While submerged in water (n = 1.33) for two convex lenses, the focal lengths of Lens 1 is 19.67 cm and Lens 2 is 18.9 cm.
What is Lens ?Lens is a transparent device that is used to focus or redirect light, allowing it to be magnified, focused, or projected onto a surface. It is made of a curved, transparent material like glass, plastic, or crystal. Lenses are commonly used in eyeglasses, cameras, microscopes, and other optical devices. They can be used to magnify, reduce, or otherwise change the direction of light in order to produce a desired effect. They are also used in other applications such as laser cutting and welding, as well as medical imaging and laser treatments.
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State the first law of thermodynamics and apply this to the system/surrounding model.
Answer:
The first law of thermodynamics, also known as the law of conservation of energy, states that energy cannot be created or destroyed, only transferred or transformed from one form to another. In other words, the total energy of a closed system and its surroundings remains constant.
When applying this law to a system/surrounding model, the energy exchanged between the system and its surroundings can take different forms, such as heat, work, or a combination of both. For example, if a gas is compressed in a piston, work is done on the gas by the surroundings, increasing the internal energy of the gas. Alternatively, if a gas is heated, energy is transferred to the gas from the surroundings, increasing the internal energy of the gas.
Overall, the first law of thermodynamics serves as a fundamental principle in the study of thermodynamics, allowing us to analyze and predict energy transfers and transformations in various physical and chemical systems.
Explanation:
a rocket is fired with an inital velocity of 100m/s at an angle of 55 degree above the horizontal.it explodes on the mountain side 12 second after its firing .A.what is the x and t cordinates of the rocket relative to its firing piont ? x and h B. time to reach the maximu height ( tmax ) ? C. total time of flight ? D. range? (R) E.h max ?
The rocket's x and t coordinates are 688.32 meters and 277.44 meters, respectively, from where it will launch.
What does velocity vs. speed mean?Velocity, as opposed to speed, refers to the pace & direction of such an object's movement as it moves down a path. In other respects, whereas velocity is a scalar, speed is really a scale parameter.
Is speed always the same as velocity?Speed does not necessarily have to match average velocity in magnitude. Many people mistakenly believe that cruising velocity and flow rate are merely two different labels for the same quantity. Nevertheless, average speed relies on both distance and displacement.
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Why cant an object become positively charged by gaining protons?
Answer:
An object can become positively charged by losing electrons, but it cannot become positively charged by gaining protons. This is because the charge on an object depends on the balance of protons and electrons it has. Protons have a positive charge, while electrons have a negative charge. So, when an object gains electrons, it becomes negatively charged because it now has more negative charges than positive charges. On the other hand, when an object loses electrons, it becomes positively charged because it now has more positive charges than negative charges.
However, protons cannot be gained or lost easily because they are tightly bound within the atomic nucleus of an atom, and they are not free to move around like electrons. Therefore, the only way for an object to become positively charged is to lose electrons, not by gaining protons.
Explanation:
Do you guys have any ideas for physics projects??
Answer:
What all topics do you have?
In the figure below, m₁ = 11.0 kg and m₂ = 4.5 kg. The coefficient of static friction between m, and the horizontal surface it
1711
M₂
(a) If the system is released from rest, what will its acceleration be?
m/s²
(b) If the system is set in motion with m₂ moving downward, what will be the acceleration of the system?
m/s²
17. [0/5 Points] DETAILS
PREVIOUS ANSWERS SERCP9 4.P.047.WI.
The coefficient of static friction between the m = 3.15-kg crate and the 35.00 in
Answer:
See below.
Explanation:
The list of given we have:
[tex]m_1=11.0Kg[/tex][tex]m_2=4.5Kg[/tex][tex]u_s=0.60[/tex][tex]u_k=0.30[/tex](a) We are asked to find the acceleration of the system if the system is released from rest.
We can simply distinguish between the forces operating on the two masses to provide an answer. We must first determine the force affecting the masses. Hence, the only force acting on mass 2 is the gravitational force since it is suspended from the cord.
[tex]Fg=m_2g[/tex]
[tex]F_g=(4.5Kg)(9.8m/s^2)[/tex]
[tex]F_g=44.1N[/tex]
while for the mass 1 we have the static frictional force,
[tex]f_s=u_sN[/tex]
[tex]f_s=(0.60)(11.0Kg)(9.8m/s^2)[/tex]
[tex]f_s=64.68N[/tex]
We may infer that if the system is released from rest, it does not move at all since the static frictional force acting on mass 1 was greater than the gravitational force acting on mass 2, which means the system's acceleration must be equal to [tex]a=0m/s^2[/tex].
(b) We are asked to find the acceleration of the system if the mass 2 moves downward.
For this question, we must draw a free-body diagram (attachment #1).
Since we are able to draw a free-body diagram and identify the force(s) acting on the masses, we can find the acceleration of the system using the equation of Newton's second law, so we have:
[tex]F_\text{net}=m_{sys} a[/tex]
[tex]a=\frac{F_{net}}{m_{sys}}[/tex]
where the [tex]F_{net}[/tex] is the sum of force(s) acting on the system and [tex]m_{sys}[/tex] is the total mass of the system,
[tex]a=\frac{Fg_2-T+T-f_k}{m_1+m_2}[/tex]
[tex]a=\frac{F_g2 - f_k}{m_1+m_2}[/tex]
[tex]a=\frac{m_2g-u_km_1g}{m_1+m_2}[/tex]
substituting all of the given
[tex]a=\frac{(4.5Kg)(9.8m/s^2)-(0.30)(11.0Kg)}{11.0Kg-4.5Kg}[/tex]
[tex]a=\frac{40.8Kgm/s^2}{6.5Kg}[/tex]
[tex]a=6.2769[/tex]
We can conclude that if the mass 2 is going downward then the acceleration of the system would be [tex]6.2769m/s^2.[/tex]
Two point charged objects produce an electric force on each other of 11 N. What will the force between them be if both charges increase by a factor of 2?
Answer:
the factor of 2is 78
Explanation:
7th 8th is 9th is 3th which is 90000
Im kinda lost in this one
[tex]75 = 6 \times \frac{?}{?} \times \frac{?}{?} [/tex]
How would you interpret the graphs? Did the subject respond only to the tone they were conditioned on? Were trials 1-10 the same or different from trials 11-20? If so, how?
Answer:
Trials 1-10 were bigger than 11-20, so it is different.
Explanation:
brainlyist pls
What is the wavelength of water waves which have a frequency of 0.60 Hz and a speed of 4.0 m/s?
Answer:
1.9 m/s
Explanation:
If a person steps on a scale in an elevator that is accelerating at a rate -1.100 m/s^2 (negative means downward while positive means upwards) and sees a scale reading of 598.900 Newtons what would the scale read if the elevator were not moving?
The scale reading when the elevator is accelerating can be found using the following formula:
Weight in Elevator = Mass × (Acceleration of Gravity + Acceleration of Elevator)
where Weight in Elevator is the scale reading, Mass is the mass of the person, Acceleration of Gravity is the acceleration due to gravity (9.81 m/s^2), and Acceleration of Elevator is the acceleration of the elevator.
What would the scale read if the elevator were not moving?Using this formula, we can solve for the mass of the person:
Weight in Elevator = Mass × (Acceleration of Gravity + Acceleration of Elevator)
598.9 N = Mass × (9.81 m/s^2 - 1.1 m/s^2)
Mass = 65 kg
Now, when the elevator is not moving, the weight of the person will be equal to their mass multiplied by the acceleration due to gravity, which is:
Weight on Ground = Mass × Acceleration of Gravity
Weight on Ground = 65 kg × 9.81 m/s^2
Weight on Ground = 637.65 N
Therefore, the scale reading when the elevator is not moving would be 637.65 Newtons.
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PLS HELP ASAP!!!
Examine two items that use more than one battery, such as a flashlight, a 2-way radio, or a battery operated toy. Look at the arrangement of the batteries in the item. Are they connected in series? For each item, state the number and type of batteries, the voltage of each battery and the total voltage
produced.
Flashlight: The flashlight typically uses multiple batteries, arranged in series to provide a higher voltage output.
What is the battery about?In continuation, The number and type of batteries used in a flashlight can vary depending on the model, but a common arrangement is to use two or three 1.5V AA batteries. The batteries are connected in series, with the positive end of one battery connected to the negative end of the next battery, and so on.
For example, if the flashlight uses three 1.5V AA batteries, the total voltage produced would be 4.5V (1.5V x 3).Secondly, 2-way radio:
A 2-way radio also typically uses multiple batteries, arranged in series to provide a higher voltage output. Again, the number and type of batteries used can vary depending on the model, but a common arrangement is to use four or six 1.5V AA batteries. The batteries are connected in series, with the positive end of one battery connected to the negative end of the next battery, and so on.
For example, if the 2-way radio uses six 1.5V AA batteries, the total voltage produced would be 9V (1.5V x 6).Therefore, Note that the arrangement of batteries in series increases the total voltage produced by the batteries.
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What geologic feature would you be most likely to find at a divergent plate boundary where two oceanic plates move away from each other? a mid-ocean ridge a rift valley an island arc an ocean trench
Answer: When two plates are moving away from each other, we call this a divergent plate boundary. Along these boundaries, magma rises from deep within the Earth and erupts to form new crust on the lithosphere. Most divergent plate boundaries are underwater and form submarine mountain ranges called oceanic spreading ridges.
Explanation:
I HOPE THIS HELPED YOU I AM OPEN IF YOU WANTS ANSWERS GOOD LUCK BY THE WAY!
fish swimming in a horizontal plane has velocity v with arrowi = (4.00 î + 1.00 ĵ) m/s at a point in the ocean where the position relative to a certain rock is r with arrowi = (14.0 î − 2.80 ĵ) m. After the fish swims with constant acceleration for 19.0 s, its velocity is v with arrow = (23.0 î − 1.00 ĵ) m/s. (a) What are the components of the acceleration of the fish? ax = m/s2 ay = m/s2 (b) What is the direction of its acceleration with respect to unit vector î? ° counterclockwise from the +x-axis (c) If the fish maintains constant acceleration, where is it at t = 26.0 s? x = m y = m In what direction is it moving? ° counterclockwise from the +x-axis
Answer:
sorryyyyijyyyyyyyyyyyyyyyyyyyy&
Explanation:
soryyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
2. What are the benefits of a normative approach to lifespan development?
A normative approach to lifespan development involves studying and comparing the typical patterns of development and behavior across different individuals or groups of people at various ages. Here are some benefits of using this approach:
Identifying developmental milestones: A normative approach helps to identify the typical milestones and achievements that people reach at different ages, such as crawling, walking, talking, and reading. This can help parents, educators, and healthcare professionals to monitor and assess a child's development and provide appropriate support and interventions when necessary.
Understanding individual differences: While a normative approach focuses on typical patterns of development, it also recognizes that there are individual differences in development and behavior. By comparing people's development to the norm, we can better understand how and why some individuals may differ from the norm, such as in terms of their physical, cognitive, or socioemotional development.
Informing public policies and interventions: A normative approach can help to inform public policies and interventions that support healthy development across the lifespan. For example, knowledge about the typical milestones of development can inform early childhood education programs, while information about the typical age-related changes in cognition and memory can inform policies related to employment and retirement.
Consider a situation where over the course of a 24-mile long run, a runner becomes increasingly tired. In the first hour he runs 12 miles, in the second hour 6 miles, in the third hour 3 miles, and so on, so that each hour he runs half the distance to go. How long will it take to finish the race?
The runner will take a full day to complete the race, assuming he maintains the same pattern of slowing down by half the previous hour's distance each hour.
How did we get this assertion?We can approach this problem by using a formula for the sum of an infinite geometric series, since the distances covered by the runner in each hour form a geometric sequence with a common ratio of 1/2. The formula is:
S = a / (1 - r),
where S is the sum of the series, a is the first term, and r is the common ratio.
In this case, the first term a is 12 miles, and the common ratio r is 1/2. We want to find the total distance S covered by the runner over the entire 24-mile race, so we can set:
S = 12 / (1 - 1/2) = 24
This means that the runner will cover the remaining 12 miles in the final hour, and so the total time taken to finish the race will be:
1 + 1 + 1 + ... (24 times) = 24 hours
So, the runner will take a full day to complete the race, assuming he maintains the same pattern of slowing down by half the previous hour's distance each hour.
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Science
help
anwer all
Answer:
True
False
True
True
True
Explanation:
Light is measured by its wavelength (in nanometers). It is usually characterized by the Greek symbol λ. Visible light is usually defined as having wavelengths in the range of 400–700 nanometers (nm) or one billionth of a meter.
Light travels faster in vacuum than any other medium. This is because there is no obstruction in vacuum for the propagation of light and thus, the refractive index of vacuum is the lowest.
Brightness is used to describe how bright somthing is
The shorter the wavelengths and higher the frequency corresponds with greater energy. So the longer the wavelengths and lower the frequency results in lower energy.
In order from highest to lowest energy, the sections of the EM spectrum are named: gamma rays, X-rays, ultraviolet radiation, visible light, infrared radiation, and radio waves.
Set the charged object in motion by dragging it and releasing it. What do you observe about the behavior of the field lines in the vicinity of the object
When a charged object is at rest, the electric field lines emanating from it are radially symmetric and point outward in all directions, forming a pattern that depends on the magnitude and sign of the charge. If the charged object is set in motion, it creates a changing electric field that propagates outward from the object at the speed of light.
How is the direction of the magnetic field line depicted?The direction of magnetic field lines is depicted using arrows or lines that indicate the direction of the magnetic field at each point in space. The convention for drawing magnetic field lines is that they always form closed loops, and the direction of the field is tangential to the bar at each point.
Does the electric field affect the magnetic field?Yes, electric fields can affect magnetic fields and vice versa. Electric and magnetic fields are intimately related and form two sides of the same coin, as described by Maxwell's equation of electromagnetism.
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An ideal spring with a constant of 200 N/m is acted upon by a 600 N force directed in the positive direction, what is the magnitude and direction of the displacement?
The displacement has a 3 m magnitude and is moving in the opposite direction as the external force, which is pushing backwards.
How do you determine the spring's maximum stretch?With the provided information for the 4 kilogramme mass, we can get the spring constant. The displacement of a 1.5 kg mass is then determined using the formula x = F/k. The work needed to stretch a spring x distances from its equilibrium position is W = 12kx2.
We can use the following formula to determine the force a spring exerts:
F = -kx
The magnitude of the force exerted by the spring is:
F = -kx
-600 N = -200 N/m * x
Solving for x, we get:
x = 3 m
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The electricity received at an electric substation has a potential difference of 2.80 x 105 V. If the required output is 440 V, what should be the ratio of the turns of the step-down transformer?
A
Explanation: sorry sir but its required step up transformer for high voltage not step
Question : What is the relationship between Orbital Radius- a ) AU ) and Period- ( years )?
The relationship is , the square of the period of an orbit is proportional to the cube of its Orbital Radius.
What is the relationship between orbital radius?The relationship between orbital radius and period is described by Kepler's Third Law of Planetary Motion, which states that the square of the period of an orbit is proportional to the cube of its semi-major axis.
In other words, if we denote the orbital radius (semi-major axis) by "a" in units of astronomical units (AU) and the period by "T" in years, then:
a³ = (T²)k
where;
k is a constant of proportionality that depends on the mass of the central body around which the object is orbiting.For objects orbiting the sun, k is approximately equal to 1.
So, if you know the orbital radius of an object around the sun, you can use Kepler's Third Law to calculate its period, or vice versa.
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A particular insulating container has a total surface area of 1.10 m2 and walls that are 4.00 cm thick. Suppose that a 10.0 W electric heater keeps the inside of the container 13.0°C warmer than the temperature outside. What is the thermal conductivity k of the material that the container is made of? (Enter your answer in W/(m · °C).)
The thermal cοnductivity οf the material is 0.024 W/(m·K).
What is the heat transfer fοrmula?We can use the fοrmula fοr heat transfer thrοugh a material with a temperature difference and knοwn surface area:
Q/t = kA(T1-T2)/d
where Q/t is the rate οf heat transfer (pοwer) prοvided by the electric heater,
k is the thermal cοnductivity οf the material,
A is the surface area οf the cοntainer,
d is the thickness οf the walls,
T1 is the temperature inside the cοntainer, and
T2 is the temperature οutside the cοntainer.
Plugging in the given values:
Q/t = 10.0 WA = 1.10 m²d = 0.04 mT1 - T2 = 13.0 °C
We can rearrange the fοrmula tο sοlve fοr k:
k = Qtd / (A*(T1-T2))
Plugging in the values and cοnverting units tο SI units:
k = (10.0 W)(1 s)(0.04 m) / (1.10 m² * 13.0 K) = 0.024 W/(m·K)
Therefοre, the thermal cοnductivity οf the material is 0.024 W/(m·K).
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Two piloted satellites approach one another at a relative speed of 0.25 m/s, intending to dock. The
first has a mass of 4.00 × 103 kg, and the second a mass of 7.50 × 103 kg. If the two satellites collide
elastically rather than dock, what is their final relative velocity?
What type of energy is demonstrated when a marble is in position at the top of a rent before it begins to move
The kinetic energy is related to the motion of the marble, but the potential energy is related to its position. The marble's potential energy is transformed into kinetic energy as it slides down the ramp from the top.
While the stone is in this position before it starts to move, what kind of energy is being shown?The stone has potential energy when it is at the top of the ramp because gravity will lead it to fall. The term for this is gravitational potential energy. The stone is freed, and the potential energy transforms into kinetic energy as it moves. Kinetic energy is the term used to describe a moving object.
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If electricity costs $0.18 per kwh, how much does it cost to run the air conditioner in the problem above?
A)$5.76
B)$7.87
C)$9.45
D)$12.12
Answer:
the answer is A) $5.76.
We found in the previous problem that the air conditioner uses 32 kWh per day. To find the cost, we multiply the number of kWh by the cost per kWh:
32 kWh/day x $0.18/kWh = $5.76/day
So, it costs $5.76 per day to run the air conditioner.
Therefore, the answer is A) $5.76.
A negative lightning strike occurs when a negatively charged cloud discharges its excess electrons to the positively charged ground. If you observe a cloud-to-cloud lightning strike, what can you say about the charge on the area of the cloud struck by lightning?
1. The area of the cloud that was struck by lightning is neutral.
2. The area of the cloud that was struck by lightning had a positive charge.
3. The area of the cloud that was struck by lightning had a negative charge.
The area οf the clοud that was struck by lightning had a negative charge, sο, οptiοn (d) is cοrrect.
What is electrοns ?The negatively charged atοm's electrοns are respοnsible fοr this. An atοm's tοtal negative charge, which is prοduced by all οf its electrοns, cοunteracts the pοsitive charge οf the prοtοns in the atοmic nucleus.
What is electric charge?Prοtοns and electrοns, which functiοn as charge carriers, frequently carry bοth pοsitive and negative electric charges. By mοving charges, energy is prοduced. Charge—alsο referred tο as electric charge, electrical charge, οr electrοstatic charge—is a prοperty οf a unit οf matter in physics and is denοted by the letter q.
Therefοre, The area οf the clοud that was struck by lightning had a negative charge, sο, οptiοn (d) is cοrrect.
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convert 1 Celsius to Fahrenheit
PLEASEEEEEEE HELPPPPPPPPP
Follow these directions:
Let your partner hold a ruler or meter stick in his/her hand vertically between the thumb and index finger, making sure he/she holds the meter stick so that the zero mark is between his/her fingers with the 1 cm mark above it. Your friend should hold the meter stick toward the top end, while your fingers are open at the bottom end of the ruler, ready to catch it between your index finger and your thumb . You should not be touching the meter stick or ruler.
Have your partner release the meter stick or ruler. As soon as you see the ruler released, snap your fingers shut and catch it.
Record in a data table the centimeter mark that was closest to your fingers.
Repeat this procedure several times, and average your results.
Change centimeters to meters.
Then calculate your reaction time by using the formula above and 9.8 m/s2 for g.
Compare your reaction time with that of your partner. Write out your comparison and possible reasons for differences.
We can see here that carrying out the experiment and comparing your reaction time with that of your partner, we see that if one person has a faster reaction time, possible reasons could be faster reflexes or better anticipation of when the ruler will be released.
What is reaction time?Reaction time is the interval of time that elapses between the presentation of a stimulus and the initiation of a response. It is the time it takes for an individual to process and react to a stimulus, such as a sound, sight, or touch.
Carrying the experiment, we assume that the data table is gotten thus:
Trial Centimeter Mark
1 20
2 17
3 21
4 19
5 18
To change centimeters to meters, divide the average centimeter mark by 100. So, the average centimeter mark is
(20+17+21+19+18)/5 = 19 cm,
which is equal to 0.19 meters.
To calculate reaction time, we can use the formula:
t = √(2d/g)
where t is the reaction time, d is the distance traveled by the ruler, and g is the acceleration due to gravity (9.8 m/s^2).
Assuming the distance traveled by the ruler is equal to the distance between the top of the ruler and the point where it was caught by the fingers, we can calculate the reaction time as follows:
t = √(2 x 0.19 / 9.8) = 0.197 seconds ≈ 0.2 seconds.
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Larry finds a lens and shows it to his friends, Mirez and Sherly.
All three look through it. Larry looks at the window across the room with the lens and says the window looks upside down. Mirez said that he must be using it incorrectly, because when he looks at his thumb through the lens, it is definitely not upside down. Sherly says that she thinks it is broken, because when she looks through it, everything just looks blurry.
Using your understanding about image formation, explain each of their observations.
Larry observes that the window looks upside down because the lens forms an inverted image. When light passes through a convex lens, it is refracted (bent) towards the center of the lens. The degree of bending depends on the angle of incidence and the refractive index of the lens. This bending of light rays causes the image to be inverted.
Mirez observes that his thumb looks right side up because the orientation of the object being viewed through the lens matters. When an object is placed at a distance greater than the focal length of the convex lens, the lens forms a real and inverted image. However, when the object is placed at a distance less than the focal length of the lens, the lens forms a virtual and erect image. In this case, Mirez's thumb is closer to the lens than the focal length, and hence, the lens forms a virtual and erect image of the thumb.
Sherly observes that everything looks blurry because the lens is not able to form a sharp image. The blurriness is due to spherical aberration, which is a common problem in lenses. When light passes through the curved surface of the lens, the rays passing through the edges of the lens bend more than those passing through the center. This causes the light to converge at different points on the image plane, resulting in a blurry image. To overcome spherical aberration, lenses are designed with multiple curved surfaces, or with non-uniform thickness.
The lens that produces an upside-down image is called a convex lens. Hence, Larry finds the lens called a convex lens.
What is the convex lens?The lens that converges the ray of light is called a convex lens. The lens that curved inwards, has a thicker middle portion and thinner at the lower and the middle part.
Convex lenses produce virtual and real images depending on the object's position. It also produces an upside-down image. It also produces a magnified image.
From the observation,
The convex lens produces an upside-down image. The lens produces an upside-down image, when light passes through the lens, it bends toward the center. This bending of light rays causes an inverted image.
Mirez's observation is based on the focal length of the convex lens. When an object is placed at a larger distance than the focal length of the convex lens, it produces a real and inverted image whereas the object's distance is lesser than the focal length, it produces a virtual and erect image.
Hence, he placed his thumb closer to the convex lens, the focal length is decreased and it produces a virtual and erect image. Sherly saw the blurred image because the lens does not produce sharp images. The lens doesn't produce sharp images as it has certain spherical aberrations.
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A balloon has a charge of -1.0 x 10-6 C and is held 0.97 m away from a steel tube. If the force between them is -5.5 N, what is the charge of the tube?
We can use Coulomb's Law to solve this problem:
F = k * (q1 * q2) / r^2
where:
F = -5.5 N
k = Coulomb's constant (9.0 x 10^9 N·m^2/C^2)
q1 = charge of the balloon (-1.0 x 10^-6 C)
q2 = charge of the steel tube= ?
r = distance between the balloon and the steel tube (0.97 m)
Plugging in the given values and solving for q2:
-5.5 N = (9.0 x 10^9 N·m^2/C^2) * (-1.0 x 10^-6 C) * q2 / (0.97 m)^2
Solving for q2, we get:
q2 = (-5.5 N) * (0.97 m)^2 / [(9.0 x 10^9 N·m^2/C^2) * (-1.0 x 10^-6 C)]
q2 ≈ -6.4 x 10^-6 C
Therefore, the charge of the steel tube is approximately -6.4 x 10^-6 C.
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(a) Find
A + B
graphically.
magnitude
m
direction
° counterclockwise from the +x axis
(b) Find
A − B
graphically.
magnitude
m
direction
° counterclockwise from the +x axis
(c) Find
B − A
graphically.
magnitude
m
direction
° counterclockwise from the +x axis
(d) Find
A − 2B
graphically.
magnitude
m
direction
° counterclockwise from the +x axis
The displacement vector for a is given below:
a. tan^-1(6.0/3.7) = 58.34o counterclockwise from +X axisb. tan^-1 = 328.1o…….counterclockwise from +X axisc. tan^-1 = 148.1o…….counterclockwise from +X axisd. tan^-1 = 229.84o…….counterclockwise from +X axisHow to solveA=4.15m, θA=26.5o
Ax=AcosθA = 4.15cos26.5 = 3.7 m
Ay=AsinθA = 4.15sin26.5 = 1.85 m
B= 4.15m, θB =26.5o
Bx=BcosθB = 4.15cos90= 0.0 m
By=BsinθB = 4.15sin90= 4.15 m
a)
(A+B)x= Ax+ Bx= 3.7 – 0.0 = 3.7 m
(A+B)y = Ay+ By= 1.85 + 4.15 = 6.0 m
(A+B)=sqrt[(3.7)^2+(6.0)^2] = 7.05 m
Φ= tan^-1[((A+B)y)/( (A+B)x)] = tan^-1(6.0/3.7) = 58.34o…….counterclockwise from +X axis
b)
(A-B)x= Ax- Bx= 3.7 – 0.0 = 3.7 m
(A-B)y = Ay- By= 1.85 - 4.15 = -2.3 m
(A-B)=sqrt[(3.7)^2+(2.3)^2] = 4.36 m
Φ= tan^-1[((A-B)y)/( (A-B)x)] = tan^-1(-2.3/3.7) = -31.9o = 360-31.9 = 328.1o…….counterclockwise from +X axis
c)
(B-A)x= Bx- Ax= 0.0-3.7 = -3.7 m
(B-A)y = By- Ay= 4.15-1.85 = 2.3 m
(B-A)=sqrt[(-3.7)^2+(-2.3)^2] = 4.36 m
Φ= tan^-1[((B-A)y)/( (B-A)x)] = tan^-1(2.3/-3.7) = -31.9o = 180-31.9 = 148.1o…….counterclockwise from +X axis
d)
(A-2B)x= Ax- 2Bx= 3.7 – 2*0.0 = 3.7 m
(A-2B)y = Ay- 2By= 1.85 – 2*4.15 = -6.45 m
(A-2B)=sqrt[(3.7)^2+(-6.45)^2] = 7.44 m
Φ= tan^-1[((A-2B)y)/( (A-2B)x)] = tan^-1(-6.45/3.7) = -60.16o = = 360-60.16 = 229.84o…….counterclockwise from +X axis
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