Answer:
[tex]q / q_{1} = 2[/tex], assuming that [tex]q_{1}[/tex] and [tex](q - q_{1})[/tex] are point charges.
Explanation:
Let [tex]k[/tex] denote the coulomb constant. Let [tex]r[/tex] denote the distance between the two point charges. In this question, neither [tex]k[/tex] and [tex]r[/tex] depend on the value of [tex]q_{1}[/tex].
By Coulomb's Law, the magnitude of electrostatic force between [tex]q_{1}[/tex] and [tex](q - q_{1})[/tex] would be:
[tex]\begin{aligned}F &= \frac{k\, q_{1}\, (q - q_{1})}{r^{2}} \\ &= \frac{k}{r^{2}}\, (q\, q_{1} - {q_{1}}^{2})\end{aligned}[/tex].
Find the first and second derivative of [tex]F[/tex] with respect to [tex]q_{1}[/tex]. (Note that [tex]0 < q_{1} < q[/tex].)
First derivative:
[tex]\begin{aligned}\frac{d}{d q_{1}}[F] &= \frac{d}{d q_{1}} \left[\frac{k}{r^{2}}\, (q\, q_{1} - {q_{1}}^{2})\right] \\ &= \frac{k}{r^{2}}\, \left[\frac{d}{d q_{1}} [q\, q_{1}] - \frac{d}{d q_{1}}[{q_{1}}^{2}]\right]\\ &= \frac{k}{r^{2}}\, (q - 2\, q_{1})\end{aligned}[/tex].
Second derivative:
[tex]\begin{aligned}\frac{d^{2}}{{d q_{1}}^{2}}[F] &= \frac{d}{d q_{1}} \left[\frac{k}{r^{2}}\, (q - 2\, q_{1})\right] \\ &= \frac{(-2)\, k}{r^{2}}\end{aligned}[/tex].
The value of the coulomb constant [tex]k[/tex] is greater than [tex]0[/tex]. Thus, the value of the second derivative of [tex]F[/tex] with respect to [tex]q_{1}[/tex] would be negative for all real [tex]r[/tex]. [tex]F\![/tex] would be convex over all [tex]q_{1}[/tex].
By the convexity of [tex]\! F[/tex] with respect to [tex]\! q_{1} \![/tex], there would be a unique [tex]q_{1}[/tex] that globally maximizes [tex]F[/tex]. The first derivative of [tex]F\![/tex] with respect to [tex]q_{1}\![/tex] should be [tex]0[/tex] for that particular [tex]\! q_{1}[/tex]. In other words:
[tex]\displaystyle \frac{k}{r^{2}}\, (q - 2\, q_{1}) = 0[/tex].
[tex]2\, q_{1} = q[/tex].
[tex]q_{1} = q / 2[/tex].
In other words, the force between the two point charges would be maximized when the charge is evenly split:
[tex]\begin{aligned} \frac{q}{q_{1}} &= \frac{q}{q / 2} = 2\end{aligned}[/tex].
write any five effect of human activities on the earth and explain each of them in brief
Answer:
here Humans impact the physical environment in many ways: overpopulation, pollution, burning fossil fuels, and deforestation. Changes like these have triggered climate change, soil erosion, poor air quality, and undrinkable water. These negative impacts can affect human behavior and can prompt mass migrations or battles over clean water.
Explanation:
The wavelength of a radio wave in a vacuum is 295 meters. Calculate its wavelength in water? (nwater = 1.33)
The wavelength of the radio wave in water is 222nm
Calculating radio wave in waterThe relationship between the refractive index wavelengths in a vacuum and in water is given by:
n = λ1/λ2
So,
let λ1 be the wavelength of light in a vacuum
λ2 be the wavelength of light in water.
nwater = 1.33
Plugging in values, we have
n = λ1/λ2
1.33 =295 m /λ2
λ2 = 295 m/1.33
= 221.80nm
≈222nm
Therefore the wavelength of radio wave in water is 222mn.
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PLS HELP
Bill is riding his bicycle at 3.2 m/s. He accelerates at 0.53 m/s2 over a period of 1.2 seconds.
What is Bill's final velocity in m/s?
V(final) = V(initial) + a•t
Take the numbers you know, pluggum in, and you should get 3.836 m/s .
Note: This is just the final speed. Without any direction information, there's no way to find the velocity.
which of the following statement is correct?
a. Reflecting telescope uses convex lenses while refracting telescopes uses concave lenses.
b. both telescopes are using the combination of concave and convex lenses.
c. Reflecting telescope uses a concave lenses while refracting telescopes uses convex lenses.
d. None of the the statements above are correct.
Answer:
D. None of the the statements above are correct.
Explanation:
Microscopes and telescopes are major instruments that have contributed hugely to our current understanding of the micro- and macroscopic worlds. The invention of these devices led to numerous discoveries in disciplines such as physics, astronomy, and biology, to name a few. In this section, we explain the basic physics that make these instruments work.
Answer:
d. is the answer hope it helps
Describe an exothermic reaction involving sulphuric acid.
Answer: The hydration reaction of sulfuric acid is highly exothermic. If water is added to concentrated sulfuric acid, it can boil and spit dangerously. You should always add the acid to the water rather than the water to the acid for safety.
hope this helps!
you know that there are 1609 meter in a mile. the number of feet in a mile is 5280. what is the speed snail from problem 7 per minute.
Answer:
We know that 1 meter = 100 centimeters, and 1 foot = 12 inches.
So (1,609 meters) x (100 centimeters/meter) = (5,280 feet) x (12 inches/foot)
The second fraction on each side of the equation is equal to ' 1 ', because
the numerator is equal to the denominator, so sticking it in there doesn't
change the value of that side of the equation. But now we can cancel some
units,and wind up with the units we need.
(1,609 meters) x (100 centimeters/meter) = (5,280 feet) x (12 inches/foot)
(1,609 x100) centimeters = (5,280 x 12) inches
160,900 centimeters = 63,360 inches
Divide each side by 63,360 : 2.54 centimeters = 1 inch
Explanation:
A 3.00 m long rod (I=1/3ML2) with a mass of 10.0 kg is set so that it pivots around its end. The rod is pulled back until it is horizontal and released. A small spherical ball with a mass of 4.00 kg is placed directly under the pivot point of the rod so that the end of the rod strikes the ball when it is vertical.
What is the angular velocity at the bottom before it hits the ball?
Hi there!
Assuming the rod is pulled back 90° (π/2 radians), we can use angular kinematics to solve.
Using the equation:
[tex]\omega_f^2= \omega_i^2 + 2\alpha \theta[/tex]
[tex]\omega_f[/tex] = final angular velocity (? rad/sec)
[tex]\omega_i[/tex] = initial angular velocity (0 rad/sec)
[tex]\alpha[/tex] = angular acceleration (rad/sec², must solve for)
[tex]\theta[/tex] = angular displacement (π/2 rad)
Recall Newton Second Law's rotational equivalent:
[tex]\Sigma \tau = I\alpha[/tex]
τ = Torque (Nm)
I = Moment of inertia (kgm²)
α = angular acceleration (rad/sec²)
Setting the pivot point at the end, and knowing that the force of gravity works at an object's center of mass (1.5m from the rod's end), we can solve for the angular acceleration.
[tex]\tau= F \times r\\\\\tau = W \times r = 10(9.8) * 1.5 = 147 Nm[/tex]
Now, solve for the moment of inertia given I = 1/3ML² at one of its ends:
[tex]I = \frac{1}{3}(10)(3^2) = 30 kgm^2[/tex]
Solve for the angular acceleration:
[tex]147 = 30\alpha\\\\\alpha = 4.9 \frac{rad}{sec^2}[/tex]
Now, we can use the kinematic equation to solve.
[tex]\omega_f^2 = 0 + 2(4.9)(\frac{\pi}{2}})\\\\\omega_f = \sqrt{2(4.9)(\frac{\pi}{2})} = \boxed{3.923 \frac{rad}{sec}}[/tex]
Ajajahsehahsjhabs Oh ya haha is coming over here for a
waste water can be purified naturally by
Answer:
waste water can be purified naturally by sunlight, temperature, filtration, adsorption, sedimentation, biodegradation,
Answer:
Filtration, sedimentation, or distillation
A woman wearingg shoes with stiletto hells weigh 550n andvthe area of heels is 1cm2 find the pressure
P = F : A
[tex]\tt P=\dfrac{550~N}{0,0001~m^2}=5.5\times 10^6~Pa[/tex]
Find the mass of a football player who has 1200 N of force and has an acceleration of 1.5 m/s2 ?
Answer:
800 kg is your answer.
Explanation:
[tex]Solution,\\\\Force(F)=1200N\\\\Acceleration(a)=1.5m/s^{2} \\\\As,\\\\F=ma\\\\1200=m*1.5\\\\m=\frac{1200}{1.5} \\\\m=800kg[/tex]
Which of the following pictures shows a ray reflecting off a concave mirror?
Select one:
a. A
b. B
c. C
d. D
Answer:
A
Explanation:
What I Know Directions: Read and understand the questions below. Choose the letter of the best answer, Write the chosen letter on a separate sheet of paper. 1. Which of the following is abasic unit of distance?
A inch
B. feet
C. meter
D. yard
(science)
How are alloys different than metallic elements?
While alloys are melted mixtures of two or more metals, true metals are unadulterated components. Due to their tendency to be shinier, heavier, and harder than the majority of materials, as well as the fact that they are great heat- and electricity-conductors, metals, and alloys are simple to differentiate from nonmetals.
What are alloys?As a compound or a solution, an alloy is a metallic material made up of two or more elements. Although carbon, a nonmetal, is a crucial component of steel, alloys typically contain metals as their own constituents.
Typically, the mixture of elements is melted to create an alloy. In very early periods, the value of alloys was discovered; brass (copper and zinc) and bronze (copper and tin) were particularly significant.
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50 N Vertical 10 N Horizontal Force X can you find force x?
Answer:
45
Explanation:
A 0.137 kg mass on a string
is swung in a vertical circle of radius
0.400 m. At the top of the circle, it
moves at 2.33 m/s. What is the
tension in the string at that point?
(Unit = N)
https://brainly.com/question/26500837
Answer:
.516
Explanation:
I typed this into Acellus and it was correct.
On average, how many times a month can we see a full moon?.
Answer:
Once
Explanation:
The time between new moon and the end of the cycle of the moons is about 29.53 days, which is roughly a month
The current flowing through a lamp is 1. 5 A. It is plugged into a 120 V outlet. What is the resistance of the lamp? Ω.
Answer:
80 [Ω].
Explanation:
according the formula I=U/R, where U=120[V], I=1.5[A], the required resistance can be calculated
[tex]R=\frac{U}{I}; \ => \ R=\frac{120}{1.5}=80[Ohm].[/tex]
If a spaceship weighs 2500kg and is traveling at the speed of light, how much energy does the ship have?
Answer:
Explanation:
KE = 1/2mv²
speed of light = 299,792,458
≅300,000,000 m/s
KE = 1/2 X 2500kg x 300,000,000²
A truck travels at a constant speed of 45 m/s. How much work did the truck engine do during a 2 hour period if it supplied a force of 25 kN of force.
The work the truck engine did during the 2 hour period is 8.1 × 10⁹ J
WorkFrom the question, we are to determine how much work the truck engine did
Work is given by the formula
Work = Force × Distance
First, we will determine the distance traveled by truck
From the formula,
Distance = Speed × Time
From the given information
Speed = 45 m/s
Time = 2 hours = 2×60×60 = 7200 secs
Then,
Distance = 45 × 7200
Distance = 324000 m
Now, for the work done
Work = Force × Distance
From the given information,
Force = 25 kN = 25000 N
Therefore,
Work = 25000 × 324000
Work = 8.1 × 10⁹ J
Hence, the work the truck engine did during the 2 hour period is 8.1 × 10⁹ J
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As you hold a book at rest in your hand two forces are being exerted on the book
Answer:
a. gravity & hand on book
b. yes - 3rd law
c. no, the are acting on the same object
Hope this helped!
Answer:
The first force is your hand holding the book up, and the other one is gravity pulling the book down. Hope i helped :D
Explanation:
The magnitude of the magnetic field generated by an electromagnet is:.
We have that the magnitude of the magnetic field is determined by the amount of current produced.
The magnitude of the magnetic field generated by an electromagnetGenerally, the magnetic field strength is called the tesla This is measured as one Newton per ampere-meter.
Electromagnet is a magnet where the magnetic field is created by an electric current,
Therefore the magnitude of the magnetic field is determined by the amount of current produced
For more information on Magnets
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a roller skater starts from rest (velocity initial=0m/s) and speeds up a final velocity (10m/s) what is the acceleration during a time of 2 seconds
Answer:
10-0÷2=5 that's the answer
covert 1000 kg/m3 into 1g/cm3
Answer:
1 g/cm³
Explanation:
1 kg = 1000 g
1 cm = 0.01 of a meter
1 m³ = 100 cm * 100 cm * 100 cm = 1,000,000 cm
1,000 kg / 1 * 1000 g / 1 kg
^ divided by 1,000,000 cm
1,000,000 divided by 1,000,000 = 1 g/cm³
which would cause a greater change in energy of motion doubling the weight or doubling the speed why
Answer:
Doubling the speed.
E - M v^2
M = W / g energy is proportional to weight
But energy is proportional to v^2
PLEASE HELP!
Will Mark Branliest
Calculate the speed of a wave that has no frequency of 3.50 HZ a wavelength of 1.75cm and an Amplitude of 4.25.
Answer:
I'll assume that "no frequency of 3.50 Hz" is supposed to read "a c frequency of 3.50 Hz"
Explanation:
A wave's speed is given by Speed = Distance/Time.
In this case the distance and time are provided: The wavelength is 1.75cm and the time between each wave is (1/3.50) seconds/cycle. That is, the wave travels 1.75 cm every (1/3.50) or 0.2857 seconds. The amplitude has no bearing on this calculation, unless it is 6.5 km high and in your lab.
In that case we'd like to know how much time we have before it reaches us across the 10 m room.
(Distance)/(Time) = 1.75 cm)/(0.2857 sec) = 6.125 cm/second is the speed of the wave.
For a 10 meter room (1000 cm), that would give us (1000cm)/(6.125 cm/sec) = 163 seconds to reach and close the exit door.
PLEASE PLEASE HELP ME WITH THIS
List the three things forces are needed for on Earth.
List the three things forces are needed for on Earth.
LiftThrustdragweightI added another one just cause there's four things forces are needed for on earth :-)
PLEASE HELP ME!!!
Which statements describe French control of its colonies? Choose four correct answers.
France established a system of direct rule.
France encouraged Africans to assimilate into French culture.
France granted equal rights to all Africans.
France allowed Africans to benefit from their natural resources.
France encouraged Africans to adopt French traditions.
France weakened the power of black Africans.
The French encouraged the African people to take on the culture of the French.
What are colonies?Colonies refers to areas which the Europeans allocated to themselves after they occupied Africa in the 18th to 19th centuries. They ruled these areas directly until they eventually secured independence.
The following are the statements that describe the French control of its territories;
France encouraged Africans to assimilate into French culture.France weakened the power of black Africans.France encouraged Africans to adopt French traditions.France established a system of direct rule.Learn more about French rule:https://brainly.com/question/3067618?
Need Help very important i will mark who gets this right brainiest.