Δt) by:
[tex]$\Delta t' = \frac{\Delta t}{\sqrt{1 - \frac{v^2}{c^2}}}$[/tex]
where v is the velocity of the clock, c is the speed of light, and the square root is taken using the binomial approximation (since v << c).
We know that Δt' = Δt - 2.7 ns and Δt = 1 day = 86400 seconds. Substituting these values and simplifying, we get:
[tex]$86400 - 2.7 = \frac{86400}{\sqrt{1 - \frac{v^2}{c^2}}}$[/tex]
Squaring both sides and rearranging, we can solve for v:
[tex]$v = c \sqrt{1 - \left(\frac{2.7}{86400}\right)^2} \approx 4.53 \text{ m/s}$[/tex]
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A substance is boiled repeatedly and stirred, but the solute never mixes with the solvent. Which best describes why?
Answer:
The solute and solvent have distinct chemical characteristics.
Explanation:
The solute and solvent could not have been mixed at the current temperature. The solute and solvent have distinct chemical characteristics. There was more pressure. The mixture was fully saturated.
Hope this helped :)
Answer: The fact that the solute does not mix with the solvent even after boiling and stirring repeatedly could be due to various reasons:
Insolubility: The solute may be insoluble in the solvent, meaning it cannot dissolve in it. This could be because the solute particles are too large or have a different molecular structure compared to the solvent. For example, oil and water do not mix because oil is non-polar while water is polar.
Immiscibility: The solute and solvent may be immiscible, which means they cannot form a homogeneous mixture. Immiscibility occurs when there is a significant difference in polarity or density between the solute and solvent. An example of immiscible substances is oil and water, where they form separate layers instead of mixing.
Saturation: The solvent may already be saturated with the solute. Saturation occurs when the solvent can no longer dissolve any more of the solute at a given temperature. Further boiling and stirring would not result in any additional mixing.
Chemical reaction: There might be a chemical reaction occurring between the solute and solvent, leading to the formation of a new substance or a precipitate. This can prevent the solute from dissolving completely in the solvent.
To determine the specific reason why the solute is not mixing with the solvent, it would be helpful to know the nature of the solute and solvent, as well as any other conditions or factors involved in the process.
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a wheel of radius 15 cm has sa rotational inertia of 2.3 kg m^2. the wheel is spinning at a rate of 6.5 revolutions per second. a frictional force is applied tangentially to the wheel to bring it to a stop. the work done by the torque to stop the wheel is most nearly:
The work done by the torque to stop the wheel is -1918 J.
The given parameters are:
- Wheel radius (r): 15 cm = 0.15 m
- Rotational inertia (I): 2.3 kg·[tex]m^{2}[/tex]
- Angular velocity (ω): 6.5 revolutions per second = 6.5 * 2π rad/s ≈ 40.84 rad/s
To find the work done by the torque to stop the wheel, we can use the rotational work-energy theorem: W = 0.5 * I * (ω_[tex]f^{2}[/tex] - ω_[tex]i^{2}[/tex]), where W is the work done, ω_f is the final angular velocity (0 rad/s), and ω_i is the initial angular velocity.
Plugging in the given values:
W = 0.5 * 2.3 kg·[tex]m^{2}[/tex] * (0^2 - 40.84 rad/s^2)
W = 0.5 * 2.3 kg·[tex]m^{2}[/tex] * (-1667.86 rad^2/s^2)
W ≈ -1918.24 J
Since work is done against the frictional force to bring the wheel to a stop, the work done is negative. Therefore, the work done by the torque to stop the wheel is most nearly -1918 J.
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dust-ignitionproof equipment must be designed and built in a manner that excludes dusts and prevents arcs, sparks, or heat that may be generated inside of the enclosure from causing ignition of ? of a specified dust on or in the vicinity of the enclosure.
Equipment that is designed to be dust-ignitionproof must be constructed in a way that prevents dust from getting inside and removes the possibility that heat, sparks, or arcs generated inside the apparatus would result in explosions or fires.
This is due to the fact that dust can be extremely hazardous in some working situations and can result in mishaps that could harm personnel or harm equipment.
In order to work safely in dusty environments, it is crucial to design and construct dust-ignitionproof equipment that can do so by avoiding the ignition of any dust that may be present inside or around the equipment. The ability to operate the machinery safely without endangering their health or safety is thus guaranteed.
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dheepthi started from point a in south direction. after walking for 4 m she turned to her right and walked 5 m. now she turned to her left and walked 3 m after which she turned to her right. now she walked 4 m and turned to her right again and walked 15 m. now finally she turned to her right and after walking for 7 m, she stopped at point b. what is the distance ab?
The distance traveled by Dheepthi from point A to B is 29.5m.
To find the distance AB, we need to use Pythagoras' theorem, which states that the square of the hypotenuse (the longest side) of a right triangle is equal to the sum of the squares of the other two sides.
In this case, we can break down Dheepthi's journey into a series of right triangles.
First, she walks 4m in the south direction from point A. Then, she turns right and walks 5m, forming a right triangle with legs of 4m and 5m.
Using Pythagoras' theorem, we can calculate the hypotenuse (her distance from point A) to be 6.4m.
Next, she turns left and walks 3m, forming another right triangle with legs of 1.6m (the remainder of her distance south) and 3m. Using Pythagoras' theorem again, we can calculate the hypotenuse of this triangle to be 3.4m.
Then, she turns right and walks 4m, forming a right triangle with legs of 1.6m and 4m. The hypotenuse of this triangle is 4.2m.
Finally, she turns right again and walks 15m, forming a right triangle with legs of 4.2m and 15m. The hypotenuse of this triangle is 15.5m.
Adding up all of these distances, we get a total distance of 6.4m + 3.4m + 4.2m + 15.5m = 29.5m. Therefore, the distance AB is 29.5m.
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how much time will pass when it goes from one-half initial voltage to one-fourth its initial voltage
The time taken is twice the time taken to decrease from the initial voltage to one-half initial voltage.
How much time will pass when it goes from one-half initial voltage to one-fourth its initial voltage?The amount of time it takes for a voltage to decrease from one level to another depends on the characteristics of the system generating the voltage.
Assuming that the voltage is decreasing exponentially over time, the time it takes for a voltage to decrease from one level to another can be calculated using the formula:
[tex]t = -(ln(Vf/Vi))/λ[/tex]
where t is the time taken, Vi is the initial voltage, Vf is the final voltage, and λ is the decay constant of the system generating the voltage.
If the voltage decreases from one-half its initial voltage to one-fourth its initial voltage, then [tex]Vi = 1, Vf = 1/4[/tex], and the voltage has decreased by a factor of 2.
Assuming that the decay is exponential, the time it takes to decrease by a factor of 2 is:
[tex]t = -(ln(1/2))/λ[/tex]
We can simplify this expression using the fact that [tex]ln(1/2) = -ln(2)[/tex], which gives:
[tex]t = ln(2)/λ[/tex]
Similarly, the time it takes to decrease by a factor of 4 is:
[tex]t = -(ln(1/4))/λ = ln(4)/λ = 2ln(2)/λ[/tex]
So, the ratio of the time taken to decrease from one-half initial voltage to one-fourth initial voltage is:
[tex]t(1/4) / t(1/2) = (2ln(2)/λ) / (ln(2)/λ) = 2[/tex]
Therefore, the time taken to decrease from one-half initial voltage to one-fourth initial voltage is twice the time taken to decrease from the initial voltage to one-half initial voltage.
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A 52 V battery powers a pair of 36 resistance resistors connected in series. What is the current flowing through the system?
Answer:
Total Voltage V=36*2Ω = 72Ω
We can use the formula V=IR
V=voltage
I=current
R=resistance
V=IR
I= 52/72
I=13/18
I=0.722Ahow far apart are the object and image produced by a converging lens with 35.5- cm focal length when the object is 45 cm from the lens?
To find the distance between the object and image produced by a converging lens with a 35.5 cm focal length when the object is 45 cm from the lens, you can use the lens formula:
1/f = 1/do + 1/di
Where:
f = focal length (35.5 cm)
do = object distance (45 cm)
di = image distance
Step 1: Plug in the values for f and do:
1/35.5 = 1/45 + 1/di
Step 2: Subtract 1/45 from both sides:
1/35.5 - 1/45 = 1/di
Step 3: Find a common denominator and subtract:
(45 - 35.5)/(35.5 * 45) = 1/di
9.5/(35.5 * 45) = 1/di
Step 4: Take the reciprocal of both sides:
di = (35.5 * 45)/9.5
Step 5: Calculate di:
di ≈ 168.42 cm
So, the object and image produced by the converging lens with a 35.5 cm focal length when the object is 45 cm from the lens are approximately 168.42 cm apart.
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on the centered zipper, what is the only part of the work that is done on the outside of the garment?
The only part of the work that is done on the outside of the garment is the basting or pinning of the zipper tape to the fabric.
The rest of the work is done on the inside of the garment. The zipper teeth are inserted between the layers of the fabric and the seam is sewn in place. The seam is then pressed open and the zipper is opened up to expose the teeth.
The zipper tape is then folded back and stitched in place, creating a clean finish on the inside of the garment. The final step is to topstitch the zipper on the outside of the garment, which reinforces the zipper and adds a decorative touch.
Overall, the centered zipper is a popular and versatile choice for many types of garments and can be easily customized to suit individual preferences.
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Show that the form of Newton’s second law is invariant under the Galilean transformation. According to Newton’s second law, the net force acting on an object is equal to the product of its mass and acceleration. Newton’s second law of motion is given by following expression:
Newton’s second law of motion states that the force F acting on an object of mass m produces an acceleration a in the object, and is given by, F = ma. The law s invariant under Galilean transformation.
The Galilean transformation is a set of equations that describe the relationship between two reference frames that are in relative motion with constant velocity. It has no effect on the form of Newton’s second law because it only involves a change of coordinates and time, which do not affect the physical laws.
To see this, consider two reference frames S and S', where S' moves with constant velocity v with respect to S. Let an object of mass m be at rest in S, and let F be the net force acting on it in S. According to Newton’s second law in S, we have:
F = ma
Now, let us apply the Galilean transformation to the equation. The position of the object in S' is given by:
x' = x - vt
where x is the position of the object in S, and t is time. Taking the derivative of x' with respect to t, we get:
v' = dx'/dt
= dx/dt - v
= v - v
= 0
This means that the velocity of the object is the same in both reference frames. Similarly, the acceleration is also the same in both reference frames, since it is the derivative of velocity,
a' = dv'/dt = da/dt = a
Therefore, we can write Newton’s second law in S' as,
F' = ma'
where F' is the net force acting on the object in S'. Substituting a' = a, we get:
F' = ma
which is the same form as in S. Thus, we see that the form of Newton’s second law is invariant under the Galilean transformation.
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A computer hard disk starts from rest, then speeds up with
an angular acceleration of 190 rad/s until it reaches its final
angular speed of 7200 rpm. How many revolutions has the disk
made 10. 0s after it starts up?
The final angular speed of the hard disk is 766.9 rad/s, and it takes 4.04 s to reach this speed with an angular acceleration of 190.0 [tex]rad/s^2[/tex].
To take care of this issue, we want to utilize the equation that relates the rakish removal of a pivoting object to its precise speed increase, time, and beginning rakish speed. The equation is given by:
θ = 1/2 * α * [tex]t^2[/tex] + ω0 * t + θ0
Where θ is the complete point pivoted by the plate, α is the precise speed increase, t is the time slipped by, ω0 is the underlying rakish speed, and θ0 is the underlying point.In this issue, the circle begins from rest, so ω0 = 0. The rakish speed increase of the plate is given as 190 [tex]rad/s^2[/tex], and the last precise speed is 7200 rpm.
We want to change the last precise speed from rpm over completely to rad/s by increasing it with 2π/60. In this manner, the last precise speed is 240π rad/s.We can now substitute these qualities into the recipe and compute the absolute point pivoted by the circle after 10.0 seconds:
θ = 1/2 * 190 [tex]rad/s^2[/tex] * [tex](10.0 s)^2[/tex] + 0 rad/s * 10.0 s + 0 rad
θ = 9500 rad
To change this point over completely to the quantity of insurgencies, we partition it by 2π, as one unrest compares to a point of 2π radians. Consequently:
θ in transformations = 9500 rad/(2π rad/unrest) = 1507 upheavals
Accordingly, the plate has made 1507 insurgencies after 10.0 seconds from its underlying state.
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The complete question is:
A computer hard disk starts from rest, then speeds up with an angular acceleration of 190.0 [tex]rad/s^{2}[/tex]until it reaches a final angular speed of 7300.0 rpm.
(a) What is the final angular speed in units of rad/s? rad/s.
(b) How long does it take for the disk to reach this angular speed? s
(c) How many revolutions (not radians) does it make in getting to the final angular speed? rev
(d) Once the disk reaches its final angular speed, it continues rotating at this same speed. How many revolutions has the disk made 10.0 s after it started up from rest?
what is an expression for x1(t) , the position of mass i as a function of time? assume that the position is measured in meters and time is measured in seconds.
The expression for x1(t) , the position of mass i as a function of time, is x1(t) = x1_0 + v1_0 * t + 0.5 * a1 * t²
To find an expression for x1(t), the position of mass 1 as a function of time, we need to consider the following terms:
1. Initial position (x1_0): The position of mass 1 at time t=0.
2. Initial velocity (v1_0): The velocity of mass 1 at time t=0.
3. Acceleration (a1): The constant acceleration acting on mass 1, if applicable.
Now, we can use the general equation for the position of an object as a function of time:
x1(t) = x1_0 + v1_0 * t + 0.5 * a1 * t²
Where x1(t) is the position of mass 1 at time t, x1_0 is the initial position, v1_0 is the initial velocity, a1 is the acceleration, and t is the time in seconds.
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the speed of sound in air is 332 m/s. humans have sensitivity to sound frequencies from 20 hz to 20,000 hz. a. what is the longest sound wavelength we can hear? (5 pts) b. what is the shortest sound wavelength we can hear? (5 pts)
The longest sound wavelength we can hear is 16.6 m while the shortest sound wavelength we can hear is 0.0166 m.
We can use the formula for the speed of sound to find the longest and shortest sound wavelengths humans can hear:
speed of sound = frequency × wavelength
Let's first solve for the longest wavelength (a):
a. Longest wavelength = speed of sound / lowest frequency
Longest wavelength = 332 m/s / 20 Hz
Longest wavelength = 16.6 m
Now, let's solve for the shortest wavelength (b):
b. Shortest wavelength = speed of sound / highest frequency
Shortest wavelength = 332 m/s / 20,000 Hz
Shortest wavelength = 0.0166 m (or 1.66 cm)
So, the longest sound wavelength humans can hear is 16.6 meters and the shortest sound wavelength we can hear is 0.0166 meters (1.66 centimeters).
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An astronaut of mass 75 kg is floating in space holding a 20 kg fire extinguisher. If she throws the extinguisher forward at a velocity of 3.5 m/s, what will be her resulting velocity?
Momentum is defined as mass multiplied by velocity, so the total momentum before the extinguisher is thrown is 70 kg*m/s.
What is Velocity?Velocity is a vector quantity that measures the rate of change of an object's position. It is determined by the displacement of an object over a given period of time, and is usually expressed in terms of distance over time.
The astronaut's resulting velocity will be the same as the fire extinguisher's velocity, 3.5 m/s.
This is because the astronaut and extinguisher have the same mass and momentum must be conserved.
Momentum is defined as mass multiplied by velocity, so the total momentum before the extinguisher is thrown is 75 kg * 0 m/s + 20 kg * 3.5 m/s
= 70 kg*m/s.
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question 4 a photon with a longer wavelength is more energetic than a photon with a short wavelength. travels slower than a photon with a short wavelength. is more blue than a photon with a short wavelength. has a lower frequency than a photon with a short wavelength.
A photon with a longer wavelength has a lower frequency than a photon with a short wavelength, the correct option is (d)
The wavelength and frequency of a photon are related to its energy and color. Photons with shorter wavelengths have higher frequencies and higher energy, while photons with longer wavelengths have lower frequencies and lower energy.
This is described by the equation E = hf, where E is energy, h is Planck's constant, and f is frequency. Therefore, a photon with a longer wavelength has a lower frequency than a photon with a shorter wavelength, the correct option is (d)
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The complete question is:
A photon with a longer wavelength
a) is more energetic than a photon with a short wavelength.
b) travels slower than a photon with a short wavelength.
c) is more blue than a photon with a short wavelength.
d) has a lower frequency than a photon with a short wavelength.
e) All of the above
What happens when thermal energy is applied to a substance q
When thermal energy is applied to a substance, the particles in the substance start to vibrate more rapidly, and the average kinetic energy of the particles increases.
What happens when thermal energy is applies to a substanceAs a result, the temperature of the substance increases. The amount of thermal energy required to increase the temperature of the substance by a certain amount is called the specific heat capacity of the substance.
The way the substance responds to the applied thermal energy also depends on its physical properties, such as its mass, density, and thermal conductivity. For example, a substance with a high thermal conductivity will transfer heat more rapidly to its surroundings, while a substance with a low thermal conductivity will retain heat more effectively.
If the applied thermal energy is sufficient, the substance may undergo a phase change, such as melting or boiling, as the increased kinetic energy overcomes the intermolecular forces holding the particles together.
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